Physical methods of gas analysis

Chapter 9

Physical methods of gas analysis Physical methods employed in gas analysis can basically be divided into two groups. The first group consists of methods based on the determination of a characteristic physical constant, e.g. the thermal conductivity, refractive index, magnetic properties, density, viscosity, etc. These methods are most often used in the analysis of binary mixtures or their equivalents, i.e multicomponent systems in which either one component has properties that differ greatly from the others, or when the ratio of the other components is constant. Prior separation of the components of the gas mixture is not then necessary. These methods are also widely used in the identification and determination of the individual components separated from mixtures. The second group, separation methods, employs various physical phenomena such as diffusion, condensation, distillation, adsorption, desorption, and mass spectrometry. This group also includes gas chromatograpy, the most modem method of gas analysis. All these separation methods can be combined with the physical methods in the first group, and new detectors are constantly being developed. 9.1. Thermal conductivity One physical constant which is characteristic of a pure gas and can be useful for analysis is thermal conductivity. The specific thermal conductivity of a gas is defined using the thermal flux between two surfaces, and is the heat transferred between two surfaceseach of area 1 cm2 , set 1 cm apart, with a temperature difference of 1 °C, between which the gas is flowing. At very low pressures (1-10- 3 Pa), the thermal conductivity of gases is very dependent on pressure changes (see Sect. 4.2.). However, 123

at atmospheric pressure it is not significantly affected by the gas pressure and density, and depends only on the type of gas and absolute temperatures of the two surfaces. 9.1.1 BASIC RELATIONSHIPS

It follows from the kinetic theory of gases that the mean free path of molecule L is given by the relationship L=

1 1

(9.1)

+

2ns2(1 + T) where s is the diameter of the molecule, n is the number of molecules per unit volume, T is the thermodynamic temperature, and C is the Sutherland constant which is characteristic for the given gas (C= 1.48 Tv where Tv is the boiling point of the gas at 101.325 kPa). The Sutherland constant is proportional to the potential energy of the molecule (to the intermolecular attractive forces) and is thus closely connected with the Van der Waals constant, a. The thermal dependence of C, expressed by the fraction C/T, is a consequence of the fact that, as the temperature increases, the constant contribution of the potential energy decreases relatively compared to the increasing kinetic energy. The internal friction in the gas is characterized by its dynamic viscosity 7, given by the relationship (9.2)

7 = knuML/NA

or, after substitution for L from Eqn. (9.1), kM 2w21 + T

(9.3) NA

where k is a constant, M is the molar mass of the gas, and u is the mean velocity of the molecule, which is proportional to T 1/ 2 . It follows from this relationship that the internal friction is independent of the pressure (number of molecules per unit volume). 124

The thermal conductivity is defined by the relationship (9.4)

X = ECVq

where is a factor describing the energy change in a collision between two molecules and cv is the specific heat capacity (at constant volume). Substitution for in Eqn. (9.3) yields X=

kcvMu 22(1 + T )NA

(9.5)

and, because cvM = Cv, the molar heat capacity at constant volume X=

ekCvu

(9.6)

2s2(1 +T ) Similarly, the thermal conductivity according to Eqn. (9.6) is independent of the number of molecules per unit volume, i.e. of the pressure. The dependence of the thermal conductivity on the molecular structure is apparent from these equations. As the number of atoms in the molecule increases, the value of the factor decreases. This constant has value 2.52 for monoatomic gases, 1.9 for bioatomic gas molecules and 1.75 for triatomic gases. The thermal conductivity increases with decreasing molecular diameter and with increasing velocity of molecular motion. Consequently, hydrogen has the highest thermal conductivity, which is an order higher than all other gases. The specific thermal conductivity is given either as an absolute value or as a relative value, related to the value for air. Table 9.1 lists the specific thermal conductivity values and the temperature coefficients for some gases and vapours. The relationship between the thermal conductivity and the temperature does not follow unambiguously from Eqn. (9.6). A number of authors have derived complex relationships for individual gases which, however, are not generally applicable for analytical purposes. The most useful, though not completely rigorous, relationship is the approximately linear dependence At = Xo(1 + At)

(9.7)

where Xo is the specific thermal conductivity at 0 ° C, Xt is the thermal conductivity at t ° C, and A is the temperature coefficient of the thermal 125

TABLE 9.1. Specific thermal conductivities of gases and vapours at 0 C Gas or vapour

A102 Wm-' K -1

X/Xair

Acetylene Ammonia Argon Butane Nitrogen Ethane Ethylene Helium Chlorine Nitrogen oxide Dinitrogen oxide Sulphur dioxide Carbon monoxide Carbon dioxide Oxygen Methane Neon Propane Hydrogen sulphide Water

1.90 2.18 1.62 1.35 2.43 1.82 1.75 14.57 0.72 2.08 1.48 0.79 2.09 1.47 2.46 3.02 4.44 1.50 1.20

Hydrogen Air

17.41 2.44

0.770 0.897 0.685 0.552 0.996 0.750 0.735 5.97 0.322 0.878 0.646 0.344 0.964 0.605 1.015 1.25 1.991 0.615 0.538 0.775 at 100 C 7.15 1.00

A (K)

0.00311 0.00264 0.00583 0.00763 0.00262 0.00495 0.00303 0.00655 0.00256 0.00455 at 100 C 0.00261 0.00253

conductivity. As the temperature coefficient depends on the particular gas, the specific thermal conductivities of two gases can be identical at a given temperature, e.g. air and CO., at 325 C, air and NH,, at 65 C, air and acetylene at 100 o C, air and SO2 at 450 o C, air and water vapourat 200 o C. This fact is useful in the analysis of ternary mixtures. However, the measuring temperature must be very carefully chosen in this case, to avoid errors introduced by small differences in the thermal conductivities. In the analysis of mixtures of gases that do not react together, the additive relationship Xs = 126

,8Xi

(9.8)

can mostly be used to calculate the thermal conductivity. Here, Xs is the specific thermal conductivity of the mixture, Xi is the specific thermal conductivity of component i, and i is the volume concentration of component i. This rule has many exceptions. For example, ifthe mixture contains gases with very different molar masses, the determined thermal conductivity values are lower than the theoretical values. This situation was first found in the measurement of the thermal conductivities of mixtures of hydrogen and oxygen. Mixtures of H 2 + CO2, He + Ar, and other mixtures with hydrogen behave similarly (Fig. 9.1). On the other hand, the thermal conductivities of mixtures are sometimes higher than predicted by the mixing rule. This occurs when one component of the mixture has a dipole moment, the other has a greater electronic symmetry, and both gases have large Sutherland constants. This situation occurs in the analysis of a mixture of nitrogen (air) + water vapour, or nitrogen (air) + acetylene (Fig. 9.2). As most gases do not have a dipole moment, the linear dependence is most affected by the difference in the molecular masses. 9.1.2 WORKING CONDITIONS

Thermal conductivity values are usually measured in thermostatted cylindrical cells through which a fibre is stretched in the direction of the axis. This filament is heated by a constant electric current. The thermal equilibrium of the wire in the cell, through which the test gas mixture flows, must primarily result from the thermal conductivity of the mixture. Losses due to thermal conductivity of the filament and convection

16

0.60

12 0.36

E

'E

o4

0.08 10 Fig. 9.1. The thermal conductivity of a binary mixture.

127

1.06

0.86

0

0.5

1.0

Wai r Fig. 9.2. The thermal conductivity of air-water, and air acetylene mixtures.

must be small or constant in order to be neglected. Losses through thermal conductivity of the filament are negligible because of the ratio of its length (20-30 mm) to its diameter (0.02-0.05 mm). Losses through convection can be limited by decreasing the coefficient of heat transfer and the surface of the chamber. The former is especially important and depends greatly on the gas flow-rate. The lower the flow-rate, the smaller this coefficient becomes. However, the flow-rate can be decreased only to a limited extent because this leads to an increase in the response time of the detector, i.e. in the period required to establish thermal equilibrium in the filament. The filament is heated by a constant current and is fitted in the centre of the conductivity cell where it is surrounded by the gas with thermal conductivity . The temperature of the test element of the filament is tf, cell wall temperature tb, filament radius rf, and cell radius rb. The heat, dQ, lost through a surface element dF, perpendicular to the direction of heat propagation, in unit time is given by the Fourier law as dQ= -

dF

d t

(9.9)

where dt/dr is the temperature gradient perpendicular to the filament axis. Surface dF lies on the jacket of the cylinder parallel with the filament axis, with length dl. It holds at distance r from the filament axis that dF= 2rrdl 128

(9.10)

Eqn. (9.9) then has the form dQ = X27rr dl dr

(9.11)

so that dt=

dQ A d

2

dr r

(9.12)

Integration of this expression with respect to r yields the law of heat distribution perpendicular to the filament axis dQ 2X dl In r + C1

t=

(9,13)

Integration constant C1 is calculated from the conditions when r

rf

and t= tf, so that

t = tf

r 2 dQTXd d In rf

It follows for r = rb and t = dnQb

(tf - tb)27rX dl lnrb

(9.14) tb

that (9.15)

rf

The heat loss per unit time from the whole filament can be found by integration of Eqn. (9.15) along the whole filament: Q=

(tf-

n

tb)2TX9I

b

(9.16)

rf

The equation of thermal equilibrium for the detector with filament with resistance R heated by current I has the form 2R= (tf-

tb)27

(9.17)hl

Inrb rf 129

In this equation R and X correspond to the temperature at thermal equilibrium. It holds for constant detector parameters and gas that R= f(X)

(9.18)

and thus (9.19)

R = f(()

where qp is the content of the test component in the mixture expressed as a volume traction. If the filament resistance at temperature 0 °C is R o and the thermal conductivity of the gas at 0 °C is X , then R = Ro(1 + atf)

(9.20)

A = X,(1 + AO)

(9.21)

where a is the temperature coefficient of the filament, A is the temperature coefficient of the thermal conductivity, t is the mean temperature of the filament, and 0 = (tf + tb)/2 is the mean temperature of the gas in the chamber. Substitution of the expressions for R and in Eqn. (9.17) yields the relationship tf-

I 2RO(1 + atf ) =

2 I1(t tb)X01 + Att rb

tb\ r b

Inrb rf

Introduction of k = 2

(9.22)

i/in rb/rf, the geometric constant of the cham-

ber, and using an approximate calculation method yields

tftb = tf

130

Ro - [1 11 + kX0

~

2

A) 1 R0 + (a_)kX h, ja

A)tbI~

(9.23)

so that

R=Ro

+ atb

+

k

°

[1 +

(-

+ (a-A)tb

(9.24)

Examination of Eqns. (9.22-9.24), which include the main variables employed in the design and working of the detector, permits the choice of a suitable value of I2Ro and working temperature of the filament, t,, when the other quantities are constant. It is difficult to design detectors to measure the absolute thermal conductivities of gases or gas mixtures. Heat loss through the filament must be distinguished from convection and radiation losses. The main difficulties encountered in measuring absolute values include elimination of the gradient in the thermal conductivity which results from the temperature gradient and density gradient in the chamber, locating the filament exactly in the centre of the chamber, and compensation of the temperature differences between the gas and the solid surface. Because of these difficulties, two cells are used in normal analytical practice, one containing the test gas mixture and the second a reference gas. The determination depends on measuring the ratio of the resistances of the filaments in the two cells. When the gases in the two cells are identical, this ratio will equal one. However, when the gases are different, this ratio will differ from one by a value proportional to the difference in the compositions of the reference and test gases. The filament material is an important parameter in the cell construction. Product ap is a useful criterion when comparing filaments of different materials (where a is the temperature coefficient of the resistance and p is the specific resistance), and is roughly proportional to the sensitivity of the instrument. Table 9.2 gives the values of a, p and ag for a number of metals and alloys. The choice of metal is also affected by other conditions. For example, antimony and bismuth, which have high a p values, cannot be used as they cannot be drawn out to form filaments. The use of a thermistor in place of a metal filament has been very promising, as thermistors have much higher ap values than commonly used metals. Thermistors employed in thermal conductivity sensors are beads with a diameter of about 0.3 mm, covered with a thin layer of glass, and fitted on a platinum-iridium filament with a diameter of about 0.02 mm (Fig. 9.3). Thermistors with various resistance values are available (from 5002 to 20 MS2) and are paired to have the same 131

TABLE 9.2 Characteristic constants for some metals Metal

Specific resistance, p (L(2/cm 3 ) (20 C)

Thermal coefficient of the resistance, (a 103 ) (20 C)

a-o/ 103 (20 C)

Silver Copper Aluminium Tungsten Nickel Platinum Pt+ 10% Ir Iron Invar Kovar Antimony Bismuth

1.62 1.72 2.82 5.75 7.24 10.6 24.6 9.78 75 49 41.7 120

3.61 3.93 4.21 4.54 4.91 3.69 1.2 6.34 2.0 3.8 3.6 4.0

4.58 5.15 7.07 10.89 13.21 12.03 5.95 19.82 17.32 26.60 23.26 43.82

resistance values and temperature characteristics. Thermistor detectors are used mainly at low and slightly elevated temperatures. Fig. 9.4 depicts the dependence of the sensitivity of thermistor cells with temperature compared to detectors with metal filaments. 9.1.3 SENSOR DESIGN

The specific thermal conductivity has been employed in gas analysis from the beginning of the 20th century. Thermal conductivity detectors, also called catharometers, have undergone considerable development and are now among the most widely used sensors.

a)

b)

c)

d)

Fig. 9.3. Method of fixmeasuring fixing theod elements inthe thermal conductivity detector. a, b, c Filament sensors, d thermistor sensor, T = thermistor.

132

2 500 2000

I E

E 1500 1000

500

400

40

150 -

f/ C

200

250

Fig. 9.4. The dependence of the sensitivities of filament and thermistor detectors on the temperature.

Modem thermal conductivity cells are usually located in a metal block with a cross-section of about 1 cm and length of about 5 cm. Each block contains cavities for location of filaments made of tantalum, platinum, silver, tungsten, nickel, or kovar, or filaments plated with gold or silver, or coated with a layer of quartz or glass. Fig. 9.3 depicts various means of fixing the filaments. The cells readily attain thermal equilibrium, their manipulation is simple, and they can easily be replaced by other standard commercial cells. In some special cases where the analyzed gases could corrode the detector metal, it is preferable to employ glass cells and to protect the filament with a layer of glass or quartz. Three types of cells can be distinguished by the location of the filament in the gas stream: flow-through, diffusion, and semi-diffusion: these differ in their response rate, and sensitivity to changes in the gas flow (see Sect. 10.5.8.). As mentioned above, relative measurements are employed in practice, where two- or four-cell systems are connected in a Wheatstone bridge (see Fig. 9.5). A four-cell bridge is twice as sensitive as a two-cell system. Two cells can be connected either in series or in parallel. The latter arrangement gives a more stable baseline, while the former is somewhat more sensitive. The detector sensitivity is affected by the working conditions according to the relationship S = K2R S=KI2 R R

-(

t)

( tf - tb)

(9.25) 133

where S is the signal magnitude, K is a constant, I is the electric charging current, R is the electric resistance of the fibre, Xr is the specific thermal conductivity of the reference gas, As is the specific thermal conductivity of the sample, tf is the fibre temperature and tb is the block temperature. It thus generally holds that greater sensitivity can be attained by increasing the charging current, using filaments with high resistance, using a reference gas with high thermal conductivity (H2 of He), and employing a large temperature difference between the filament and the block. In selecting conditions it is important that the use of a large charging current should not lead to instability of the baseline, to chemical reaction or thermal cracking of substances, or to burning of the filament. The block temperature must be selected to avoid condensation of vapours in the sensor. The sensitivity can be increased by decreasing the sensor volume and replacing the metal filament by a thermistor for temperatures below 100 ° C. 9.1.4 UTILIZATION OF MEASUREMENT OF THE THERMAL CONDUCTIVITY

Gas analysis methods based on the measurement of thermal conductivity are useful for binary mixtures or their equivalents, which consist of gases with sufficiently different thermal conductivities. Equivalents to

a

b) Fig. 9.5. Connection of a thermal conductivity detector in a Wheatstone bridge. (a) Two-cell system, (b) four-cell system; M1, M 2 = measuring cells, R1, R 2 = reference cells; the M1 -R1 and M2 -R2 pairs must have the same resistances; A = input for the analyzed gas, B = input for the reference gas, R = recorder.

134

binary systems are multicomponent systems where, for example, part of the gas consists of a mixture with a constant component ratio, or the analyzed component has a thermal conductivity very different from the others, or the thermal conductivities are similar, or the amounts of some components have already been found by another method. Even when the mixture cannot be considered as binary or equivalent to binary, analysis by thermal conductivity measurement is feasible. The component of interest can be removed after passing through the first cell, using absorption, condensation, or chemical reaction, so that the sample entering the second cell is free of interference, and the change in response is then proportional to the amount of the remaining substance. Various analyses of this kind are carried out in analytical laboratories and in industry, where thermal conductivity detectors are widely used as automatic alarms. A number of instruments have been described for controlling the composition of reaction mixtures. Examples include the content of nitrogen and hydrogen in the synthesis of ammonia, the analysis of an ammonia-air mixture prior to catalytic oxidation of ammonia, the determination of ammonia in its mixture with hydrogen and nitrogen in the Haber-Bosch synthesis. Other applications are in product quality control (in rare gas production), and in safety devices TABLE 9.3 Applications of thermal conductivity measurements Gas determined

Measured in medium

Measuring range (vol.%) Minimum Maximum Minimum Maximum

H2 Ar

N2

0-0.2 0-2.5

air

0-2.5

C12

HCI

or

SO2

CO2 H2 S CH 4 C2H2 H2 C12 H2 HC1 Ar H2 H2

0-1

0-1

HCI C12 C12 02 Ar Flue gas

0-2.5 0-2.5 0-1 0-5 0-0.2 0-2.5 0-0.2 0-2.5 0-2 0-1 0-0.5

0-100

0-5 0-100

135

such as control of the purity of electrolytic hydrogen and oxygen, the measurement of organic solvents in the working atmosphere, the control of mine gases, and following the sulphur dioxide content in flue gases. An important application is in the determination of oxygen dissolved in water through stripping with hydrogen, where the amount of oxygen in the hydrogen is determined after establishment of equilibrium. Table 9.3 gives some applications. Measurement of the thermal conductivity is a universal method that can be used to determine gases and all substances that can be converted to the gaseous state. Because of the great differences in thermal conductivities, this method is very sensitive for the determination of hydrogen or of gases in hydrogen, where it is used most extensively. It is, however, less sensitive than, for example, optical or electrochemical methods, for other mixtures. The measuring range varies from tenths to hundred of percent. The relative measuring error is about 2%, although this can reach 4% for the lowest ranges. A number of analyzers are described in the commercial literature and have practically identical designs. They differ in the use of two- or four-cell systems, and use flow-through, diffusion or semi-diffusion cells, depending on the purpose of the analysis. The sensor is usually a platinum filament, which can be protected by a thin glass layer for the analysis of corrosive gases. The detector block is made of brass, steel or stainless steel. A number of companies manufacture non-explosive versions. Thermal conductivity analyzers can be used under extreme conditions and are useful for both organic and inorganic substances. The electric signal can be used for remote control, recording, signalling or regulation. They have been used widely as gas chromatographic detectors (see Sect. 10.5.8.). The widest ranges of instruments based on thermal conductivity measurements are manufactured by the Hartmann and Braun (Caldos), Ados (Therm-Ado), Maihak (Thermor), and MSA and Kent Industrial Measurements (Thermatron) companies, which also market portable versions. A number of other companies, the best known of which is Gow-Mac, manufacture thermal conductivity detectors specially for gas chromatography. 9.2. Interferometry Interferometry is a physical method that, like refractometry, is based on measuring the refractive index. In refractometry the refractive index 136

is measured directly by recording the limiting angle. In contrast, interferometric determinations measure the difference in the refractive indices of the test and reference substances using the shift in the interference spectrum.

9.2.1 BASIC RELATIONSHIPS

The refractive index of a substance is defined as the ratio of the velocity of light in a vacuum to the velocity in the substance. Consequently, these indices have values greater than unity for real media. The refractive indices of gases are much lower than those of liquids or solids. As examples, the refractive indices of water in various states are given in Table 9.4, and those for a number of gases are given in Table 9.5. Commercial refractometers which measure the refractive indices of solids and liquids can be used for values in the range from 1.3000 to 1.84000. It can be seen from Table 9.5 that these cannot be used for determinations of gases, as the maximal measuring precision is only + 0.0001 refractive index units. The refractive index depends on the temperature of the substance, wavelength of light used, and on all factors that can affect the concentration of the substance in the cuvette. Imprecision resulting from changes in the temperature, density, pressure, instrumental characteristics, etc., can be eliminated by differential measurement. The refractive indices of substances with known and unknown refractive index values are measured under identical conditions, yielding a difference from which the value for the unknown sample can be calculated. Differential measurements suffer from anarrow measuring range but, on the other hand, small differences in the refractive index (0.0001 units) can be determined with relatively high precision. Consequently, differential

TABLE 9.4 Refractive index of various forms of water Refractive index Ice at 0° C Water at 25 ° C Steam

1.3049 1.33287 1.000249

137

TABLE 9.5 Refractive indices of some gases and vapours Gas or vapour

Refractive index

Acetone Ammonia Argon Benzene Nitrogen Helium Chlorine Chloroform Oxygen Methane Nitrogen oxide Dinitrogen oxide Carbon monoxide Carbon dioxide Sulphur dioxide Carbon disulphide Hydrogen sulphide Hydrogen Air

1.001078 1.000373 1.000281 1.001700 1.000296 1.000036 1.000773 1.001436 1.000271 1.000444 1.000297 1.000516 1.000335 1.000448 1.000686 1.001478 1.000644 1.000132 1.0002926

refractometers are used more often; these instruments are also called interference refractometers or interferometers. The principle of the interferometer was discovered by Young in 1802, in an experiment to demonstrate the wave nature of light. It follows from wave theory that, when two light waves are in phase and havethe same amplitude and direction, the resultant amplitude is equal to the sum of the two amplitudes and the intensity of the light ray, which is proportional to the square of the amplitude, is four times greater than that of the simple wave. If the waves are in opposite phases,the resultant amplitude and intensity of the beam are equal to zero. Young's experiment is depicted in Fig. 9.6. The light from source S passes through two narrow slits Si and S2, which are very close together and form two new coherent sources. If a screen D is placed behind these slits, a number of dark and light lines can be seen parallel to the slits. These lines disappear when one of the slits is covered. The distance between the dark and light lines is directly proportional to the wavelength of the light used, and indirectly proportional to the distance between the slits. When white light is used, then the central line A is 138

S

A

S

A~

Fig. 9.6. The Young experiment. S = Light source, S1, S 2 = slits, D = shield, A = central strip.

white and the subsequent lines have slightly red and blue edges. When monochromatic light is used, all the lines are the same colour. Arago later carried out an experiment in which an optical medium with refractive index na was replaced by a medium with index nb for constant beam path length; when n a > nb, then the set of lines is shifted towards the substance with index na. The number of lines, h, corresponding to the shift from the central line, A, yields the difference in the refractive indices of the substances according to the equation n

= n--

n

=

hX

(9.26)

is the wavelength of the light employed, and L is the pathwhere length of the light beam in the medium with refractive index n a. If monochromatic light is employed, the shift in the interference spectrum cannot be determined because all the lines are the same colour. Consequently, white light is used, where only the central line is white. The analytical application of interferometric measurements is based on the validity of the Biot-Arago law, which expresses the relationship 139

between the refractive index of a mixture and the indices of the individual components: x

n = Xn1

,

X2 + ln2

+

(9.27)

where n is the total index of the mixture, x and x2 are the mole fractions of the gas components in the mixture and n and n2 are the refractive indices of the individual components. Instead of the refractive index, the value R = (n - 1) 106, i.e. the refractivity is often used, avoiding the necessity of listing values with many figures after the decimal point. 9.2.2 INSTRUMENTATION

The first analytical interferometer was constructed by Rayleigh and was used in 1910 by Haber and Lwe for gas analysis. Laboratory interferometers consist of a light source, collimator, cylindrical space with cover, and telescope. They are fitted with glass cuvettes of various lengths (10, 25, 50 and 100 cm). A scheme of the instrument (Carl Zeiss, Jena) is depicted in Fig. 9.7. Rays from the point light source (1), a six-volt light bulb, fall on slit (2) and pass parallel through collimator (3). Lens (4) located immediately in front of the collimator objective bends the light rays. One light beam

1i

Z10

b

b)

Fig. 9.7. A laboratory interferometer. 1 = Light source, 2 = slit, 3 = collimator, 4 = lens, 5 = cuvettes, 6 = compensation plate, 7 = lid, 8 = micrometer screw, 9 = binoculars, 10 = ocular, 11 = auxiliary plate; a = slide view, b = view from above.

140

passes under the cuvettes and is directed by plate (11) into the telescope (9) and then forms the bottom immobile interference band in the occular (10). The second part of the beam passes through the cuvettes (5) and compensation plate (6), enters the telescope and forms the upper interference spectrum in the occular. If the cuvettes contain substances with different refractive indices, then a phase shift occurs with a magnitude proportional to the difference in the refractive indices of the two media, producing shifts of the upper mobile interference band, which can completely disappear. The light pathlength can be varied using the adjustable compensation plate (6) until the interference bands merge (see Figs. 9.8a,b,c). The plate is turned using a calibrated micrometer screw (8), with a scale of 0 to 3000. These readings correspond to the difference in the refractive indices of the reference and test substances. The shape and position of the interference bands can also be affected by factors such as the adjustment of the telescope, the position and focussing of the light bulb, the cuvette positions, and cuvette tempering. Cuvette selection The accuracy of interference measurements depends on the use of a suitable cuvette length, i.e. on the light pathlength through the test material. The longer the cuvettes, the greater the accuracy; however, the concentration range of the analyzed substance that can be measured is simultaneously decreased. Consequently, it is necessary to first determined the cuvette dimensions which give a suitable compromise. To do this one needs to know the qualitative composition of the mixture, the refractive indices of the individual components, and their minimum percentages prior to the analysis. A suitable cuvette length can then be calculated from the relationship 100hX L= c(n 2 c(n - n)

a)

(9.28)

b)

c)

Fig. 9.8. Shift of the interference spectra.

141

where h is the number of interference lines, X isthe wavelength of the light employed to calibrate the instrument, c is the test component concentration, and n, and n2 are the refractive indices of the components of the mixture. Example: The interferometer was calibrated with light with wavelength X equal to 5.5 10 - 4 cm. A shift of one interference line corresponds to 30 divisions on the screw scale. As a maximum of 3000 divisions can be read on the screw, the greatest number of h values that can be read is equal to 100. Substitution yields the relationship for calculation of the maximal cuvette length: 100 x 100 x 5.5 10 Lmax

cmax(n2 - nl)

4

5.5 Cmax(n2

-

nl).

A minimum of one division can be read on the screw scale. If a shift of one interference line corresponds to 30 divisions, then the smallest amount that can be measured is 1/30 h. The expression 100 X 30 X 5.5 10 4 c(n 2 - n)

2 10 - 3 Cin(2 - n)(9.30)

gives the shortest cuvette length that can be used to determine the minimal component content. For example, if the content of CO 2 is to be determined in the air, nair = 1.000292 nco, = 1.000448 The amount of CO2 in the mixture can be up to 20%. Thus, Lmax

max

5.5 = 1.7 ·103 mm = 170 cm 20 x 156 - 10-6

Consequently, the longest cuvette can be used (100 cm). If it is necessary to determine 0.03% CO2 in the mixture, then 2 0- 3 = 422 mm = 42.2 cm Lin 0.03x156-10 measurement. Acuvette0.03 156long is thus sufficient for ths10 A cuvette 50 cm long is thus sufficient for this measurement. 142

Reference substance selection In binary mixtures, the major component is used as the reference substance. This is often air, nitrogen or CO 2. In special cases, gases with very different refractive indices can be used, leading to a further increase in the sensitivity of the method. The reference substance can also be the analyzed gas mixture from which the test component has been removed by condensation, absorption, combustion, or some method. The measurement is based on the determination of the zero value using the reference gas. The analyzed sample is fed into the cuvette, the temperature and pressure are equilibrated, and the measurement is repeated as for the zero value. The average measured value minus the zero value is then proportional to the concentration of the test substance. Gas analysis can be carried out under stationary or dynamic conditions; in the latter case, the gas flows through the cuvette. The test and reference gases should be freed of dust which can collect on the cuvette walls and affect the interference pattern. Water vapour condensing on the cuvette walls also interferes. Consequently, the gases should first pass through a filter to remove dust and an absorption column containing silica gel or calcium chloride to remove water. If the gas is thoroughly tempered, the final position of the interference band is established immediately after introduction of the sample. Otherwise, it continues to shift until equilibrium is established; the shift to lower values is greater for warmer gases. When flowing gases are measured, manostats and flow meters must be employed to ensure constant measuring conditions. 9.2.3 DETERMINATION METHODS

Gas interferometers can be used in one of two general procedures for the analysis of binary mixtures or their equivalents. In the first, they are employed directly as measuring instruments and must be calibrated prior to the analysis. In the second, they can be used as zeroing instruments and the approximate concentration of the unknown mixture must then be known. The analyzed mixture is compared with two known mixtures and its concentration found from the concentrations of the two reference mixtures. This method is far more accurate than the former but the compositions of the reference mixtures must be known exactly. The absolute calibration method is based on calculation of the refractivity of the gas. As the velocity of light in all substances is smaller than 143

that in a vacuum, the refractivity (R) of the substance, which can be calculated from Eqn. (9.31), corresponds to the decrease in the velocity of light in the given substance:

R = (n- 1). 106

(9.31)

As the refractivity is proportional to the gas density, which is in turn proportional to the gas pressure, the refractivity can be calculated from the equation of state provided that this equation is valid for the given gas. This dependence is given by the equation 273

R= R

101

p 325 T

(9.32)

where R is the refractivity of the gas at temperature T and pressure p, and R is the refractivity at 0°C and 101 325 Pa. The change in the refractivity with pressure can be calculated from the equation 273 X 0.0002917(p, -2) AR= R -Rp 2 =101325 101 325 T T

(9.33)

where Rpl is the refractivity of the gas at pressure p, and Rp2 is the refractivity at pressure P2. The overall refractivity, R, of a binary mixture is equal to the sum of the refractivities of the components and their partial pressures R =R

P

+ R2 P

(9.34)

P

where R is the refractivity of gas 1 with pressure p, R 2 is the refractivity of gas 2 with pressure P2, and p is the overall pressure, i.e. Pi +P 2, or R =R

100 - A 100

+ R 2

Al 100

(9.35)

where A, is the present fraction of gas 1 in the mixture. If gas 1 is used as a standard in the analysis, then ARR 144

R-=

= RI _R(100- A) + RA

1 2100

(R - R)A 100

(9.36)

If R1 and R2 are the refractivities of gases 1 and 2 at 0°C and pressure 101 325 Pa, and the analysis is carried out at temperature T and pressure p, then 273 p (R, - R 2)A, AR= 101 325 T 100

(9.37)

The curve of the dependence of the interferometer data on AR can also be constructed using Eqn. (9.33). When R1 and R 2 are known, then the dependence of R on A 1 can be found using Eqn. (9.37). 9.2.4 THE USE OF INTERFEROMETRY

Interferometric measurements, which are very fast and accurate, are used, for example, in the analysis of flue gases, of ammonia during synthesis, of benzene in coal gas, or to determine impurities in gas mixtures. The frequently used interferometer from the Zeiss company is a laboratory instrument; it is not portable and is mechanically fragile. Portable instruments have been designed for production analysis. The best known manufacturer is the Japanese company Riken Keiki, which employs an ingenious approach to retain sensitivity in a small instrument (see Fig. 9.9). The rays fall on plane parallel plates where they are reflected and refracted so that one beam passes through the reference cuvette, falls on a prism where it is reflected and passes through the second reference cuvette. It then again impinges on the plane parallel

Fig. 9.9. Scheme of the interferometer from Riken Keiki Co. 1 = Light source, 2 = condenser, 3 = shutter, 4 = plane parallel plates, 5, 6= reference cuvettes, 7 = measuring cuvette, 8 = optical prism, 9 = measuring prism, 10 = measuring system of the interferometer.

145

plates where it is again refracted and enters the measuring prism. The second part of the beam, which was not reflected, impinges on a second plane parallel plate on which it is reflected and refracted. It then passes through the measuring cuvette and optical prism where it is again refracted and reflected so that it passes through the measuring cuvette once again and is reflected from a plane parallel plate to pass through the measuring prism. The interference lines are observed in the measuring part of the instrument and their mobile part can be shifted by turning the measuring prism. Interferometers manufactured by Japanese companies have various measuring ranges and quite broad application (see Table 9.6). Work in the field can be carried out using single-purpose interferometers such as those employed for analysis of mine atmospheres to determine either methane or carbon dioxide. The single-purpose instrument can be used to measure, e.g., the decrease in the oxygen and increase in carbon dioxide in exhaled air. The ratio of these gases is an

TABLE 9.6 Application of the interferometer Substance determined

Measuring range (vol.%) Minimum

Acetone Acetylene Ammonia Benzene Freon 11, 12 Hexane Oxygen in nitrogen Oxygen in water Methane Methanol Methyl chloride Sulphur dioxide Carbon dioxide Ozone in oxygen Propane Hydrogen sulphide Tetrachloromethane Hydrogen in C0 2 , N 2 Hydrogen in chlorine

0-0.5 0-2 0-20 0-1.2 0-1 0-1 0-22 0-10 0-3 0-10 0-1 0-6 0-6 0-10 0-2 0 10 0-1.2 0-100 0-5

146

Maximum 0-2 0-100 0 10

0-100 0-10 0-100

0-3

important characteristic in measuring lung efficiency. This instrument is employed in pathology and applied medicine. Interferometery almost always requires manual operation. The occasional attempts to automate these instruments have not been successful. In contrast to other methods of gas analysis, they cannot be used for automatic control or as alarms.

9.3. Absorption and emission spectrometry Changes in the energy state in individual atoms or molecules always appear in a given wavelength region. This phenomenon is characteristic for the particular substance and has been employed in analytical determinations using spectroscopic methods. These have been used extensively in the analysis of gases and vapours. The most important applications use the infrared wavelength region. 9.3.1 BASIC RELATIONSHIPS

If translational motion of the molecule is neglected, its total energy can be expressed as the sum of three type of energy: the electron energy Ee, vibrational energy Ev, and rotational energy Er: E = Ee + E v + Er

(9.38)

The electron energy corresponds to electrons grouped around the nucleus in certain energy levels. Provided that the electrons remain in their original levels, then this energy does not change; if one or several electrons pass into higher or lower energy levels, then the atom either absorbs energy (in the form of heat, light or electrical energy) or emits energy. While individual atoms have only electron energy, molecules also have vibrational and rotational energy, depending on their atomic positions. The vibrational energy is a result of the vibration of the atoms around their equilibrium positions, and the rotational energy corresponds to the rotation of the atoms around the centre of gravity of the molecule. Energy changes in molecules are not continuous. The change in the energy of the molecule from E to E 2 occurs in a step, through emission or absorption of an integral number of light quanta. The magnitude of the individual types of energy in molecules can be expressed as E >> E v >> Er. Changes in the vibrational and rotational 147

energies appear in the infrared region, while changes in the electron energy lie in the ultraviolet and visible regions. As a number of gases can emit or absorb light of a given wavelength, this property has been employed for their spectrophotometric analysis. Optical methods of gas analysis can be divided into several groups on the basis of the wavelength of the radiation, corresponding to various energy regions, and differing in the detection methods. Fig. 9.10 gives the classification of spectra according to the wavelength. Optical measurements are most often carried out in the ultraviolet ( = 0.2-0.4 ptm), visible ( = 0.4-0.7 pam) and infrared ( = 0.7-100 am) regions. The infrared region can be divided into three narrower parts: the near infrared (- = 0.7-1.2 fEm), medium infrared (1.2-10 m), corresponding to changes in the vibrational and rotational energy, and the far infrared (10-100 tm), where absorption of radiation leads to an increase in the rotational energy of the molecule. Absorption spectrophotometry has been used most widely in gas analysis. The Lambert and Beer laws are valid for gases, as they are for liquids. The amount of radiation absorbed at a given wavelength, the absorption, which is usually given in percent, can be calculated as the ratio of the intensities of the transmitted and original beams: %absorption=

-100

(9.39)

.--

where p is the intensity of the transmitted beam and original beam.

0

is that of the

aysib;e region

Y X

0.1nm Inm

P

1Onm100m 3.10 1

visib e 6 YR 0

0.4 06 25 000

rodiowoves

mltroviolef in frored

raOys U

J1Am 10cm 100cm Olcm 1cm 0cm Icm 1O OOm 3.10 3.10133.102 3.101 3.1003.109 3 10 3.10 3.10

near infrared 0.8 1 1.5 2 10OOO 5000

3

medium infrcared 4 2500

Fig. 9.10. Distribution of the spectral regions.

148

6

1

m OiOkm00kmwoveength 3.10 3.10' 3.10 frequency/ Hz

'or 8

0t 1000

15

20 500

30 wcve egrh/m wovenumber,'cm-1

The Lambert law, which expresses the dependence of the amount of light transmitted on the pathlength, , through the gas log 2 = hkl

(9.40)

is always valid. The Beer law describes the relationship between the absorption of monochromatic radiation and the concentration, c, of the absorbing gas: logy = ke

(9.41)

These two laws can be combined to form a single equation log0 = ~Ecl

(9.42)

where E is the molar absorption coefficient of the gas, which depends only on the wavelength and the type of gas. Its value can be determined for each wavelength and gas by determining the ratio 0 /0 for a known pathlength. 9.3.2 THE ABSORPTION SPECTROMETRY OF GASES AND VAPOURS The energy states of atoms and molecules are given by the energy states of their electrons, the vibrational states of the atoms, and the rotational states of the molecules. Depending on which of these states is affected by the radiation, the process can be classified into one of two groups. If the molecules of the substance absorb radiation in the ultraviolet or visible regions then their outer valence electrons enter a higher energy state. This process forms the basis for absorption spectral analysis in the electronic spectral region. If the molecules of the substance absorb infrared radiation, then they pass from lower vibrational or rotational energy states to higher states. This process forms the basis for absorption spectral analysis in the vibrational-rotational spectral region, i.e infrared spectrometry. These two types of spectrometric method provide different types of informa149

tion on the properties of the analyzed substance, and correspond to different types of procedures and instrumentation. Table 9.7 gives a survey of gases and vapours that absorb radiation in the ultraviolet region. Only coloured gases can be determined directly in the visible region. There are very few such gases (e.g. NO2 , C12, Br2 ). Photometry in the visible region is employed primarily in combination with absorption of the gas in a sensor accompanied by a suitable colour change (see Sec. 8.4.). Gas analysis based on absorption in the infrared region is suitable for gases and vapours whose molecules contain different atoms and are thus unsymmetrical. Some gases and vapours that can be determined using infrared analyzers are listed in Table 9.8. Inert gases and symmetrical diatomic molecules such as 02, N2 and H 2 cannot be detected in the

infrared region. Measurement in various spectral regions requires suitable design of the individual analyzer elements. The radiation source, optical material, and detectors must be suitably selected. The requirements on precision, accuracy, and sensitivity affect the whole analyzer design. An ideal radiation source should fulfil the following requirements: (1) It should have maximal electrical efficiency, i.e. as much as

TABLE 9.7 Behaviour of gases and vapours in the ultraviolet region Substance Acetaldehyde Acetone Ammonia Benzene Bromine Hydrogen bromide 1,3-Butadiene Ethane Ethyl benzene Formaldehyde Furane Chlorine Hydrogen chloride Isoprene Iodine Hydrogen iodide

150

max

(nm)

348 230 330-294 192, 152 280 420 182, 149 210 135 266 375-275 205 330 132 215 520 208, 178

Substance

kmax (nm)

Methane Methanol Methyl amine Methyl chloride Methyl mercaptan Ozone Nitrogen dioxide Sulphur dioxide Mercury Hydrogen, sulphide Styrene Tetrachloroethylene Thiophene Toluene Water Xylene

122 183, 150 213, 173 172, 161-154 278

254, 436 260, 160-146 287 295 235 285 167 290

TABLE 9.8 Some gases and vapours that can be determined using infrared analyzers Acetaldehyde Acetone Acetylene Ammonia Benzene Butadiene n-Butane Butenes Dimethyl ether Dimethyl formamide

Ethane Ethyl acetate Ethyl alcohol Ethyl benzene Ethylene Formaldehyde Phosgene n-Hexane Hydrogen chloride Isobutane

Nickel carbonyl Iron carbonyl Hydrogen cyanide Methane Methyl alcohol Methyl chloride Nitrogen dioxide Nitrogen oxide Dinitrogen oxide Sulphur dioxide

Carbon monoxide Carbon dioxide Propane Propylene Trichloroethylene Water

possible of the energy consumed should be emitted in the form of radiation in the required spectral region. (2) The emission of radiation should be characterized by both longterm and short-term stability. (3) The source dimensions should allow a simple optical system to focus the light beam onto the sensitive part of the detector. (4) It should have a long lifetime (ca. 10000 h). (5) It should not be expensive. These requirements are considered in the manufacture of optical analyzers. A compromise must often be made between conflicting requirements. For example, the first requirement would necessitate a high temperature which would have a negative effect on the source lifetime. The source employed for ultraviolet radiation is usually a mercury lamp with emission between 254 and 546 nm, with maximum intensity at 254 and 436 nm. Thus, instruments with mercury lamps are most sensitive for gases that absorb these wavelengths. In the near ultraviolet region, hydrogen (deuterium) discharge lamps are used, emitting continuous radiation in the range roughly 200-350 nm. Analyses in the visible region are most often carried out using a tungsten lamp emitting radiation in the region from 320 to 2000 nm. The most commonly used sources of infrared radiation are either the globar, i.e. a silicon carbide rod, or a Nernst rod, i.e. a mixture of ZrO2, CeO2 and ThO2 . Both are heated by an electric current to 1000 to 1800 °C and emit continuous infrared radiation in the region from 0.5 to 30 m. Carbon rods can also be used as radiation sources, as can platinum bands or tungsten wires, all heated to 1000 to 3000 C. Modern 151

analyzers mostly use chromium-nickel or platinum wires, emitting at temperatures of 600-1000 ° C. The material for the optical part of the instrument is selected so that it is transparent for the required wavelength region. The choice of material for the cuvettes and lenses also depends on the requirements on mechanical strength and stability, chemical resistance, and price. Various types of apparatus are used for spectroscopic analysis and separation of the required wavelength. In the ultraviolet and visible regions, filters are mostlyused to transmit only the required wavelength. In the infrared region, prisms or gratings are placed prior to the absorption cuvettes. If the resolution is to be sufficiently great in prisms instruments, then a suitable prism material must be selected. Fused quartz (to 3 im), sapphire, i.e. A1 203 (to 6 m), LiF (to 6 pm), CaF 2 (to 7 tm), NaC1 (to 15 /m), KBr (to 20 [cm), and CsBr or KRS5 [a mixed thallium bromide and iodide crystal (to 40 jim)] are mostly used. Material for the absorption cuvettes is selected to transmit efficiently the wavelength region used forthe measurements. Quartz is most suitable in the ultraviolet region, while glass is mostly used in the visible region. Cuvettes for the infrared region are made of the materials employed for the optical prisms. The cuvette length varies from 5 to 50 cm depending on the magnitude of the molar absorption coefficient and the required measuring sensitivity. The photometric part of the instrument measures the absorption of the radiation by the sample. The intensity of the transmitted ultraviolet and visible radiation is measured using photocells, photoelectric amplifiers, or gate photoelectric cells which are sensitive in this region. Several types of detector can be used for the infrared region; photoelectric and thermoelectric cells, bolometers, and pneumatic detectors are most often used. The photoelectric cells are useful for only limited parts of the infrared region. Bolometers, i.e. resistance thermometers, measure the change in the resistance of metallic conductors with the temperature. The Golay pneumatic detector is very sensitive. This detector is a chamber filled with dilute gas. The gas expands upon absorption of infrared light and exerts pressure on a membrane which acts as a mirror in the optical system between the light source and the photocell or as one half of a condenser whose capacity changes with a change in the position of this part. Spectrometric analyzers can be divided into two groups on the basis of their design. The first group consists of analyzer with a single source of radiation and single cuvette. In some designs, measurements can be 152

carried out in two wavelength regions and comparative measurements employ two radiation detectors. The second group consists of analyzers with two cuvettes, one for reference and one for measuring, and may be fitted with one or two radiation sources and detectors. Analyzers based on measurement of ultraviolet light fall into both groups. A typical analyzer with a single cuvette is shown schematically in Fig. 9.11. The beam from the UV source passes through the rotating shutter with two openings to an optical filter and then to a half-reflecting mirror, from which the reflected part of the beam passes through the measuring cuvette and then impinges on the radiation detector, while the part of the beam that passes through the mirror impinges directly on the detector. The location of the openings in the rotating shutter depends on the analytical problem. For example, one slit is empty and the second contain the analyzed gas mixture in a quartz cuvette. In this arrangement, all the radiation passing through the empty slit passes through the whole optical system while that passing through the cuvette is decreased by absorption of the wavelength corresponding to the test component. Four signals are thus obtained (two from the reference detector, Is, and Is2, and two from the measuring detector, IM1 and IM2). The absorbance by the analyzed component in the measuring cuvette is given by the relationship

A

IS2 _

IM2

IS

IMs,

I1S2

(9.43)

Isl

and is electronically treated. In this way, the unwanted effects of source instability, impurities in the cuvette, and changes in the ambient temperature can be eliminated. In another arrangement, the slits in the rotating shutter contain interference filters with different spectral characteristics, which again permit differential measurement. In the firstcase, correlation is carried out using a gas filter, while in the second case the absorbance is compared at various wavelengths. These types of analyzers are used to determine SO 2 , NO, C12, and H 2 S in concentrations of hundredths of percent by volume. The Bran and Liibbe company manufactures an analyzer (Uvametr) with a single cuvette for determination of the ozone content in air and waste gases, SO2 in combustion gases, and C12 in HC1. 153

Is 4,

10 22~~~~

F-]

5-

[I

B±_~If1 8Y~~~~~~~' J Se o 8 Fig. 9.11. Scheme of an ultraviolet analyzer with a single cuvette (Hartmann and Braun, Radas). 1 = Radiation source, 2 = motor rotating the shutter, 3 = rotating shutter, 4 = collimator, 5 = optical filter, 6 = semi-transparent mirror, 7 = measuring cuvette, 8, 9 = radiation detectors. Fig. 9.12. Scheme of an ultraviolet analyzer with two cuvettes. 1 = Radiation source, 2 = optical filter, 3, 8 = lenses, 4 = shutter, 5 = rotating shutter, 6, 7 = measuring and reference cuvettes, 9 = radiation detector.

Analyzers with two cuvettes have a single radiation source and a single detector. A rotating shutter with slits sends the light beam alternately to the reference and measuring cuvettes. The difference between the detector signals is treated electronically and gives the content of the test component. This principle is employed in the analyzer of the Withof company (Okometer), depicted schematically in Fig. 9.12. This analyzer can be used to determine C12 , SO2, NO 2, benzene vapours, and other aromatic hydrocarbons in various concentration ranges from hundredths to tenths of percent, and mercury vapour to 0.03 ppm. Similar analyzers are manufactured in the U.S.S.R. and used primarily to determine chlorine and mercury vapours. The Beckman company also manufactures a mercury vapour analyzer, and the Thermo Electron company has an instrument for determining ozone. It follows from Table 9.7 and the given applications that only a limited number of substances absorb radiation in the ultraviolet region. This fact is useful in the analysis of multicomponent mixtures, e.g. of aliphatic and aromatic hydrocarbons, leads to improved selectivity in the measurement as practically all organic substances absorb infrared radiation. Gas and vapour analyzers for the visible spectral region are mostly used in combination with a chemical reaction with a suitable absorption agent (see Sect. 8.4.). As very few gases absorb radiation in the visible region, gas analyzers are not used widely in this region. The Beckman company manufactures a flow-through photometer, which is depicted schematically in Fig. 9.13. Light from source (1) passes through the filter 154

Fig. 9.13. Flow-through colorimeter. 1 = Radiation source, 2 = filter, 3, 4 = photocells, 5 = collimator, 6 = cuvette.

(2) and impinges on the reference photocell (3). On the other side of the source, the light beam passes through the collimator (5) and absorption cuvette (6) containing the test mixture of gases and vapours, and is incident on the photocell (4). This spectrophotometer can be used in the region from 350 to 1000 nm. Radiation from 350 to 680 nm is detected using a photocell sensitive to red light. This instrument can be used to determine chlorine, nitrogen dioxide, bromine and other coloured gases. The wavelengths of light absorbed by molecules in the infrared region are a function of the overall structure of the molecules. They are characteristic for given parts of the molecule and the absorption infrared spectrum is specific for the given compound. Methods of gas analysis based on this property are used most extensively. Infrared analyzers that are commonly used in the analysis of gases can be separated into two groups: dispersion and non-dispersion. In dispersion instruments (with a selective radiation source), the radiation from the source is dispersed by passage through a prism or grating. Dispersion units move so that radiation of the required wavelength always falls on the absorption cuvette. This type of instrument is used mainly in the laboratory as it is not sufficiently mechanically robust for production conditions and is expensive. In nondispersion analyzers, the whole emission spectrum from the infrared source passes through the absorption cell. These instruments (with nonselective sources) can either have selective detectors (with positive filtration) or nonselective detectors (with negative filtration). Analyzers with positive filtration (Fig. 9.14a) consist of a nonselective source (S) of radiation which passes both through the reference cuvette (K 2), filled with a gas that does not absorb infrared radiation, and the measuring cuvette (K 1), filled with the testmixture. The test component of the mixture absorbs radiation of certain wavelengths and the remaining radiation passes through the cuvette and impinges on the detector (D 1 ). The second detector (D 2 ) receives radiation that passes through the reference cuvette with unchanged intensity. The measurement is 155

I

I i

I_

S K,

a)

l0

b)

Fig. 9.14. (a) Analyzer with positive radiation filtration. (b) Analyzer with negative radiation filtration. S = Non-selective radiation source, K = measuring cell, K, K = cuvettes, D1, D2 = detectors.

rendered selective by filling the detector with the same gas as that measured in the cuvette. The analyzed gas absorbs only radiation corresponding to its absorption bands and the detector thus does not react to other wavelengths. Consequently, a gas in the measuring cuvette that absorbs a different wavelength will not affect the measurement. The energy absorbed by the gas in the detector increases its temperature, pressure and volume. These quantities are then measured and correspond to the concentration of the test gas in the cuvette. In an analyzer with negative radiation filtration (Fig. 9.14b), all the radiation from the source of a continuous spectrum (S) first passes through the measuring cell (K) filled with the test gas mixture and is then separated into two parts. One part passes through the reference cuvette, where infrared radiation is not absorbed, and the second passes through a selective cuvette (K 1) filled with the gas whose concentration is to be determined. The two beams then pass through nonselective detectors of infrared radiation (DI, D2 ). The selectivity of the measurement depends on the fact that the radiation corresponding to the absorption band of the substance is absorbed in the cuvette filled with the same type of gas, while all the radiation passes through the reference cuvette. The different experimental arrangements of the two types of analyzers result in various advantages and disadvantages.The nonselective detector records the whole continuous spectrum with the exception of the absorbed wavelengths, i.e. it measures small differences in the intensities of the two beams, while the selective detector measures only energy at the wavelengths in the absorption region of the test gas, so that the changes in the recorded energy are much larger than for the nonselective detector. A further advantage of the analyzer with negative filtration is 156

that both light beams pass through the analyzed mixture in the measuring cuvette and are thus affected identically by irregularities inthe flow rate or by the presence of solid particles in the gas. This analyzer is mechanically more resistant and has no moving parts. Although one or other of these analyzers may be more useful in a given case, they are considered to be equally useful in general. Infrared analyzers developed rapidly after the Second World War. A number of companies manufacture both type of analyzers at present. Attempts to attain improved sensitivity and signal stability led to extension of the original analyzer design to include a rotating shutter and different detector system arrangements. The rotating shutter produces alternating irradiation of the measuring and reference cuvettes and the gas in the two parts of the membrane detector is heated in the same phase cycle. This arrangement eliminates the effect of the external temperature on the determination and an alternating signal recording is easier to treat. A scheme of this type of analyzer is depicted in Fig. 9.15. The development of interference filters with narrow transparence bands permitted the construction of a simple type of monochromatic source with high emission at the required wavelength. This element is combined with an absorption cuvette and suitable detector in a simple commercial analyzer, depicted schematically in Fig. 9.16. A disadvantage in this arrangement is that any change in the energy of the beam produces a signal and the analyzer thus reacts to impurities in the optical parts, ageing of the source or detector or other components, and changes in the background as a result of absorption by other components of the sample. These effects can be greatly decreased by employing comparative measurement at a wavelength close to the absorption band of the measured component, by using a second suitable filter in the rotating shutter. Fig. 9.17 shows a typical absorption spectrum with the bands of the measuring and reference filters, minimizing the effect of the second absorption component. This arrangement ensures that the measured signal corresponds to the content of the analyzed component alone. Similarly, the interference from other gases in the test mixture which absorb in the same part of the spectrum can be eliminated by employing gas filters, filled with the interfering component, to remove that absorption wavelength from the continuous spectrum. When the test sample is sufficiently pure, a single-cuvette analyzer can be used in the same way as an analyzer with two cuvettes. The reference and analyzed gas are fed alternately into the cuvettes at regular intervals. 157

I

1I I

5

8 Fig. 9.15. Analyzer with rotating shutter. 1= Radiation source, 2 = motor, 3 = rotating shutter, 4 = measuring cuvette, 5 = reference cuvette, 6 = detector, 7 = detector diaphragm, 8 = amplifier.

The above procedures for the analysis of multicomponent mixtures can be used with either one or two cuvettes. An analyzer has been constructed for the determination of two components in mixture which absorb in different parts of the spectrum: this contains two selective detectors in series. Because of their high sensitivity, selectivity and universal utility, applications of infrared analyzers are continuously increasing. A wide range of types of analyzers is manufactured commercially. The most important manufacturers of non-dispersion infrared analyzers with positive filtration include Hartmann and Braun (Uras), Maihak (Unor), Siemens (Ultramat), Junkalor (Infralyt), Kent Industrial Measurements (Infragas), Ados, MSA, and Thermo Electron. A number of instruments are manufactured for special applications in various versions of the basic 158

3

1 II

II l

U

Fig. 9.16. Analyzer with interference filter. 1 = Source, 2, 5 = lenses, 3 = rotating shutter, 4 = absorption cuvette, 6 = filter, 7 = detector.

apparatus and in anti-explosion units. Portable instruments are manufactured for work in the field. The gases and vapours analyzed most often using infrared analyzers and their concentration ranges are listed in Table 9.9. They are analyzed in the control and study of production

interfering component

\

\

>

I

\

determined component

h

lI r

mveengh

. wavelength

Fig. 9.17. Selection of measuring and reference wavelengths: Xm is the selected wavelength for maximum response to the test component: Xr is selected so that the absorption of interferents has the same effect on the measured and reference signals.

159

TABLE 9.9 Applications of infrared analyzers Gas or vapour

Smallest measuring range

CO CO2 CH 4 SO, C2 H6 C3,H, C4 H1 0 C2 H4 C3H6 C2H2 NH 3 NO N2 O HCN C6 HI14 C7 H1 6 Petrol

0-0.1 vol.% 0-0.002 vol.% 0-0.01 vol.% 0-0.01 vol.% 0-0.02 vol.% 0-0.01 vol.% 0-0.01 vol.% 0-0.05 vol.% 0-0.2 vol.% 0-0.03 vol.% 0-0.05 vol.% 0-0.05 vol.% 0-0.005 vol.% 0-0.05 vol.% 0-0.3 g/m 3 3 0-0.5 g/m 0-0.5 g/m3

C6 H6

0-1.0 g/m

C6HCH3 CH30OH C2HOH CH;CHO CH 3 COCH 3 H2 0 CH 2 C12 CS 2

0-2.0 0-1.0 0-2.0 0-2.0 0-1.0 0-0.6 0-5.0 0-0.5

3

g/m 3 g/m 3 g/m 3 g/m 3 g/m 3 g/m 3 g/m 3 g/m 3

processes, in testing pollution in the atmosphere, in studying biological processes, etc. These analyzers are used in continuous production control, especially in the chemical and petrochemical industries, in metallurgy, in atmospheric monitoring, in power plants and heating plants to study the combustion process, in the food industry in quality control, in agriculture, for example for control of protective atmospheres for storage of fruit and vegetables, in the automobile industry for the control of exhaust gases, and in safety and human health protection, especially in areas with danger of explosion or toxic gases. They are also used in biology and medicine, e.g. to study metabolism. 160

TABLE 9.10 Magnetic susceptibilities of gases Gas

Temperature ( C)

Susceptibility (K.10 9 )

Helium Hydrogen Neon Carbon monoxide Nitrogen Methane Ethylene Acetylene Phosgene Hydrogen chloride Ammonia Dinitrogen oxide Argon Carbon dioxide Chlorine Nitrogen dioxide Nitrogen oxide Oxygen

18 18 18 20 18 20 20 11 13 22 16 20 18 18 15 20 19 20

-0.08 - 0.18 -0.34 -0.44 - 0.53 - 0.54 - 0.56 - 0.67 -0.67 - 0.76 -0.85 -0.85 - 0.88 0.91 - 1.87 + 6.52 + 6.96 + 151.00

9.3.3 EMISSION SPECTRAL ANALYSIS

In the classical form, emission spectral analysis is used only for some special gas determinations (e.g. for qualitative determination of simple mixtures of inert gases). Experimental difficulties encountered in quantitative analysis prevent more extensive use. For example, the gas spectrum can be complicated by that of gases occluded on the electrodes. Excitation of the emission spectrum can be accompanied by chemical changes, and thus by changes in the composition of the mixture; the new components can react with the electrodes. All these phenomena can lead to distortion of the results. Instead of excitation by an electric discharge, modern emission spectral analysis of gases employs excitation of molecules by ultraviolet light or through a chemical reaction. The former principle is employed in fluorescence analyzers. For example, the SO2 analyzer depicted schematically in Fig. 9.18 employs a pulse source of ultraviolet radiation which excites the SO2 molecules to emit radiation of a longer wavelength as they return to their original state (fluorescence). The radiation flux is 161

im

yin;

I

2

Fig. 9.18. Scheme of a fluorescence analyzer. 1 = Pulsed source of ultraviolet radiation, 2 = lens, 3, 4 = filters, 5 = measuring cuvette, 6 = photoelectric multiplier.

linearly proportional to the SO2 concentration in a range from thousandths to unitsof ppm. The fluorescence radiation passes through a filter into the photoelectric multiplier, whose signal is treated electronically and yields an analog output. A pulse fluorescence analyzer of H 2 S which has been catalytically oxidised to SO2 works on the same principle. When light emission occurs as a result of a chemical reaction, process is termed chemiluminescence. The excited state is the result of an exothermal reaction where part of the energy remains in the reaction products as electronic or vibrational excitation. The excited reaction products can lose their energy directly by radiation or can transfer it to other molecules in collisions. If all these energy losses, or part of them, occur through emission of light, then this process can be termed chemiluminescence. Two types of chemiluminescence are employed in gas analysis. The first is based on the reaction of the gas sample with a reactive component, usually another gas, at laboratory temperature; the second is flame chemiluminescence. Reactions at laboratory temperature are used more often as they are more specific. In this process, the gas sample containing component S is mixed with the reactive gas R, reacting to form an emitting product P*: S + R - P*

(9.44)

This product then emits photons with a characteristic frequency: P* -- P+

162

hv

(9.45)

The flux of the emitted lightis then proportional to the concentration of P*, which is in turn proportional to the product of the concentrations of S and R. Reactive gas R is usually present in a large excess and the emitted radiation is thus directly proportional to the concentration of component S in the test gas. The emitted light is usually measured using a photoelectric multiplier, placed after an optical filter which is transparent for the wavelength of the emitted radiation. The advantages of chemiluminescence lie primarily in the fact that the signal can be greatly amplified by the photoelectric multiplier, yielding high sensitivity. The detection limit depends on the dark current of the multiplier and noise of the amplifier, and is much lower than that attainable in direct absorption spectroscopy (because absorption techniques yield a signal corresponding to the small difference between two relatively large absorbance values). Chemiluminescence measurements are very sensitiveand selective. In order for some other substance to interfere, it would have to react with the reaction gas in an exothermal reaction,involving chemiluminescence, whose emitted radiation wavelength would have to be in the region specific to the optical filter and to the spectral sensitivity of the multiplier. There are very few such reactions. The most commonly encountered quenching gases are molecular oxygen and nitrogen. As their contents in analyzed gas mixtures (usually air) do not change, the quenching effect is constant during the analysis. Only a very few chemiluminescence reactions occur at laboratory temperature, which ensures that the measurement will be highly selective but, on the other hand, this limits the very sensitive technique to a very narrow range of substances. At the present, it is used to determine ozone, nitrogen oxides, ammonia, and carbon monoxide. Chemiluminescence characterizes the reaction of ozone with a great many inorganic and organic substances. The molecules of organic dyes such as rhodamine and safranine are oxidized by ozone to yield intense chemiluminescence. The first practical chemiluminescence detector for ozone was based on its reaction with Rhodamine B applied to activated silica gel, and is the most sensitive method for ozone, with a detection limit of less than 1 ppb. The sensitivity is lower in the presence of water vapour. Fig. 9.19 depicts a block scheme of an analyzer utilizing this reaction. This method is especially useful as no further gases are required, only periodic exchange of the Rhodamine B-coated silica gel disk. An internal ozone source is necessary for periodic calibration because the sensitivity of the plate surface changes with time. 163

03 wash boff'e

9

pump Fig. 9.19. Scheme of a chemiluminescence 03 analyzer employing Rhodamine B.

A different type of monitor for ozone detection employs a homogeneous reaction with ethylene in the gas phase at atmospheric pressure, 435 with emission of radiation in the range from 300 to 600 nm (X ma nm). It is assumed that the emitting reaction-product is the excited aldehyde group. The detector response is linear in the concentration range from 0.003 to 30 ppm 03 and no interferences have been found. A block scheme of this type of reactor is depicted in Fig. 9.20.

C,2H 4 fer

03 wash bat e

Fig. 9.20. Scheme of a chemiluminescence 03 analyzer employing ethylene.

164

The method employed for the determination of nitrogen oxides is the chemiluminescence reaction between NO and 03: NO +

03 = NO* + 02

(9.46)

NO,* = NO2 + hv

The emission observed in this reaction is similar to the extinguishing of an electric discharge in the air (e.g in a thunderstorm) or in nitrogen containing traces of oxygen. It is continuous at wavelengths of 0.6-3 /Am. The chemiluminescence reaction can be used directly to determine only NO; in the detection of NOX(NO + NO2 ), NO2 must first be converted to NO. A further reaction that can be used to detect NO is that with atomic oxygen: NO +O+

M =NO

NO* = NO 2

+ M (9.48) hv

This reaction, which occurs during extinguishing of an electric discharge in the air, is accompanied by emission of radiation in the range from 0.4 to 1.4 ,lm. Any NO 2 present is rapidly converted to NO by reaction with atomic oxygen, NO 2 + 0 = NO + 02

(9.50)

as the oxidation of NO by oxygen atoms and molecular oxygen is a relatively slow process. The chemiluminescence reaction can be employed to detect large concentrations of NOx, e.g. in emission measurements. Fig. 9.21 gives the scheme of a typical chemiluminescence analyzer. Because of the quenching effect of air on the chemiluminescence of NO + O, the first analyzers contained vacuum pumps to remove a stream of air and ozone from the reaction chamber and reduce the pressure to 100-500 Pa. Detectors also contain optical filters to absorb interfering emission having shorter wavelengths (below 600 nm) which arise from the reaction of ozone with other molecules (e.g. with alkenes). The detector response is linear for NO contents between 0.001 and 10000 ppm. No interferences were found from other substances present in the air. Newer types of analyzers can also be used under conditions where the 165

Fig. 9.21. Scheme of a chemiluminescence nitrogen oxide analyzer.

gas in the reaction chamber is at atmospheric pressure. The emission quenching is greater but the chemiluminescence is still sufficient. The decrease in emission is partly compensated by using a higher sample flow-rate (1 to 21 min'), and small volume reaction-zone connected as closely as possible with the photo cathode of the photomultiplier. NO2 must be reduced to NO prior to determination. The most commonly used method involves catalytic conversion using various types of carbon (graphite, graphitized soot, carbonized sucrose): C + NO2 = CO + NO

(9.51)

A microcomputer-controlled analyzer (Fig. 9.21) works in cycles in which the analyzed air passes either through the converter or directly into the reaction chamber at thirty second intervals. The value corresponding to NO2 is found by subtracting the signal for NO from that for NO.. This analyzer has four analog outputs: a continuous signal corresponding to the instantaneous concentrations of NO or NOx and three outputs for the average concentrations of NO, NO2 and NOx . Ammonia can be oxidized to NO which is then determined by a chemiluminescence reaction. When it is present together with nitrogen oxides, two measurements must be carried out: one on the original sample and one after absorption of NH 3 in an acid. The difference corresponds to the ammonia content. 166

Carbon monoxide can be detected using the reaction CO + O = CO*

(9.52)

CO2* = CO 2 + hv

(9.53)

Radiation is emitted in the range from 300 to 500 nm. As the photoelectric multiplier sensitivity is high in this region (greater than in the region for emission by NO ) the minimum detectable amount is smaller than for NO, and varies around 1 ppb. Flame photometric detectors and analyzers employ the chemiluminescence formed during combustion in a flame. When sulphur compounds are burned in a low-temperature flame (i.e. in a hydrogen-rich flame), intense blue chemiluminescence is formed. This emission is a result of recombination of sulphur atoms formed under reducing conditions in the flame: S + S + S*

(9.54)

S2* = S2 + hv

(9.55)

Compounds with other heteroatoms in organic molecules behave similarly. For example, HPO species exit radiation during the combustion of phosphorus-containing organic substances; nitrogen-containing organic substances yield the CN group. De-excitation of the excited state is accompanied by emission of radiation with known wavelengths. The maximum emission for sulphur lies at 394 nm, for phosphorus at 525 and 656 nm, and for the cyanide group at 385 nm. Fig. 9.22 depicts a scheme of a flame photometric detector. A mixture of hydrogen and air burns in the shielded burner tip, protecting the photomultiplier from direct radiation from the flame. When the air

Fig. 9.22. Scheme of a flame photometric detector.

167

contains compounds of sulphur, phosphorus or nitrogen, chemiluminescence occurs above the shielded flame; the emitted radiation passes through a suitably selected filter to the photomultiplier. The detector response is linear in the range from 10 to 1000 ppb SO2, H 2S or CH 3 SH. It is, however, very dependent on the design. Flame photometric detectors can be used in sensitive detection of halogen compounds. A supply of indium or copper must be placed in the reaction zone of the flame. The corresponding halides (of indium or copper) are then formed in the combustion and the intensity of their emission is measured. At the beginning of the 1970s, a number of companies began to manufacture chemiluminescence and fluorescence analyzers, primarily for monitoring pollutants in the air. For example, the Thermo Electron company manufactures pulse fluorescence analyzers for SO2 and H 2 S, and chemiluminescence analyzers for NO-NO2 -NOx and NH 3. In Czechoslovakia, the Chemoprojekt Satalice company has developed a chemiluminescence analyzer for nitrogen oxides in emissions (1-10000 ppm) and missions (1-1000 ppb), and to determine ozone, and also a flame photometric detection system designed primarily for gas chromatography. 9.3.4 OPTOACOUSTICAL METHODS

Optoacoustical methods depend on the analytical utilization of optoacoustical (photoacoustical) phenomena. The photon flux (radiant energy) excites the molecules of the absorbing gas to higher energy states from which they relax by non-radiant processes. The transition leads to an increase in the kinetic energy of the molecules and their temperature or pressure increases. The radiation source can be focussed light from a conventional source such as was employed in 1880 by A.G. Bell in discovering optoacoustical phenomena. Because of the unsuitable properties of this classical source, the discovery was not applied for many years. Optoacoustical methods underwent a renaissance after the late 1960s with the development of the use of lasers. Fig. 9.23 depicts a simple block scheme of the apparatus. Optoacoustical detectors are now based on step-wise adjustable gas lasers that mostly work in the infrared spectral region. If the wavelength of the laser radiation coincides with the energy of an infrared transition of the gas molecule, radiation is absorbed and the molecule is excited to higher rotational-vibrational states. Collisions of the excited gas convert 168

Fig. 9.23. Block scheme of an optoacoustical analyzer. 1 = Laser, 2 = modulator (circuit breaker), 3 = optoacoustical flow-through cell, 4 = microphone, 5 = lock-in amplifier, 6 = recorder.

this absorbed energy into translational kinetic energy of the molecule and the pressure is increased. When radiation from a pulsed laser, or interrupted radiation from a continuous laser, is employed, pressure waves appear in the absorbing medium with the same frequency asthat of the exciting pulses. The magnitude of the waves depends on the efficiency of the absorption process, i.e. the degree of coincidence of the laser emission lines with the absorption transition (the resonance condition). The pressure waves are recorded in the detection system of the analyzer. If a microphone is employed for the detection, then the optoacoustical signal produced is recorded as a voltage change. The dependence of the magnitude of the acoustical signal on the measuring parameters is given by the relationship kC p(t) = c (t)

(9.56)

where k is the Boltzmann constant, C is the number of molecules per unit volume, c v is the isochoric specific heat of the gas, Xo is the acoustical frequency and is the radiant flux of the laser. One of the two advantages of optoacoustical detection is apparent from equation (9.56)-the direct dependence of the sensitivity on the radiant flux of the source. In contrast to spectroscopic methods which record only the ratio of the input and output radiation, the sensitivity of optoacoustical detection can be increased by increasing the laser power. Furthermore, optoacoustical methods are very sensitive because of the relatively strict validity of the resonance conditions as a result of the very small band width of the laser line. The degree of resonance for a 169

given laser line and various compounds will almost always differ. However, coincidence can occur under real conditions. This possibility can be excluded by measuring the magnitude of the optoacoustical signal using a larger number of laser lines. The set of values found will be completely characteristic for the given compound. At present, optoacoustical methods are used for routine detection of contents of the order of tenths of ppm of freons, ethylene, ammonia, vinyl chloride, ozone, SF6, etc. The best instruments have a sensitivity of tenths of ppb and the theoretical sensitivity limit of optoacoustical detection is about 0.1 ppt. 9.4. Mass spectrometry Mass spectrometry is one of the most effective methods employed in the analysis of gases and vapours. Its name does not arise from the nature of an interaction, as the test substance does not interact with electromagnetic radiation, but rather from the apparent similarity between the spectrogram obtained in emission spectroscopy and the mass spectrometer recording: in both cases a set of lines of various intensities is obtained. 9.4.1 PRINCIPLE OF THE METHOD

In mass spectrometry, neutral molecules are converted into molecular ions; in the presence of excess internal energy, these ions can split into charged fragments and radicals. The charged species (molecular and fragment ions) are then separated in a magnetic or high-frequency field. The mass spectrogram then consists of a recording of the different individual ions, characterized by their specific charge (ratio of the charge of the species, Q, to its mass, m) or, more frequently, the ratio of the mass to the charge. The mass of the species is usually expressed in atomic mass units and the charge in the number of elementary charges, e, per ion (Q = ze). If z = 1, then ratio m/e is the relative atomic or molecular mass of the given ion. In contrast to spectroscopic methods, mass spectrometry does not utilize any clearly defined property of the molecule. Consequently, complete reproducibility of the mass spectrum of a pure substance cannot be ensured even under constant conditions. The spectrum is affected to a certain degree by instrumental factors. 170

9.4.2 INSTRUMENTS, THEIR BASIC COMPONENTS AND FUNCTION

To obtain a mass spectrum, the sample must be vaporized, ionized and, assuming it is molecular, fragmentation of the molecular ion must occur. The various ions thus formed are separated according to their mass-to-charge ratio (m/ze) and then detected. The instruments in which these processes occur consist of four basic parts: (1) sampler; (2) source in which ions are formed and remain for a short time (about 1 Is) for fragmentation to occur; (3) apparatus for separation according to mass; (4) detector. A vacuum system is employed to ensure suitable working conditions in all the parts of the instrument, so that the ionization process is controlled solely by interaction between electrons and the analyzed molecules rather than by collisions between the molecules and particles. The technique for introducing the gas or vapour into the ionization chamber is of basic importance and the parameters must be strictly controlled. To begin with, the gas introduced into the chamber must have the same composition as the sample in the sample bottle. All the components of the gas mixture must have the same partial pressure in both chambers and the inlet orifice must not affect the flow of gases with different densities and viscosities. Surface phenomena (e.g. adsorption) must be suppressed. Depending on the design, the input can be cold, hot, or chromatographic. Cold systems are used for gases and volatile substances and are made of glass. Hot input is usually carried out using a sample bottle that can be heated to 300-400 ° C. The inner surface is gold-plated to prevent decomposition of the sample on the hot surface. The pressure of the gas or vapour at the input to the ion source should be 1-10 -1 Pa. Input from a chromatographic column into a mass spectrometer requires a special arrangement. In contrast to the above methods, this is a dynamic arrangement that requires separation of the carrier gas from the separated components. A great deal of attention has been paid to this step and it will be discussed in greater detail in Sect. 10.6.4. The most commonly used methods for ionization of molecules in the gas phase at present are ionization by electron impact, chemical ionization, and ionization in a field. Ionization by electron impact -the most widely used method- involves interaction of the substance with a stream of electrons emitted by a heated tungsten or rhenium cathode. The minimum electron energy required for molecule ionization is characteristic of the molecule and is termed its ionization potential. 171

Electron impact leads to the formation of a cation-radical from the neutral molecule (termed the molecular ion), which then decomposes to form various positive and neutral fragments. The whole process of fragmentation of molecular ions can be described as a complex set of subsequent and parallel first-order reactions whose rate depends primarily on the energy of the ionizing electrons. It should be pointed out that molecular ions formed during electron impact can be in various electronic and vibrational states and can thus decompose in various ways. For example, the following reactions occur in the ionization of methane by an electron beam: m/e = 16 (13.1 eV)

(9.57)

m/e = 15 (14.4 eV)

(9.58)

CH 4 - CH+ + H2

m/e = 14 (15.7 eV)

(9.59)

CH 2 + H CH 4 - H++

m/e = 1 (22.7 eV)

(9.60)

CH 4 -, CH++ 3H

m/e = 13 (23.3 eV)

(9.61)

CH 4 - H++C + 3H

m/e = 1 (29.4 eV)

(9.62)

CH 4 - CH' CH 4

-

CH

+

+ H

Thus, control of the energy of the ionizing electrons can ensure the formation of a certain type of ion in the ionization chamber. It has been found experimentally that, at electron energies greater than 50 eV, the mass spectrum depends little on this energy. It has become accepted to characterize organic compounds in terms of their mass spectra at 70 eV (less commonly at 50 eV) and these spectra are mostly given in the published literature. The mass spectra recorded under these conditions contain a great deal of information and have many peaks corresponding to ion splitting. These spectra also often include a peak corresponding to the molecular ion, which is important in identification. Attempts can be made to detect this ion at lower electron energies (16-15 eV) which are only slightly greater than the ionization potential of most organic compounds, and where there is much less fragmentation of the ions than at 70 eV. The spectra obtained in chemical ionization provide better information. Chemical ionization occurs through ion-molecular reactions with ions which are formed from a separate reaction gas interacting with the electrons. The ions react with a sample molecule through transfer of a proton or removal of H- or an electron, leading to formation of an ion of the analyzed molecule with a single positive charge. The energy trans172

ferred to the neutral molecule during interaction with ions is usually much smaller than during electron impact; this is reflected in an increase in the intensity of the peaks of molecular ions and a decrease in fragmentation of the substance. The ion source of a mass spectrometer works at elevated pressures (about 102 Pa) and the concentration of the reaction gas is about 103 greater than that of the analyzed compounds. Reaction gases are usually quite simple molecules: CH4 , isobutane, N2 0, and less commonly NH 3, H20, CO, (CH 3 ) 4Si, (CH 3 )2 NH, He, Ar, N2 , C02, etc. The character of the ions formed, the interaction with the analyzed substance, and thus the character of the mass spectrum depend on the type of reaction gas (its ionization potential, number of hydrogen atoms, electron lone pairs and vacant orbitals). For example, methane is ionized in the ion source to form CH+ and CH+ as primary ions which then react with methane according to the equations CH+ + CH 4 -* CH;++ CH 3

(9.63)

CH+ + CH 4 - C 2H+ + H2

(9.64)

The CH+ and C 2 H' ions can no longer react with methane but can react with a small amount of the sample (XH) which is fed into the source: CH+ + XH - XH+ + CH 4

(9.65)

C 2H+ + XH - X++ C 2H 6

(9.66)

The XH' and X + ions can break into further fragments, yielding the mass spectrum. Chemical ionization does not lead to the formation of molecular ions but rather M + H or M - H ions. To obtain an even simpler spectrum, other reaction gases can be used instead of methane, such as isobutane (C 3H+ ions), ammonia (NH' ions), or water (H 3 0 + ions). These ions also ionize through proton transfer (and thus act as acids in the gas phase) and have lower energy so that fragmentation of the XH+ ions is minimal. Some instruments can be used to detect negative M- ions. These can also be formed during chemical ionization, through capture of thermal electrons by molecules of the organic substance. Thermal electrons are formed in the ions source as a result of deceleration of the original 173

electron beam by molecules of the reaction gas. The results obtainedso far do not permit generalization of the behaviour of various compounds under these conditions but it has been found that some organic nitrogen-containing compounds can be detected in amounts as small as 10-18 g. It can thus be assumed that this method will be useful in the analysis of trace concentrations of organic compounds. In field-ionization the sample molecules are exposed to the effect of an electric field with a high potential gradient. A sharp-edged anode (covered with whiskers) is placed at the exit from the ion source and there is a large potential difference between the cathode and anode (105 V cm-1). This electric field is sufficient to remove electrons from the gas molecules lying in it. It is assumed that high fields affect the potential energy of the molecule so that the electron passes through the energy barrier to the anode by the quantum mechanical tunnelling effect. The practical consequence of this effect is the formation of a molecular ion that is not excited, so that only very slight fragmentation occurs. Thus, practically every compound will yield the M+ or (M + 1)+ ion and the spectrum is very simple. The mass spectrum of a substance is a discrete function which describes the variation of the ion flux with the specific charge or, more frequently, its reciprocal value (m/ze). For this purpose, the set of ions formed in the ion source must be separated according to their mass and charge. This step is carried out in mass analyzers which are based on a number of principles. In the most commonly used arrangement, the ions leaving the ion source through the outlet slit are accelerated in an electric field with potential difference U, and their total energy is given by the relationship Ekin=

my 2

2

= Uze

(9.67)

where v is the ion velocity. They then enter the magnetic field where a force perpendicular to the electric field acts on the accelerated particles. A centripetal force of Bzev acts on the ions in the magnetic field, where B is the magnetic induction field producing curvature of the ion path. This force must be in equilibrium with the centrifugal force acting on the ions, mv2/r, where r is the radius of the circular path: mv2 r

174

Bzev

(9.68)

or v=

Bzer m

m

(9.69)

Substitution for the ion velocity in Eqn. (9.67) yields (Bm zr)=

Uze

(9.70)

or m ze

B 2 r2 2U

(9.71)

The ion path is more or less curved according to the magnitude of m/ze. The radius of the path which is needed for the ion to impinge on the detector is determined by the geometry of the spectrometer, and is thus constant. Mass spectra can be recorded either by varying the acceleration voltage V at constant magnetic field, or by varying B at constant accelerating voltage V. Older instruments were fitted with permanent magnets and thus employed the former principle, while modern instruments employ electromagnets in whichthe magnetic field is varied. The arrangement used most commonly in chemical analysis is depicted in Fig. 9.24. Mass spectrometers with a single magnetic field sector are termed single focussing instruments. Good spectrometers of this type can have a resolution of up to 5000, where the resolution R is defined as R= m

(9.72)

where m is the ion mass and Am is the difference in mass between two separated peaks. For example, a resolution of 5000 indicates that an ion with m/e of 5000 will be separated from an ion with m/e of 5001 (or m/e of 50.00 from m/e of 50.01). A resolution of 500 is sufficient for common applications in organic chemistry. Ions can also be separated in the absence of a magnetic field. A quadrupole analyzer (Fig. 9.25) is a typical non-magnetic analyzer. It consists of four cylindrical rods 20-30 cm long symmetrically placed around a common axis. The electrodes are connected so that opposing 175

.

j

Fig. 9.24. (a) Dempster mass spectrometer. (b) Sector mass spectrometer. 1= Ion source, 2 = magnetic field, 3 = collector slit, 4 = collector. 176

rods have the same potential. The ions move between electrodes in a field that has two components: static and high-frequency. A potential of UX =U+UF cosS

t

(9.73)

is applied to one pair of electrodes, where UF is the amplitude of the high-frequency voltage with angular frequency , and U is the direct current voltage. The potential of the second pair of electrodes is such that U = - U. Ions with a given m/ze ratio can pass through the analyzer according to the UF and w values. The remaining ions oscillate in a transverse direction until they impinge on one of the electrodes or on the shutter at the end of the quadrupole analyzer. These analyzers are smaller than magnetic analyzers and have less stringent requirements on low input pressure. However, the ion discrimination is very strong and appears as a considerable decrease in the peak intensity compared to that obtained in magnetic analyzers. This effect can be eliminated either by special design (increasing the electrode volume, use of correction ion shutters prior to the analyzer or of compensation electronic circuits) or by using correction factors in spectral evaluation. Analyzers based onmeasuring the time-of-flight are completely different. The ions leave the ion source through a long tube and impinge on

Z

2 ( U+ Vcos

t)

unstable path

Fig. 9.25. Quadrupole analyzer. The ions leave the ion source in the direction of the z-axis. The rod length is about 20 cm, with radius about 2 cm.

177

the detector according to their m/ze value. It follows from Eqn. (9.67) that the velocity of an ion leaving the electric field equals V

1 2Uze

/

Uz

(9.74)

Every ion moves with a velocity that is inversely proportional to the square root of its mass. The time required for the ion to pass along path L (the length of the tube) is given by the relationship t=

L

(9.75)

The time difference characterizing the separation of ions 1 and 2, --

A t =L

/t = L

Fm-

2)

m2

-Uzi V2Uze 2

(9.76)

(9.77)

then depends on the difference in the square roots of the ion masses. The resolution of this analyzer is about 500 at an upper mass limit of 1000. The general character of the spectrum at a given ionizing electron energy depends on a great many additional factors that cannot be exactly defined. Primarily, the intensity of the lines in the spectrum depends on the time they spend in the ion source and mass analyzer, i.e. on the geometry of the instrument and acceleration voltage, as well as on the temperature of the ion source and of the system through which the substance enters the mass spectrometer. When the acceleration voltage is decreased or the temperature is increased, the degree of fragmentation of the molecular ions usually increases. The character of the spectrum also changes with a change in the pressure in the ion source. Consequently, the spectra of a single compound obtained on different instruments under different conditions need not be identical. Comparison of spectra obtained on various instruments has indicated that the greatest difference in the line intensities (up to a several-fold variation) occurs in the region of low m/e values (m/e < 40). Consequently, these peaks are usually neglected in identification and comparison with literature data. The reproducibility of the relative intensities of lines for ions with 178

m/e > 100 is good (assuming that the peak with maximal intensity, with which the intensities of the other peaks are compared, does not have a low m/e value). Ions are detected in modern instruments using photoelectric multipliers without glass vessels. They capture ions separated in the ion separator and record then after amplification. The signal is recorded by a fast-loop oscilloscope on light-sensitive paper, or by a chart recorder, or is recorded through an analog-digital convertor on computer storage media. 9.4.3 APPLICATIONS

Mass spectrometry is irreplaceable in the analysis of gases and vapours, especially for identification of substances or structure determination. Type analysis of more complex mixtures can be carried out but qualitative analysis of the individual components is not possible. The components must first be separated, preferably by gas chromatography. Combination of gas chromatography with mass spectrometry and computer processing of the results is one of the most effective methods for the solution of very complex analytical problems. It can be expected that a given molecule will yield a characteristic composition of fragment particles which will differ from that of other molecules. However, this assumption is not always fulfilled. As with other spectroscopic methods, the analyst must be capable of correctly interpretating the spectrum which requires considerable knowledge and experience. Mass spectrometry is a technique that yields an unusually large amount of information. In contrast to other methods, such as NMR, infrared spectrometry, etc., one of its great advantages is its sensitivity, which can permit analysis of nanogram amounts of sample. However, all the fragmentation mechanisms have not yet been elucidated. Compounds are most often identified by comparing the recorded spectrum with published spectra. As mentioned above, the comparison must be made carefully, as the spectra can be affected by instrumental parameters. Compilations of spectra are available either in handbooks, or on storage media for fast computer evaluation. The criteria employed in identification are primarily the masses of the most common ions and the order of their number and the masses of the ions in the higher regions of the spectrum. A different type of classification is preferable for computer treatment. Above a mass of 29, the mass spectrum is 179

divided into sections with 14 mass units, corresponding to homologous increase by one CH2 group, and the two strongest peaks are selected from each part. This approach permits the testing of identity from spectra from different spectrometers. A number of lines can overlap in the spectra of mixtures of gases and vapours. It is then necessary to know the relative frequencies of the lines of the individual components of the sample. The composition of the mixture can then be determined by drawing up and solving a set of linear equations, provided that the sensitivity of the instrument (expressed in the partial pressures of each component per unit recorded by the instrument) is known. If the analyzed mixture has n components and if the instrument records a line with height I corresponding to mass m , , then the linear equation can be written in the form SlX

1

+ S 12 x

+Sn,X

...

= 1

(9.78)

where S,, is the height of the line with mass m, corresponding to a unit pressure of component 1 (determined for the pure component) and x is the partial pressure of this component in the sample. In general, S,, is the height of the line with mass m corresponding to unit pressure of component n, and x, is its partial pressure in the sample. In this equation, the values of x are unknown and the values of S are constants found from calibration graphs for the individual n components. If the spectrum consists of (n - 1) additional lines with heights I 2, - I n corresponding to masses m2... m, then a complementary set of linear equations can be written: Si x + S12X2 + · · + Szn, = I1 S21X

SnX

+ S22x2 + 1+

* + S2nxn ,, =79)

:.. :S 2 ~x,2 =I)

Sn2 x2 + +

(9.79)

SnX, = In

In general, the partial pressures can be calculated from these equations by using the method of inverse matrices. This is especially useful when the series of analyzed samples has a constant qualitative composition. Control calculations permit one to test whether the mixture contains some other component. If this component has a different spectrum, then important differences would appear, and subsequent calculation could 180

yield its spectrum and aid in its identification. The system of linear equations can be solved rapidly on a computer, even for complex mixtures. It sometimes happens that all the lines overlap, for example in the analysis of a mixture of the isomers of n-butane and isobutane; however, the differences in intensities for these two compounds are sufficiently great that mathematical solution is possible. Analysis is very difficult for pairs of cis and trans isomers, which have identical spectra. In complex mixtures where it is impossible to identify all the components, it is often possible to estimate individual types of compounds relatively simply and with sufficient precision to allow their classification on the basis of their molecular mass. The following types of compounds can be distinguished relatively easily in the qualitative analysis of complex hydrocarbon mixtures: alkanes, cycloalkanes and alkenes, cycloalkenes, dienes and alkynes, and aromatic compounds. The types of ion that are characteristic for the given type of compound can be distinguished in their spectra. The technique of ionization with low-energy electrons is especially important in this connection. It also permits estimation of the distribution of the contents of the individual types on the basis of their molecular masses, branching of the alkyl chain, number of benzene nuclei in the molecule, etc. A variety of methods for the analysis of mixtures have been developed, sometimes with chemical treatment of the sample, or a combination with other physical methods. The methods for type qualitative analysis can be used only for samples for which an analytical procedure has been developed, and which can be assumed not to contain unexpected types of compounds. (e.g. for crude oil fractions from a given source). Consequently, type analysis is very important and useful for the characterization of complex mixtures. If all the components in a complex mixture are to be identified, it must be separated into the individual components before entering the mass spectrometer. A chromatographic apparatus is used in these cases, directly connected to the mass spectrometer, and can even permit identification of substances with identical mass spectra. Sect. 10.6.4 deals with the combination of gas chromatography with mass spectrometry. 9.5. The magnetic properties of gases The magnetic properties of gases can sometimes be used for their determination. Although this is possible for only a limited number of 181

gases, this method is very important, especially for the determination of oxygen. 9.5.1 BASIC CONCEPTS AND RELATIONSHIPS

Magnetic phenomena can be described in terms of the intensity of the magnetic field H and of the magnetic induction B. The magnetization, i.e. the magnetic moment related to unit volume, My, is given by the relationship Ml

B /P0

H

(9.80)

where to is the permeability of a vacuum. It then holds for the permeability of a real medium that B= H

(9.81)

Combination of these two relationships yields

Mv=H

-1)

(9.82)

Consequently, the fraction Mt,/H, defined as the magnetic susceptibility X, is given as X= H

1

(9.83)

The molar magnetic susceptibility Xm is given by the expression Xm

M

X

(9.84)

where M is the molar mass and p is the density. In 1895, Pierre Curie found that the magnetic susceptibility of gases, solutions, and some solids is temperature dependent: Xm=D+

182

C

(9.85)

where D and C are constants. Somewhat later, Langevin theoretically derived the temperature dependence of the molar magnetic susceptibility, Xm =

NA(am +

T

)

(9.86)

where am is a coefficient expressing the induced magnetic moment, mi, related to unit intensity of the magnetic field (am = mi/H), m is the permanent magnetic moment of the magnetic dipole, and k and NA are the Boltzmann and Avagadro constants, respectively. Comparison of these two relationships yields the expression for the Curie constant C: C

NAIm

2

(9.87)

The molar magnetic susceptibility is given by the structure of the molecule and can be either negative or positive. In general, an electron moving around the atom in a closed path forms a permanent magnetic field with a given dipole moment. If an external magnetic fields act on this electron, then an induced dipole moment of the opposite sign is formed. The final moment is a result of the difference between the permanent and induced moments. In many substances, the permanent dipole disturbs the paired electrons in the covalent bond, so that they have only a negative induced moment. These substances are attracted to the weakest part of the external inhomogeneous magnetic field and are termed diamagnetic. On the other hand, substances with an odd number of electrons or unpaired electrons have a much larger permanent than induced dipole moment. These substances are termed paramagnetic and are attracted to the strongest part of the external inhomogeneous magnetic field. The molar magnetic susceptibility of diamagnetic substances is negative, while that of paramagnetic substances is positive (Table 9.10). As a result of the temperature dependence of the magnetic susceptibility, an increase in temperature can lead to conversion of paramagnetic substances to diamagnetic. For example, at 0 C acetylene is paramagnetic (Xm = +1) while it becomes diamagnetic at 11°C (Xm = -0.48). Similarly, at 0 C dinitrogen oxide has a value of Xm = + 3, with a value of - 0.43 at 20 C (the Xm values are given in m3 mol- 1). If a gas mixture is placed in a heterogeneous magnetic field, the individual substances react 183

towards this field in accordance with their susceptibilities. Paramagnetic gases can be distinguished from diamagnetic in this way. Only a very few gases are paramagnetic - nitrogen oxide, nitrogen dioxide, chlorine dioxide, and especially oxygen. Their susceptibilities are an order higher than those of diamagnetic substances which thus do not interfere in the determination. The magnetic susceptibility is not determined directly in gas analysis and the determination is based on indirect measurement. 9.5.2 MEASURING METHODS

The importance of this method for the analysis of oxygen led to the development of various procedures which depend on its magnetic properties. Oxygen analyzers can be separated into three groups, based on different principles: (1) thermomagnetic instruments; (2) magnetomechanical instruments; (3) magnetopneumatic instruments. Thermomagnetic analyzers employ thermomagnetic convection (termed the magnetic wind), which was discovered by Faraday. Convection is formed in an inhomogeneous magnetic field as a result of the effect of the temperature gradient in a paramagnetic gas. Thermomagnetic convection is measured in this type of analyzer by allowing the test gas to flow through a circular chamber separated by a horizontal glass tube (see Fig. 9.26). A platinum fibre separated into two parts is wound around this tube. The two parts of the filament are connected in a Wheatstone bridge and one part of the coil is placed in a permanent magnetic field. The filament is heated to a defined temperature by an electric current and acts as a thermoanemometer, measuring the gas velocity. If a gas which does not contain oxygen passes through the chamber, no gas flows through the horizontal tube; when the gas does contain oxygen, then its paramagnetic properties lead to its being drawn into the magnetic field and thus into the horizontal tube, where it is heated. As the magnetic susceptibility decreases with increasing temperature, the heated gas is forced out by the colder gas and gas begins to flow through the horizontal tube. The gas flow-rate is directly proportional to the oxygen content in the test gas. The gas flow leads to a change in the temperature of the platinum filament, resulting in a change in the resistance, which is recorded by the Wheatstone bridge. The instrument is placed in a thermostat to ensure that the measurements are independent of the ambient temperature. The measurement can be affected mainly by the presence of other paramagnetic gases (usually nitrogen oxides) that, when present in 184

Fig. 9.26. Thermomagnetic analyzer (Hartmann and Braun). 1 = Ceramic tube, N, S = magnet poles, O = potentiometer, G = galvanometer, A = amperometer, R = rheostat.

higher concentrations or in variable compositions, should be removed prior to the determination. The magnitude of the thermal conductivity of the accompanying gases usually has no effect on the analytical results. However, they are to a certain extent dependent on the viscosity, density, and thermal capacity of the mixture. The viscosity affects the velocity of laminar flow of the gas through the tube, and the thermal capacity affects the amount of heat that the gas removes from the heated filament. These factors are considered in the design and calibration of instruments, and so approximate data on the analyzed mixture must be available. The principle described above is employed in a somewhat different arrangement in instruments in which the gas stream is fed into the measuring and reference chambers with two heated filaments connected in a Wheatstone bridge. The filament in the measuring cell is placed between the poles of a magnet. If the gas does not contain oxygen, then the flow rates through both chambers are identical. However, when the analyzed gas contains oxygen, the magnetic field in the measuring cell leads to an increased flow that is proportional to the oxygen concentration. An example of this arrangement is given in Fig. 9.27. The best known manufacturers of analyzers based on the thermomagnetic principle are Hartmann and Braun (Magnos 2T, 5T), Junkalor (Permolyt), Kent (Paramagnetic Oxygen Analyser), MSA (Thermoparamagnetic Oxygen Analyser); similar instruments are manufactured under the name MGK inthe U.S.S.R. 185

Fig. 9.27. Thermomagnetic analyzer 5T (Hartmann and Braun). V1, V 2 = Heated filaments, Rs, R2 = constant resistances.

Magnetomechanical instruments measure the force exerted on a body located in an inhomogeneous magnetic field. Fig. 9.28 depicts the design of this type of analyzer. A rod-shaped test body (1) is attached to a stretched quartz or platinum fibre (2) and suspended between the polar extensions of a magnet (3), consisting of hollow glass beads with a diameter of 2 to 3 mm filled with diamagnetic gas (N2 ), with a given magnetic susceptibility, so that they begin to rotate. The movement is proportional to the sum of the force gradients of the inhomogeneous magnetic field and the difference between the bulk magnetic susceptibilities of the test body and of the gas surrounding it. When the susceptibility of the gas changes, as a result of a change in the composition or pressure, the test body begins to rotate. Its equilibrium position is a result of the magnetic and torsion forces, acting against one another, and is indicated by a light beam reflected from mirror (4) to scale (5). The scale is calibrated directly in the partial pressure of oxygen. As the torsion suspension has no friction, it is very sensitive to changes in the oxygen content. Indication can also be carried out using the null-point method. The measuring principle and basic apparatus are the same as above but the test body is covered with a thin layer of rhodium to make it electrically conductive. Two reference electrodes maintained at a constant potential are placed close to the body to form a heterostatic electrometer. If there is no potential difference between the electrodes, the test body rotates as a result of the opposing magnetic and torsion forces. A suitable applied potential returns it to its original position. To maintain the test body in 186

I

Fig. 9.28. Magneto-mechanical analyzer (Beckman). 1 = Test body, 2 = quartz fibre, 3 = field adjusters, 4 = mirror, 5 = scale. Fig. 9.29. Magneto-pneumatic analyzer. 1 = Input of the analyzed gas, 2 = input of the reference gas, 3 = capillary, 4 = microflow meter, 5 = measuring chamber, 6 = electromagnet.

the zero position, a reflected light beam is split into two beams which impinge on photocells and have identical intensities when the body is in the zero position. Any deviation of the test body from the zero position leads to a change in the intensity of the two light beams, and produces an electric current, which is amplified to drive a motor connected to the potentiometer which measures the potential of the reference electrode. Every change in the magnetic force resulting from a change in the oxygen partial pressure is balanced by an electrostatic force. To eliminate the effect of the ambient temperature, the apparatus is placed in a thermostat. This type of instrument is manufactured by the Beckman Instruments Co., by Hartmann and Braun (Magnos 3) and by Taylor Servomex. The third group of analyzers, termed magnetopneumatic, are based on measuring the pressure difference created in two branches by the drawing of oxygen into a magnetic field. This principle is employed in various ways. One version is depicted schematically in Fig. 9.29. The reference 187

gas is fed through two branches into the measuring chamber into which the analyzed gas is also fed. The tip of one of the reference branches is placed in the field of an electromagnet. If the analyzed gas contains oxygen, it is drawn into the tip of the this branch, reducing the flow in this branch and changing the pressure difference in the flow meter in the tube which connects the two reference branches. The result is converted into an electric signal proportional to the oxygen concentration. Sensors based on thermoanemometers are employed to measure pressure differences in various types of magnetopneumatic analyzers, or the measurement may be carried out using a membrane condenser. As the analyzed gas does not come into contact with the sensor, these analyzers can be used to determine the content of oxygen in corrosive gases containing, e.g., chlorine. These instruments are manufactured by the Hartmann and Braun (Magnos 4), Siemens (Oxymat), and Maihak (Oxygor) companies. All instruments employing the magnetic properties of gases are very selective and are used primarily to determine medium and high oxygen concentrations. In spite of this high selectivity, the composition of accompanying gases must be considered because their diamagnetic or paramagnetic properties can distort the results. This complication can be avoided by calibration with a suitable accompanying gas: values are given by the manufacturers for a number of analyzers. These instruments have measuring ranges from a few percent up to 100 vol.% or exceptionally also to tenths of percent. They are not suitable for lower oxygen concentrations as they are insufficiently sensitive; it is then preferable to employ electrochemical or photometric analyzers. Static and portable versions of the analyzers are manufactured for use in explosive media. They are used most often to determine oxygen in the air and in industrial gases, to optimize combustion process conditions, to control biotechnological processes such as fermentation, and in the food industry to monitor protective atmospheres for the storage of grain and fruit. 9.6. Determinations based on density measurements The gas density (specific mass) p is defined as the mass of a unit volume of gas at temperature 0 C and pressure of 101.3 kPa: m nM P=V= 188

(9.88)

The value of p thus depends on the temperature and pressure. Results are usually given in grams per litre. The relative density Pr is the ratio of the mass of a unit volume of the gas to that of the same volume of a reference gas, usually air or nitrogen. As this is a ratio, it is dimensionless. It follows from the definition that density determination requires absolute measurements, while the relative density can be determined by simpler comparative measurements. Thus, the latter is used far more widely in gas analysis. Both methods can be applied to individual pure gases and binary mixtures or their equivalents. The individual gases are determined almost only by density measurements, either by weighing a volume of the test gas or by finding the molar mass from the mass of a liquid and the volume of its vapours. It is preferable to analyze binary mixtures or their equivalents by measuring their relative density. The precision of the method increases as the density difference between the gases in the analyzed mixture increases. A number of types of gas analyzers depend on relative density measurements. Some of which work under static conditions, while others can be used for continuous analyses. The relative density is usually determined using a gas balance which compares the float effect of a body when it is immersed in the test and reference gases. When this effect is the same in both gases they have the same density. The Edwards balance is an example of a static balance and consists of a balance arm to the ends of which are fitted a sealed, thin-walled sphere and a counter weight. The balance arm is placed in a sealed thermostated chamber connected with the source of the test gas and a manometer. The arm and the counter-weight are fitted with a pointer and scale to indicate the arm's exact position. During work, the balance is filled with dry, carbon dioxide-free air. The pressure is measured and the balance zeroed. The balance is then evacuated, filled with the test gas and again balanced. The ratio of the pressures for balancing when filled with air and with the test gas gives the relative gas density because the relative density is directly proportional to the pressure. The pressure is dependent on the temperature, so the measurements should be carried out at constant temperature, or the data recalculated to a single temperature. The Lux balance is another type of gas balance. In the original design, the gas sample is fed into a thin-walled gas sphere and the mass of the gas is compared with the float effect of the same amount of air surrounding the sphere. The relative density corresponds to the position of the 189

rider on a graded balance arm (units and tenths of the relative density) and the position of the pointer on the scale (hundredths and thousandths of the relative density). The measurement can be carried out under static conditions or continuously. Balances have been described in which an iron rod is fitted to the balance arm and the equilibrium position of the balance is maintained by a change in an electromagnetic current. The balances from the Pollux company are based on continuous measurements of the relative density. In contrast to the above types of gas balances, they permit elimination of the effects of temperature and pressure changes during the measurement. The basic design of this balance is depicted in Fig. 9.30. A number of versions are manufactured. Two thin-walled glass spheres are placed on the balance arm; the larger is filled with nitrogen, and the analyzed gas passes through the second, with openings, and surrounds the whole balance system placed in a chamber. The chamber has a volume of approximately 3 1 and a flow-rate of 2-3.1 1 min- is used. The instrument is based on buoyancy, which is proportional to the constant volume of the gas sphere and the gas density. The latter depends both on the gas composition and on the

!

Fig. 9.30. Gas scales (Pollux).1 = Densitometer jacket, 2 = balance beam, 3 = cell filled with nitrogen, 4 = cell with openings, 5 = weight, 6 = magnetic connector, 7 = box manometer, 8 = damper, 9 = gas feed, 10 = frit, 11 = compensation weight.

190

pressure and temperature in the chamber. Basically, the density of the gas under standard conditions is of interest, i.e. at 0 C and 101.3 kPa. The effect of changes in the temperature and pressure on the buoyancy of a glass sphere is compensated by a membrane chamber placed on the balance arm and connected with a compensating weight. When the barometric pressure increases, the gas becomes heavier and the buoyancy greater. The membrane in the chamber is compressed, changing the position of the compensating weight, and balancing the increased buoyancy of the sphere. A change in the temperature is compensated similarly. As the temperature increases, the gas in the chamber becomes less dense and the buoyancy is reduced. An increase in the temperature also leads to an increase in the pressure in the sphere containing nitrogen and thus also in the chamber with the membrane. The compensating weight changes its position and, as with a pressure change, equalization again occurs. This arrangement can be used to compensate both effects in the range + 5 kPa and + 15 C. Under these conditions, the measuring precision is + 1%of the scale deviation. When the temperature variation is less than + 5 C, the measuring error decreases to 0.5%. A different type of balance has two auxiliary weights placed on the balance arm, permitting adjustment of the measuring range. This type of balance is manufactured in three versions differing in their treatment and presentation of the output data. The measured data are obtained either as a recording from a penpoint recorder, or a special pneumatic converter is employed to convert the density data to the equivalent air pressure. In the third version, induction equipment placed in the balance chamber yields an amplified, measureable electric signal. The instrument can then be used for standardization. It is assumed in the use of all gas balances that the deviations from Boyle's law are negligible under the measuring conditions, and that the volume of the glass sphere does not change. One of the greatest measuring errors comes from vapour condensating on the balance arm, glass sphere and counter-weights. An error of about + 0.2% can be attained when gas balances are used very carefully. The relative density can also be measured in a dynamic arrangement in a gas stream. For example, the Ranarex instrument employs the relationship between the kinetic energy, supplied artificially to a flowing gas, and its density (Fig. 9.31). It uses a rotating propellor (1) in chamber (A) to propel the gas against the blades of an impulse wheel (2) placed opposite it in a single chamber, to produce a torsional force on the 191

r

5

Fig. 9.31. Ranarex. 1, 3 = Fans, 2, 4 = impulse wheels, A, B = chambers, 5 = torsion arm.

impulse wheel. This torsion is proportional to the gas density according to the equation. M = kn 2p

(9.89)

where M is the torsion moment, k is a constant, n is the number of revolutions of the propellor per time unit and p is the gas density. The reference gas (air) in the second chamber (B) is forced against the second impulse wheel (4), yielding a reference torsion. The ventilator in the reference chamber turns in the opposite direction to that in the test chamber, and compensates for irregularities in the ventilator speed, temperature, humidity, and atmospheric pressure. The axes of the two impulse wheels are connected by two levers and a connecting element (5) which limits the rotation of the wheels. The difference in the torsion moment leads to movement of the lever mechanism, which is transferred to the pointer on a scale. The reference and test gases are forced into the appropriate chambers by ventilators. This instrument can be used, e.g., to determine a CO2 content up to about 20% with a precision of about + 1%, or to measure the humidity of air with water contents up to 15%. The chamber is warmed to prevent water vapour condensation. A number of other types of instruments 192

based on similar principles can be found in specialized laboratories. For example, the Martin gas balance is employed as a sensitive detector in gas chromatography. As already mentioned, the above method of determination is best suited to gases with large mass differences. It is used most often in practice to determine CO 2 in various industrial gases (smoke-stack gases), to determine H 2 in mixtures with N 2 for the synthesis of NH 3, to determine H 2, 02, C0 2, SO2, C12 and CO (after its combustion to CO2) in the air, and as an indicator to monitor the density of combustion products or coal gas.

9.7. Determination based on viscosity measurements Viscosimetric methods are generally used in the containing gases with very low or high viscosities. The viscosity of a gas is proportional to its response to an external force. The retarding force is coefficient of internal friction (viscosity), given by tion for laminar flow conditions 1

rr4A p 8ul

analysis of mixtures internal friction in characterized by the the Poiseuille equa-

(9.90)

where r is the radius of a capillary tube through which the gas flows, I is its length, Ap is the pressure difference between the ends of the capillary, and u is the gas flow-rate. The gas viscosity varies with temperature according to the relationship /t = no(l + at)1/ 2 ,

(9.91)

where qt is the viscosity at temperature t, 0 is the viscosity at O C and x is the coefficient of thermal expansion of the gas. In contrast to liquids, the viscosity of gases increases with increasing temperature. Comparison of the viscosity values for a number of gases and vapours (Table 9.11) indicates that this property can be analytically useful. For example, the viscosity of nitrogen is roughly twice that of hydrogen, methane is 35% more viscous than propane, etc. Although some gases are more dense than other gases, their viscosity can be lower. 193

TABLE 9.11 Viscosities and densities of some gases and vapours Gas or vapour Air Helium Neon Argon Krypton Hydrogen Nitrogen Oxygen Carbon monoxide Carbon dioxide Dinitrogen oxide Nitrogen oxide Sulphur dioxide Ammonia Hydrogen sulphide Methane Ethane Ethylene Carbon disulphide Chloroform Diethyl ether

Viscosity

l107

Density qt. 1 0 7(t

°

C)

0C, 101325 Pa

(Pa s)

(Pa s)

(g/l)

170.8 186.0 297.3 209.6 232.7 83.5 170.7/10.9 ° C/ 189.0 166.0 139.0 135.0 178.0 117.0 91.8 116.6 102.6 84.8 90.7 91.1 93.6 67.8

182.7 (18) 194.1 (20) 311.1 (20) 221.7 (20) 246.0 (15) 87.6 (20.7) 178.1 (27.4) 201.8 (19.1) 175.3 (21.7) 148.0 (20) 148.8 (26.9) 187.6 (20) 125.4 (20.5) 98.2 (20) 124.1 (17) 108.7 (20) 90.1 (17.2) 100.8 (20) 96.4 (14.2) 98.9 (14.2) 71.6 (14.2)

1.2929 0.1784 0.9003 1.7837 3.708 0.08988 1.2505 1.4290 1.2504 1.9769 1.9778 1.3402 2.9269 0.7710 1.539 0.7168 1.3566 1.2604

For example, the density of CO2 is ca. 1.5 times greater than that of air, while its viscosity is much smaller; Kr is heavier than Ne but has lower viscosity; the density of saturated hydrocarbons increases with the number of carbon atoms, while the viscosity decreases. Viscosity measurements can be used to measure simple gases or binary mixtures. In the measurement of binary mixtures, it is preferable to replace absolute measurements by comparative measurements using a standard gas. Determination methods are based on measuring either the velocity of gas flow at constant pressure drop or the pressure difference at constant flow-rate. For example, the Hoppler viscometer utilizes the resistance to gas flow through a capillary represented by the space between a glass tube and a sphere that can pass within it. The gas is forced through the capillary under a constant pressure that depends on the mass of the sphere. The time for the sphere to fall between two lines on the tube is 194

measured. The viscosity of the gas is proportional to the product of the fall time, a factor including the sphere radius, and the density difference between the gas and the sphere. Determination of gas density using the H6ppler viscometer is accompanied by a large error if the temperature is not carefully controlled; the gas viscosity changes by 2.5-16% on a temperature change of 1C. Errors can also arise from vibration of the tube during the fall of the sphere, from the presence of dust particles on the surface of the sphere and tube, etc. Gas viscosities can also be measured by the rotating cylinder method. Two concentric cylinders, sealedat both ends, are suspended one inside the other and placed in the test gas. One cylinder rotates at a known constant rate and the other, which is suspended on a torsion fibre, is twisted by the movement of the gas molecules between the cylinders. The gas viscosity can be calculated from the rate of rotation of the first cylinder, the angle through which the second cylinder rotates, the

__ [11 __

L _s

I

I: I

f

_

2

IE

I

r -

\'x I

air

Ia

Fig. 9.32. Fagelston instrument. 1 = Capillary tube, 2 = manometer.

195

torsion characteristics of the fibre, and the gas temperature and pressure. When an oscillating disk is employed, a flat disk is suspended horizontally on torsion fibres between two similar fixed disks. All three are surrounded by the test gas. The control disk is rotated and the gas viscosity is calculated from the degree of damping of the oscillations and other data. The rotating cylinder and oscillating disk methods are probably the most accurate for the determination of absolute gas viscosities. The complexity and fragility of the instrumentation has prevented their extensive use in analytical practice. Another method of viscosity measurement (Fig. 9.32) is based on comparison of the differences in the ratios of the viscosities to the densities of two gases, the test and reference gases (the latter is usually air). The two gases pass through capillary tubes (1) connected to a manometer (2) which measures the pressure difference between the two. If the ratio of the viscosity to the density is the same for both gases, then both will exert the same pressure. However, if the viscosity or density of one of the gases is different from the other, a pressure difference is formed, in which the system with a lower viscosity-to-density ratio exerts the greater pressure. This type of instrument is especially sensitive for organic vapours with high density and low viscosity. 9.8. Diffusion process analysis Analytical methods based on diffusion processes utilize effusion, transfusion or thermal diffusion. 9.8.1 EFFUSION

Effusion is the flow of gas through a small orifice in a vessel. At low gas pressures, the mean free path of a molecule can be greater than the diameter of the orifice. Under these conditions, the number of molecules passing out through the opening is the same as that impinging on a section of the vessel wall of the same size, and the concentration of the gas in the vicinity of the orifice does not change. It is known that, for an ideal gas, the mean arithmetic velocity of the molecules is inversely proportional to the square root of the molar mass according to the relationship 8RT 78R _= ~M 196

(9.92)

When various gases pass through the orifice at the same pressure and temperature, the number of molecules passing will depend only on their velocities, because the number of gas molecules in the vessel will be the same for all gases. As the time is inversely proportional to the velocity, the time required for effusion of a given amount of gas is given by the square root of its molar mass, or -in terms of Graham's law- the relative velocity of the molecules of the effusing gases under constant conditions is inversely proportional to the square root of their densities:

t= - =

=

(9.93)

This gas behaviour occurs only when the mean free path is greater (preferably at least 10 times greater) than the diameter of the orifice. As it is difficult to ensure openings of the required size, effusion measurements are usually carried out at low pressures where the mean free path of the molecule is sufficiently long. If there is a pressure difference between the two sides of the opening, a gas stream is formed and the amount of gas flowing out through the orifice is proportional to the pressure difference. It is necessary that the opening be smooth; if the edge of the orifice is deformed, viscosity effects which differ with the gas can become important. Bunsen was the first to measure effusion to determine the density of gases or the compositions of binary mixtures. The Schilling effusiometer is the most widely used instrument of this kind. It consists of a thickwalled cylinder acting as a water thermostat. Inside the cylinder is placed a calibrated glass tube fitted with a three-way stop-cock and outlet orifice in which a small platinum capillary is placed. Water is forced out of the glass tube by the test gas and the outlet orifice is opened. The time required for the water to flow back between two lines on the glass tube is measured. This experiment is carried out with both the test and the reference gas (air) and the gas density is calculated from Graham's law, the known viscosity of air, and the two effusion times. Both air and the test gas must be saturated with water vapour and the appropriate corrections must be made. A glass sphere can be used instead of a cylinder. The effusiometric determination of gas density, and thus of the concentrations of gases in a binary mixture, is accompanied by a number of errors. The diameter of the outlet opening is usually 0.15-0.30 mm. As 197

this increases, the precision of the method decreases, because gas flows out through a large orifice by both effusion and streaming. The pressure difference at the orifice should be reproducible as it determines the degree of streaming. At atmospheric pressure, the mean free path of gases is much less than the diameter of the orifice and then Graham's law is no longer precisely valid. Consequently, most commercial effusiometers are provided with correction tables for individual gases. Attempts have been made to automate effusion measurements. Mercury was used as a confining fluid and the tube was fitted with two platinum wires in place of lines. As soon as the mercury reached the first contact, an electric timer was started, and then stopped when the mercury reached the second contact. Mercury is a good confining fluid as it prevents condensation of water vapour in the outlet and its vicinity, but it cannot be used for analysis of gases containing hydrogen sulphide and other reacting gases. As indicated in the introduction to this method, effusion processes can be used for partial separation of the components of multicomponent gas mixtures, because the velocity of a gas molecule depends on its mass. When a binary mixture flows out through the orifice, the first portion will be richer in the lighter gas and the second in the heavier gas. 9.8.2 TRANSFUSION

If two gases are separated by a porous wall then they penetrate through it until they are completely mixed. This process is termed transfusion. Capillary diaphragms are equivalent to outlet orifices so that, as with effusion, diffusion through small pores occurs according to Graham's law (see Eqn. (9.93)). The effectiveness of the separation depends on the permeability of the material. The selection of the pore size is important as it must permit free motion of the molecules. If the pores were too small and too numerous, the molecular seive effect or adsorption could become important. Transfusion separation of gases is mostly carried out using quartz, palladium or other metals, ceramic filters (e.g. bacterial), etc. Comparison of the relative diffusion rates of various gases through quartz is useful for evaluating the separation efficiency of this material (Table 9.12). For example, hydrogen diffuses through quartz six times more slowly than does helium. Difficulties connected with complete diffusion separation of gas mixtures have resulted in transfusion being used only for special gas sep198

Fig. 9.33. Diffusion indicator scheme. 1 = Chamber containing the analyzed gas, 2 = diffusion chamber, 3 = manometer.

arations, e.g. for determining admixtures in light gases, such as H 2 , He, CH4 , as well as NH 3 , CO, 02, etc. when present in a mixture with gases of much higher molecular weight. Bunsen was the first to employ transfusion to separate gas mixtures. Using this method, He and H 2 can be separated in a palladium capillary at 450 ° C, Ne and He on a quartz diaphragm at 600-900 C, and Ar from Ne, or isotopes of Ne and hydrogen by repeated transfusion. This principle was used in the development of the atomic bomb to separate the isotopes 235U and 238U in the form of UF6 . A simplified scheme of an instrument based on transfusion separation is depicted in Fig. 9.33. The analyzer has two chambers separated by a porous glass diaphragm, ceramic filter, or some other porous material. Chamber (2) is filled with air, while the analyzed gas flows through chamber (1). The light component in the test gas diffuses into chamber (2) faster than air in the opposite direction, thus increasing the pressure in chamber (2), which is recorded on a manometer. As a result of transfusion, the concentration in the two chambers begins to equalize. The maximum pressure is proportional to the concentration of the diffusing component in the original mixture. The pressure is measured with a very sensitive liquid, or membrane differential manometer that can measure units of Pa. 9.8.3 THERMAL DIFFUSION

When a mixture of two gases flows through a vertical tube whose outside is cooled by a water jacket, and in the centre of which is placed TABLE 9.12 Relative diffusion rates of various gases in quartz at 900 ° C Gas

Relative rate

He

62.4

H2

11.0

N2 Ar

1.8 1.0

199

an electrically heated wire, the gas molecules move as a result of thermal diffusion. While convection leads to flow of the warm gas upwards and the cold gas downwards, the light gas molecules move towards the hot wire and the heavy molecules towards the tube walls. The gas mixture is thus enriched in the lighter fractions at the top of the tube and in the heavy fractions at the bottom. If a sufficiently long tube is employed, the two components can be separated. Thermal diffusion has been employed as a separation method primarily in the separation of isotopes, e.g. of chlorine (in hydrogen chloride), neon and krypton. 9.9. The utilization of adsorption in gas analysis The increase in the concentration of certain species (molecules, ions) on the surface of a solid substance or at the interface between two substances as a result of intermolecular forces is termed adsorption. The molecular forces which cause the deviation of the properties of real gases from those of ideal gases play an important role in adsorption. These are basically electrokinetic forces, i.e. dispersion forces resulting from the electron distortion in neighbouring molecules. As a result of electron motion, even molecules with a symmetrical electron density distribution have fluctuating deviations from the mean density, i.e. they have fluctuating dipoles, quadrupoles, etc. As the molecules approach one another, these fluctuating properties of the various molecules cease to be independent, resulting in a net attractive forces, termed dispersion forces. Electrostatic forces operate in a number of cases -as orientation forces (in the adsorption of polar molecules on surfaces which have a permanent electrostatic charge due to ions or dipoles) and induction forces (where a dipole moment is induced in adsorbed molecules by the permanent electrostatic charge on the surface or vice versa). All these forces are attractive and, as the adsorbed molecule approaches the adsorbent molecule, become equal to the repulsive forces, and rapidly increase at small distances. One of the typical characteristics of adsorption interactions is that the adsorbed molecule does not interact with only a single site on the surface of the adsorbent (ion, atom or molecule forming the adsorbent lattice), but with manyneighbouring sites. The overall interaction resulting from dispersion forces is always greater than the interaction with a 200

single site on the surface, while the overall electrostatic interaction can be smaller than that with a single site on the surface (interaction of the dipole of the adsorbate molecule with a cation surrounded by anions in the adsorbent lattice). A further peculiarity of adsorption interactions which differentiates them from the interactions between molecules in a gas is the usually close contact between the adsorbate and the molecules, ions, and atoms on the surface of the adsorbent. Consequently, interactions between adsorbent species and the adsorbate are analogous to interactions in condensed systems, such as solutions, where the distances between the species are also usually small. Thus, adsorption often has many features in common with molecular association in liquids. Hydrogen bonds are often formed during adsorption between the adsorbate molecules and functional groups or ions on the adsorbent surface. The formation of molecular complexes with hydrogen bonds often involves nonspecific dispersion, orientation and induction interactions [e.g. in the adsorption of water, alcohols, ethers, amines, etc. on adsorbents with hydroxyl groups e.g. (silica gel)]. Specific interactions are also present in the adsorption of molecules which have accessible regions of high electron density, for example 7r-bonds, on their surface with hydroxyl groups and cations. Donoracceptor interactions are also found in adsorption on conductors and semi-conductors. The action of these types of intermolecular forces is designated in general as physical adsorption. More or less labile compounds can be formed on the sorbent surface as the result of secondary bonding. In contrast to physical adsorption, this process is characterized as chemical adsorption or chemisorption. Further differences between physical adsorption and chemisorption result from the differences in the intermolecular forces. The heat of physical adsorption of a gas is relatively small, of the same order as its heat of condensation. The heat of chemisorption is much larger, being comparable to the heat of the corresponding chemical reaction. Chemisorption is specific and depends on the chemical affinity between the adsorbent and the adsorbed substance, while physical adsorption can occur between any surface and the adsorbed substance. The rate of physical adsorption is greater: chemisorption requires supply of the activation energy, which can be very small, for the necessary bond to be formed. It can be deduced from the shape of the adsorption isotherm that 201

chemisorption always occurs in a monomolecular layer, while physical adsorption can be involve multimolecular layers. 9.9.1 BASIC RELATIONSHIPS

The degree of adsorption of a gas depends on its nature, on its external pressure, the temperature, and the type of adsorbent. It has been found from the dependence of the degree of adsorption on the pressure and temperature that these conditions affect the amount of adsorbed gas. A reversible equilibrium is usually formed between the gas and solid phases. At equilibrium the amount of gas adsorbed per unit surface area, or per unit of adsorbent mass, is a function of the temperature and pressure a = f(p,T)

(9.94)

This relationship has been termed the thermal adsorption equation. When only the pressure is varied and the temperature is constant, then it is termed the adsorption isotherm: a = f(P)T

(9.95)

which is of the greatest importance for the description of adsorption processes. Graphical plots of this relationship can be divided into five types according to the character of the adsorption (Fig. 9.34). Type I corresponds to monomolecular adsorption (physical and chemical), while the other types are known only for physical adsorption and, according to Brunauer, correspond to adsorption in several layers. Freundlich derived an empirical relationship, valid at low pressures, for the type I adsorption isotherm (an example is the adsorption of gases and vapours on active carbon): a = k p"

(9.96)

where a is the amount of adsorbed gas, p is the equilibrium pressure, k is a constant dependent only on the native of the adsorbent, and n is a constant depending on the type of adsorbed gas. 202

9

U A

I _I

P

Pc a

a

l

I

P

V

P0

P

Po

Fig. 9.34. Basic types of adsorption isotherms.

For higher pressures, Langmuir developed a relationship from kinetic concepts: this can be written in the form

V

'1-Pvmbp -c P l+bp

(9.97)

Ps

where v is the volume of adsorbed gas at equilibrium pressure p, vm is a constant giving the amount of gas required to completely cover the surface with a monomolecular layer, Ps is the pressure at which the gas at the given temperature condenses, and c is the adsorption coefficient. Langmuir based the derivation of this equation on the assumption that the forces between the adsorbent surface and the gas are chemical in nature. The Langmuir equation is valid not only for chemical but also for physical adsorption, assuming that it occurs in only a monomolecular layer. Other authors (Williams-Henry, Magnus) have derived similar equations to describe adsorption in a monomolecular layer. They are based on various concepts and are essentially identical with the Langmuir 203

equation. Langmuir assumed that the adsorbed molecule is retained at the surface by a single active site, while Williams assumed that each adsorbate molecule is held between neighbouring sites on the surface; Magnus based his derivation on the assumption that the forces between the adsorbent surface and the gas are electrostatic in nature. Brunauer, Emmet and Teller derived an equation for the adsorption isotherm which describes allof the five types of dependence. The general form of this equation is given by the relationship P PS Ps

o(

_

_=

Pm)

c11 + C-1 mC

TmmC C

p p

(9.98) 9.98P

where C is the equilibrium constant, dependent on the difference in the heat of adsorption in the first layer AH a and the heat of condensation AH1 : C = exp

Ha_ Ht RT

(9.99)

When AH a > AH', adsorption occurs according to an isotherm of type I, II or IV. When AH a < AH', adsorption occurs according to isotherm III or V. Types IV and V correspond to polymolecular adsorption on a highly porous adsorbent, and the attainment of a saturated state at pressures close to the saturated vapour pressure ps is a result of capillary condensation. The shape of the isotherm is affected both by interactions between the sorbing substance and the adsorbent as well as the interactions between the adsorbate molecules. 9.9.2 ADSORBENTS It is necessary in studies of the effect of the adsorbent on the adsorption process to consider the adsorbent's structure, its method of preparation, the amount of it and, in the analytical separation of gases, the shape of the adsorption bed. The structure of the adsorbent affects physical adsorption especially when dispersion forces are the predominant factor in the process. These 204

forces are then more important than orientation forces, which are a function of the permanent dipole moment of the adsorbed molecules, and than induction forces, which depend on the polarizabilities of the molecules. The adsorption analysis of gases is usually carried out using various types of active carbon, silica gel, molecular sieves, or organic polymers. Active carbon Active carbon has a high specific surface area (800-1000 m2 g-l) and consequently a large adsorption capacity. Its structure is analogous to that of graphite. It consists of parallel planes of carbon atoms in a hexagonal arrangement. However, in contrast to graphite, theselayers are rotated around perpendicular axes by various angles and overlap irregularly. This arrangement results in a large number of pores and thus a large internal surface area in active carbon, compared to which the external geometric surface area is negligible. Dubinin has stated that various types of active carbon contain three different kinds of pores. The largest, macropores can usually be observed with an optical microscope and have radii of 10-5 -10 -4 cm. These macropores cannot participate in the actual adsorption process and only facilitate the penetration of the adsorbate molecules into the inner parts of the carbon grains, and thus act as transport routes. Smaller, transition pores can be measured either by the mercury expulsion method or using an electron microscope. Their radii lie in the range from 7 . 10 - 7 to 1.7 · 10 - 6 cm. Transition pores are also of no great importance in adsorption. Only in the final stage of adsorption of organic vapours are these pores filled as a result of capillary condensation at high equilibrium pressures of the liquified vapour. This appears as an asymptotic increase in the adsorbed amount, close to the saturated vapour pressure, on isotherms of types II and III. The smallest type of pores, micropores, cannot be observed directly, even using an electron microscope. Dubinin and coworkers studied these pores using adsorbates with various molecular dimensions and concluded that the pore size approaches molecular dimensions. These pores are of the greatest importance for the adsorption process. Adsorption and desorption occur completely reversibly in them, in contrast to the processes in transition pores. In general, all three types of pores can be found in active carbon. In 205

fine-grained carbon, the transition pores have very smallvolumes, so that the carbon contains practically only macropores and micropores. Silica gel Silica gel is partly hydrated SiO 2 and is a typical adsorbent on which specific interactions occur. Depending on the conditions of preparation, i.e. the pH and the ratio between the rates of polymerization and condensation, silica gel can be obtained with various porosity characteristics. For example, silica gel with small pores is obtained in acidic media (pH = 4), while wide-pore silica gel is formed in weakly alkaline media. As the elementary structure of silica gel consists of spherical species with quite regular dimensions, the pore size is also quite uniform. Most commercial silica gels contain a mixture of A1203 and Fe203, contributing to the irreversible sorption, which can also have a catalytic effect. To ensure wide application of silica gel, methods have been developed for the preparation of a chemically pure material with a narrow distribution of wide pores. Depending on the preparation method, silica gel can be obtained with a specific surface in a range from units to hundreds of m2 g-l. Hydrothermal treatment has been found useful (i.e. at high temperature and water vapour pressure) in the production of wide-pore material with a relatively small specific surface area and high hydroxyl group concentration. Molecular sieves Molecular sieves are natural or synthetic crystalline aluminosilicates (zeolites), characterized by high sorption selectivity and capacity. Their crystal lattice consists of SiO4 and A10 4 tetrahedra. The SiO 4 group is electrically neutral as a result of sharing of its oxygen atoms, while the A10 4 group has a single negative charge, compensated by a cation (Li+, Na + , K+ , Ca 2 + , Sr 2 + , etc.). An increase in the temperature leads to loss of the water of crystallization, while the crystal lattice structure is retained, to yield a system of cavities and channels, of defined dimensions, in which selective sorption of substances occurs as a result of the sieve effect. These substances must have molecules whose critical diameter (diameter of the smallest cross-section through the sorbate molecule) is the same as or smaller than the channel dimensions. Table 9.13 lists the critical diameters of a number of molecules. Various types of crystalline zeolites are prepared synthetically. Molec206

TABLE 9.13 Critical diameters of some molecules Molecule

Critical diameter (nm)

H2 02 N2 C2 H6 C2 F6 C2 C16 CF4 CC14 CBr4 CI 4 SF 6

0.24 0.28 0.30 0.44 0.53 0.68 0.53 0.68 0.74 0.82 0.60

ular sieves of types A and X are manufactured commercially. The crystal lattice of type A molecular sieve has cavities, with a diameter of 1.14 nm, connected by channels with a free diameter of 0.4 nm. As the diameter of the inlet opening is 0.42 nm, this type is designated as molecular sieve type 4A (NaA in the Soviet literature). When the sodium atoms in the lattice are exchanged for calcium, of which only half as many are required because of their larger charge, the effective diameter of the inlet openings increases to about 0.5 nm. This sieve is designated 5A (CaA in the Soviet literature). Type X molecular sieves in the sodium form have the same chemical composition as type A sieve, but different crystallographic structure. This type of sieve has cavities with a diameter of 1.16 nm, with inlet openings through which a sorbate molecule with a diameter of about 1 nm can pass. This sieve is designated as 13X (NaX in the Soviet literature). In contrast to type A sieve, exchange of the sodium ions for calcium leads to a decrease in the effective diameter of the inlet openings to about 0.9 nm. This sieve is designated as 10X (CaX in the Soviet literature). Ion exchange can occur with a number of other metals, so that molecular sieves can be prepared with various connecting channel diameters and thus various selectivities for the adsorption processes. In addition to selectivity based on the sieve effect, molecular sieves also exhibit chemical selectivity as a result of the metal ions in the crystal lattice. These cations interact strongly with polar or polarizable adsorbates. Consequently, the more polar or less saturated compounds are preferably adsorbed. 207

Molecular sieves belong to a group of substances for which inclusion phenomena are important. The sorbate molecule entering the cavity forms an inclusion compound, stereospecifically, without the formation of chemical bonds. A number of other compounds, e.g. urea, thiourea, cyclodextrins, and graphite form inclusion compounds, which are very selective because of their various cavity shapes that are either permanent or are formed on contact of the two components.

Organicporous polymers This group consists of synthetic sorbents that are mostly produced by suspension copolymerization of a mixture of monofunctional and polyfunctional monomers in the presence of an inert component acting as a cross-linking agent. Very fine differencesin the selectivity of the copolymers can be attained by various combinations of monomers with different functional groups, and choice of the type and amount of crosslinking agent. Both nonpolar and very polar sorbents can be prepared, which are able to undergo variously selective interactions. Independent of the polarity, their porous structure can contain openings in the range from 7 to 40 nm. They are thus sorbents with transition pores and macropores. Their adsorption capacity is, in general, lower than for microporous sorbents (active carbon, silica gel) even when they have large specific surface areas (100-800 m2 g-l). The chemicals most often employed are styrene-divinylbenzene, ethylvinylbenzene-divinylbenzene, and acrylonitrile-divinylbenzene copolymers, polyacrylates, polyvinylpyridines, polyvinylpyrrolidones, and polystyrenes. These substances include, e.g. Porapak polymers (manufactured by Waters Associates Inc., U.S.A.) and series 100 Chromosorb (John-Manville Co., U.S.A.), which are selective over the whole polarity scale. The XAD polymers are also manufactured in a wide range of polarities; these are synthetic Amberlite-type resins that have no exchangeable functional groups. A macroporous (pore diameter 72 nm), slightly polar sorbent based on poly(2,6-diphenyl-p-phenylene oxide), manufactured by Applied Science Lab. (U.S.A.) under the name Tenax GC, has been widely used. Of all the porous plymers, this sorbent has the smallest specific surface area (ca. 25 m2 g l) and its adsorption capacity at laboratory temperature is thus small. It is, however, widely used because of its high thermal stability (300-450 C), low sorption of water vapour, and negligible catalytic activity. 208

9.9.3 ADSORPTION METHODS IN GAS ANALYSIS

The specific properties of individual adsorbents have been utilized for both analytical and preparative purposes. Suitable choice of conditions permits very effective separation of multicomponent mixtures. These methods have replaced the now obsolete, tedious, and difficult fractional condensation or distillation of substances, and are often useful where earlier methods met with failure. A mixture of gases can be separated in two ways: either by fractional adsorption or by fractional desorption. In fractional adsorption, the adsorption rate is decisive. An equilibrium that is temperature and pressure dependent can be established in a time period of several seconds to several hours. In practice, the method of fractional desorption is used most often: the gas mixture is first adsorbed on a suitable adsorbent and then the individual fractions are gradually desorbed by decreasing the pressure, increasing the temperature, or by replacement by some other gas. There is a critical desorption temperature for each gas, at which it can be quantitatively desorbed into a vacuum. Differences in the sorption of gases on various sorbents, such as active carbon or silica gel, can be employed for separation of various binary mixtures such as N2 -0 2, N2-Ar, N 2-CO, N 2 -CH4, CO CH4 , 02-Ar. The different behaviour of individual gases on these absorbents is shown in the order in which they are desorbed and in the sharpness of the separation. More complex gas mixtures can be separated by suitable combinations of variously selective adsorbents. One of the first applications was the complete analysis of a mixture of hydrogen and hydrocarbons up to C5 . After cooling, the analyzed mixture was fractionally adsorbed onto active carbon and aluminium oxide. The temperature was gradually increased to yield hydrogen as the first fraction; methane then desorbed from the active carbon at about 20 C. The third fraction containing ethane and propane, and the fourth, propane and butane, were desorbed from aluminium oxide at 300 ° C. The individual gases that are separated from the mixture by fractional adsorption or desorption are mostlydetermined by physical methods. For example, the determination can be based on measurement of the gas density or, preferably, the thermal conductivity which yields a greater sensitivity using a smaller amount of gas. Adsorption methods are used primarily for the separation of hydrocarbon mixtures or to separate the heavier inert gases. Development of 209

these methods has led to modern, efficient and fast gas chromatographic analysis, which has gradually replaced the original adsorption methods of separation. 9.9.4 THE USE OF ADSORBENTS IN TRACE ANALYSIS

The use of adsorption methods in the analysis of trace amounts of substances has become increasingly important especially in connection with the monitoring of pollution of the air by gases and vapours of organic substances. The concentrations of some gases in the air are so small that they cannot be analyzed in the external atmosphere at all, even using very sensitive and selective detectors. They can be monitored in working atmospheres only in special cases (e.g. the analysis of organic solvent vapours). Thus, the pollutants must be concentrated and isolated prior to analysis. A number of basically different preconcentration techniques have been developed, including condensation by freezing out, absorption by reagents in solution or applied to a suitable inert support, absorption in pure solvents, and physical adsorption on solid substances. Methods based on physical adsorption are used most often at present; their advantages include the ability to release the adsorbed material back into the gas phase through thermal desorption, or into a liquid phase of a suitable solvent. The accuracy of the data obtained from the analytical treatment of the sample depends on the reversibility of the physical adsorption process. Preconcentration methods can be classified as conservation, equilibrium, and diffusion, depending on the task to be solved, i.e. on the basis of the relationship between the total masses of the individual substances in the sample and their concentration levels. In the first two methods, the test gas samples are transported to the concentration medium by convection, as the air at the interface is in constant motion. In conservation preconcentration, a defined sample volume is drawn through a sorbent bed at a constant flow-rate. It is necessary to know the conditions for quantitative dynamic adsorption from the test gas stream. The conservation method is used most frequently. Equilibrium preconcentration is based on the assumption that air acts as an inert gas and that none of its main components significantly affects the equilibrium adsorption distribution ratios of the test substances. The gas is drawn through the sorbent at an arbitrary rate until 210

equilibrium is established. This method requires a relatively constant concentration range of the substances in the analyzed air. Molecules of the substances can accumulate at the adsorbent surface only when the air is quiescent at the interface. In contrast to the previous methods, in diffusion preconcentration the transport of the substances to the sorbent is controlled purely by steady-state diffusion. Preconcentration is carried out using collectors. Collectors for equilibrium and conservation methods are various types of sampling tubes with adsorbents and must primarily ensure the best contact between the flowing air and the sorbent. In diffusion preconcentration, the basic function of the collector (a passive dosimeter) is to ensure completely stationary conditions to allow steady-state diffusion of the substance to the sorbent. Consequently, most dosimeters consist of three independent parts: the dividing component, the diffuser, and the sorbent vessel. The dividing component provides aerodynamic resistance which prevents the molecules of the test substances passing into the diffuser by convection (frit, metal grid, glass fibres, etc.). The diffuser is usually a block of inert material with one or more cavities containing a homogeneous diffusion medium, a stationary air layer. The sorbent is placed next to the diffuser and is protected on the remaining sides against direct contact with the air by the vessel walls. Practically all known adsorbents, and especially active carbon and silica gel, have been tested for their ability to concentrate trace amounts of substances. Adsorbents based on molecular sieves and organic polymers came into use later. Active carbon is recommended as a universal sorbent for sampling of practically all nonpolar and medium-polar industrial solvents, such as alkanes and their chloro-derivatives, aromatics, acetate esters, ketones, ethers, etc. Active carbon is also employed to sample monomers such as styrene, vinyl chloride, acrylonitrile, vinyl acetate, and acrylacrylates. Hydrophobized active carbon had been found useful for preconcentration of alcohols, formaldehyde, acetic acid, and other very polar substances. The adsorbed samples can be desorbed only using liquids (usually carbon disulphide or dimethylformamide). Thermal desorption is insufficiently rapid except for very volatile substances. Carbon molecular sieves form a special group of carbonaceous sorbents, having highly uniformpores, and practically only micropores. They have been found especially useful for sampling of very volatile freons, alkanes, and also of ethylene oxide, methyl bromide, etc. The adsorbed components are released by thermal desorption. 211

Graphitized carbon black is a special carbonaceous material with very low specific surface area (10-100 m2 g 1). Oxygen-containing organic substances such as ketones and acetates can be very readily desorbed from these substances, which is not the case with molecular sieves. Silica gel, in a variety of grades, is a widely used polar sorbent for trace analysis. Except for completely nonpolar paraffins, practically all organic substances can be preconcentrated on it. It is used for sampling alcohols, esters, ketones, amines, nitro compounds, nitrogen-containing heterocyclic compounds, aromatics, chlorinated unsaturated hydrocarbons, dimethyl- and diethyl sulphate, acrylacrylates, etc. It is also useful at low temperatures for accumulation of C4 and C 5 alkanes, H2 S, SO2 and vinyl chloride. Samples of medium and high-boiling substances are desorbed by liquids. Thermal desorption is employed up to temperatures of about 300°C but the effect of humidity must be considered (possible hydrolysis, etc.). Organic polymers can also be used for preconcentration, especially series 100 Chromosorb, Porapak, and Amberlite XAD. They are selected on the basis of their polarity and of the chemical properties of the test substances. Tenax has been very popular in recent years. In addition to its high thermal stability, it is inert to water. Except for volatile substances with a boiling point below 80 ° C, Tenax has been used for practically all substances, especially for alkanes, olefins, chlorinated hydrocarbons, ketones, esters, etc. Substances are thermally desorbed from Tenax. Sample tubes are manufactured commercially, e.g. by the Supelco Co., using active carbon, silica gel, molecular sieves, etc., as the sorbent. They are scaled at both ends in an inert gas atmosphere. Passive dosimeters are packed with material based on active carbon and are manufactured by a number of companies, e.g. Drager, Mine Safety Association, and DuPont.

9.10. Radiometric methods Modem chemical gas analysis also involves the determination of radioactive gases and the use of radiochemical methods to determine inactive gases. The methods of activity measurement and instrumentation for this purpose are far too broad a subject to be discussed here. Only methods which can be used for gas analysis will be mentioned, and 212

the reader is referred to the basic radiochemical literature for further information on the instrumentation, etc. Two basic methods can be used in the analysis of radioactive gases. Either the gas is fed directly into the detector (flow-through ionization chamber or Geiger-Miller tube) or it is separated from the detector by the counter window. In some cases, the radioactive gases are fixed by adsorption on solid substances (e.g. active carbon) or by dissolving in liquids. Measurement using window tubes is used relatively rarely, as low-energy radiation is absorbed to a considerable degree by the window material and the measuring efficiency is thus greatly decreased. The test gas is usually fed directly into the detector. It is important in this type of method to determine the way in which a change in the concentration of the test radioactive gas affects the characteristics of the measuring instrument. In addition, it is necessary to consider adsorption of the radioactive gas on the detector walls, which can affect the results of later measurements (i.e. the memory effect). Radioactive substances in the gas state are mostly measured using ionization chambers, Geiger-MiUller tubes and proportional counters. Emanometric methods are employed to determine the natural radioactivity of soil, mine air, water, and mineral springs, as given by the radon content. Radon contained in water is transferred to the ionization chamber by bubbling air through the water. Proportional counters are used to measure gas compounds labelled with 14C and 3H. Some gases can be dissolved directly in the liquid scintillation solution, and for high measuring efficiency, the solubility must be adequate. The gas concentration in the solvent will increase with increase concentration in the gas phase. As the temperature also strongly affects the gas solubility, it is preferable to carry out the measurement at lowered solution temperature. Most gases do not quench fluorescence, so the measuring efficiency is about 95%. Depending on whether the gas is dissolved in water or organic solvents, the scintillator is dissolved in a mixture of aromatic hydrocarbons with dioxane, or in the aromatic hydrocarbon alone with the addition of a substance to ensure good solubility of the gas. CO2 and H2 S are measured using a scintillation solution containing, e.g., phenylethylamine, ethanolamine, or alkaline hydroxide, while SO2 is analyzed using mercury tetrachloride or a mixture of H2 0 2 and H2SO4 . Nonradioactive gases can be determined mainly by two groups of 213

methods: those based on gas ionization, and radiochemical release radioreagent methods. Methods based on gas ionization depend on the fact that, (at constant temperature, pressure, and source of ionizing species), the ionization in a gas depends on its electronic structure. If a binary mixture contains gases with different electronic structures, the relative ionization current values vary with the composition of the mixture. The measurement is carried out in a flow-through ionization chamber. A suitable two-chamber system (having measuring and reference chambers) is employed in a compensating arrangement. The radiation source is an enclosed /-source, usually 63Ni, 147Pm, or, less often, 90Sr. This principle is also employed in ionization detectors for gas chromatography (Sect. 10.5.8). a-Radiators are open radiators and can be used only in radiochemical P21Po) (24 Am, laboratories with suitable equipment. Gas analyzers which work by measuring the ionization current in a mixture of two gases are employed to measure the composition of mixtures such as H 2 + N2, H2 + C0 2, H 2 + C2 H4 , N2 + C0 2 , N2 + NO, and C2 H4 + C2 H 6, or to determine the content of chlorine, ammonia or sulphur dioxide in the air. These determinations are very rapid and precise and can be used in automatic control of gas mixtures in the chemical industry. In addition, the sensitivity of the method permits its use in automatic alarms for toxic or combustible gases (CO, S02, CH 4, etc.). Radioreagent release methods are based on the chemical reaction between the test gas and a radioactively labelled reagent in the solid or liquid phase. In the reaction a radioactive component is released in an amount proportional to the amount of test gas. This principle forms the basis for a very sensitive method for the determination of oxygen dissolved in water, in which metallic thallium labelled with the radioisotope 204Tl is oxidized. 02 + 420Tl + 2H 20

420 4 T1+ + 40H

An equivalent amount of thallium ions is transferred to solution and the radioactivity of the solution is measured. Down to 10- 10% oxygen can be determined in this way. SO2 in the air can be determined by reaction with a alkaline solution of iodate labelled with the radioisotope l31I: 5S02 + 2131IO 214

-

+ 4H 2 0

131I2 + 5S042-+ 8H +

The released iodine is separated from the solution by acidification and extraction, and its activity is proportional to the SO2 content in the air sample. This reaction can be used to determine down to 10-8% sulphur dioxide. The use of radioactive kryptonates has found broad application. Here the radioactive 85 Kr is not bonded chemically, but rather crystallization of a melt of, e.g., hydroquinone, in an atmosphere of radioactive krypton forms an inclusion compound inwhich the krypton is homogeneously distributed. The analyzed substances readily disrupt the structure of the labile inclusion compounds, releasing a corresponding amount of 85Kr. The method is especially useful for the analysis of gases in a flow-through apparatus, and the concentration of the reacting component is found either from the decrease in the krypton activity or by continuous measurement of the krypton released. This method is very sensitive and permits the determination of down to 10-7% SO2 and C102, to 10-8% 03 using hydroquinone kryptonate, 10-9% 02 using kryptonated graphite, and to 10-3% H2 using kryptonated PtO2 . In conclusion, it should be pointed out that working with radiochemicals, and the use of radiochemical methods, require special safety precautions. 9.11. Preparation of mixtures of gases and vapours The methods used for the preparation of mixtures of gases and vapours are inherently less precise than those for the preparation of solutions, because of the properties of the gas state. Temperature and pressure changes must be carefully controlled; the gas cannot be weighed simply, and volumes can changeduring manipulation. Methods for the preparation of gas mixtures can be divided into static and dynamic methods. In the former, the mixture is prepared and stored in closed vessels, which limits the volume that can be prepared. In contrast, dynamic methods can be used for the preparation of any required volume. In the preparation of gas mixtures, attention must be paid to the main component, which is usually air, nitrogen or argon. This component is termed the zero gas, as it is usually used to zero the measuring apparatus. Requirements on the purity of the zero gas increase with our increasing abilities to determine ever lower amounts of trace gases. These requirements depend on the type of gas determined, the measur215

ing method, and the substances that can interfere. In some determinations, all the accompanying gases need not be removed, and the zero gas can be a mixture which models the conditions in the atmosphere. For example, the flame photometric determination of SO 2 must be carried out using a gas mixture which contains CO 2 in the same amount as the surrounding atmosphere. The zero gas is purified in several steps: (1) removal of solid particles, (2) drying, (3) removal of unwanted substances by oxidation or some other suitable reaction, (4) adsorption of the reaction products. It is essential in the preparation of a standard gas mixture that all the components be completely mixed to form a homogeneous mixture. The mixing time in static methods depends on the size and shape of the vessel, the diffusion characteristics of the components, and the turbulence during mixing. It takes a long time (weeks to months) for mixtures to become homogeneous through diffusion alone. Turning the vessel over reduces this time to several minutes. The mixing is accelerated if steel or glass rods are placed in the vessel; glass beads or aluminium foil can also be used. Another method is based on alternately heating and cooling one part of the vessel with hot and cold water, producing flow of the mixture. A mechanical or magnetic stirrer is mostly used in exponential diluters. Complete mixing is also essential in dynamic methods, where it is especially important that laminar flow does not occur. It has been found for mixtures with Reynolds numbers greater than 2100 that the mixing is sufficient at a distance equal to ten times the tube diameter. Complete mixing can also be attained by combining two perpendicular gas streams. The method of storing gas mixtures is also important, especially when long-term storage is required. The composition must be stable over long times at the given temperature and pressure. Chemical changes and adsorption processes that might occur can be avoided either by preconditioning the vessels and apparatus, or by special treatment of the walls of the storage bottle, usually with a layer of aluminium or PTFE. 9.11.1 STATIC METHODS

Static methods are based on the transfer of a known sample volume or mass to a vessel of known volume. This is carried out using various types of bottles, plastic bags, or pressure vessels. The gravimetric method is the most precise; the substance is transferred to a preweighed, dry, 216

clean vessel which is again weighed with the required precision. To prevent adsorption on the vessel walls, it must be preconditioned. A method for preparing mixtures at high pressures is based on the principle of partial pressures in a static system. Assuming ideal gas behaviour, the volume concentration of a component in the mixture would be proportional to its partial pressure. However, because most gases do not behave ideally at high pressures, a correction must be made for their compressibility. The method of partial pressures is not very accurate and errors vary from 5 to 20%, depending on the concentration. In exponential (logarithmic) dilution (Fig. 9.35), the static sample preparation method is combined with continuous sampling. The test mixture is prepared by the static method in a large vessel, from which it is carried out by a constant stream of the zero gas. The concentrations of the test substances in the diluter vessel decrease exponentially with time, and the actual concentration can be calculated from the relationship c=

+

ce

(9.100)

t/V

where c is the initial concentration in the diluter (of volume V), c is the actual concentration at time t, and v and vl are the volume flow-rates of the zero and dilution gases. This method is often employed to calibrate gas chromatographic detectors and continuous analyzers. It is very useful and precise, but can be used for only a limited number of substances and for binary mixtures.

sample chamber

flow meter

gas

gas

Fig. 9.35. Exponential diluter.

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9.11.2 DYNAMIC METHODS

Dynamic methods for the preparation of standard mixtures of gases and vapours have a number of advantages. In contrast to static methods, they can be used to prepare mixtures of any substances, including reactive components, to yield a continuous gas mixture stream. Adsorption factors can be practically neglected, as equilibrium is established in a dynamic system between the surfaces of the walls and the gas stream. One of the great advantages of dynamic methods is that they can be used to prepare gas mixtures having very low component concentrations (down to the ppb range). A number of methods are based on the dynamic preparation of gas mixtures, of which permeation and diffusion are especially useful both under laboratory conditions and in the field. The basic dynamic method involves mixing two or more gases flowing at a known constant velocity. Fig. 9.36 depicts the basic scheme for multi-stage dilution. It is essential that the flow-rates be precisely maintained and that the introduction of the components into the main gas stream be carried out under constant conditions. This method is often used in combination with permeation and diffusion systems. In the injection method, gases and vapours are introduced into the gas stream using various types of injection equipment, such as injection pumps, or motor-driven injection syringes. The preparation of a standard mixture with a constant, known concentration depends on reproducible, regular, component addition. A number of injection systems have been designed for various purposes. One of the most commonly employed systems, especially for the preparation of low concentrations, utilizes diffusion through a plastic tube wall which is permeable for the test substance present in a liquid phase. The method is basically a membrane separation process, whose )er lower concentration

Fig. 9.36. Scheme of two-stage gas mixing.

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driving force results from the concentration difference on the opposite sides of the tube walls, at which a liquid-vapour equilibrium exists. Consequently, the temperature in this equipment must be maintained constant ( 0.1 ° C). At constant temperature, the amount of permeated gas is directly proportional to the membrane's surface area, and inversely proportional to its thickness. Suitable choice of the material, the thickness of the tube wall, and the length and diameter of the tube permits transfer of the test substance over a relatively wide concentration range. The amount of substance leaving the permeation tube per time unit is found by weighing. The permeating substance can be diluted by a stream of the zero gas to the required concentration. Permeation tubes are usually made of PTFE or polyethylene. There are various designs (Fig. 9.37) and a number are marketed commercially. Diffusion apparatus works on a similar principle to permeation tubes. Here, the substance diffuses through a glass capillary which separates the storage bottle, containing the liquified test substance, from the tube through which the zero gas flows.Suitable choice of the diameter and length of the capillary permits the preparation of mixtures with contents of 0.1-100 ppm. This equipment is also useful for substances with low vapour pressure at normal temperatures. Fig. 9.38 depicts a basic diffusion apparatus design. A number of standard mixtures can also be prepared by electrochemical generation of the required component. The amount of substance generated is given by Faraday's law and can be varied over a wide range by adjusting the current. Electrochemical generation is used most often

10 - 30 cm

liquid sample 1,

sample

PTFE

tube

storage bottle

r- mixture

stainless steel le

thermostat

| Is;

m~~~~

I

IX

permeation membrane

zero gas ampoule Fig. 9.37. Permeation apparatus.

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Fig. 9.38. Diffusion evaporator.

to prepare mixtures with hydrogen or oxygen and can also be employed for a number of other substances such as 03, C0 2, CO, C12, 12, H2S, and nitrogen oxides. However, electrolytic methods have a number of practical limitations resulting from the nonlinear dependence of the yield of substance on the current, and from changes in composition resulting from vaporization. Reactive, dangerous, or highly corrosive components can be prepared by chemical reactions. This method is employed for the preparation of a number of organic substances, such as vinyl chloride, acrolein, and acrylonitrile, and inorganic gases. An example is the preparation of a mixture of air and a low concentration of ozone, using an ultraviolet discharge lamp fitted with an adjustable shield which permits variation of the ozone concentration. The amount of ozone produced is so reproducible that this method is used to calibrate analyzers of ozone and nitrogen oxides. The following reaction is utilized, NO + O3 = NO2 + 02 which is very fast. The reaction is quantitative, with an equilibrium constant of about 10 7 so that the concentration of two components can be determined when that of the third component (NO, NO 2 or 03) is known. This method is termed titration in the gas phase. It follows that standard gas mixtures can be prepared by a number of methods. None is universal and the preparation of a standard mixture is never simple. As the requirements on the determination of ever smaller amounts of gases increase, such as the need to determine pollutants in 220

the air, suitable instrumentation must be designed and procedures developed for the preparation of standard mixtures containing materials in very low concentrations. The development of simpler calibration techniques for these low concentrations, for work in the field, requires consideration of the stabilities of these mixtures.

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