Mechanism of atomization at constant temperature in capacitive discharge graphite furnace atomic absorption spectrometry

S~fbochimkuActa.Vol. 36B.No. 5.p~. 427 ta438.1981. PtintedinGreat Britain.

Mechadsm

of atomization at

dishuge

graphite

furnace

0031-6987/81/0SO427-12SO2.00/0 Q 1981PcrgamonRessLtd.

constant atomic

temperature absorption

C. L. CHAKRABARTI,* C. C. WAN, R. J. TEXEY, H. A. HAMED and P. C. BERTEL~ Department

in capacitive

spectrometry S.

B. CHANG,

of Chemistry, Carleton University, Ottawa, Ontario KlS 5B6, Canada (Receiued 14 January 1981)

W-At constant temperature (isothermal) maintained throughout in the capacitive discharge technique, the measured absorbance’ at any time t due to concentration of analyte atoms can be given by: absorbance = p[AL{k,/(k, - k&exp (-k,t) -exp (-k,t)], where p is a function of the oscillator strength (a constant) and the efficiency with which the analyte atoms are produced, [Al, is the initial concentration of the analyte atoms, kl and k, are first-order rate constants for formation and decay of analyte atoms, respectively. This technique yields k, B k, and k, r >>k2t; and so the above equation reduces to: absorbance ap[AL, resulting in large enhancement in sensitivity. In the case of lead, the immediate precursor of the gaseous lead monomer is the gaseous lead diier, which is partly lost by diffusion of the lead dimer with a first-order rate constant, k,. The kinetic parameters k,, k, and k, have been evaluated, and the values of k, at diierent temperatures used to draw the Arrhenius plots, from which activation energies of the ratedetermining steps have been determined. The activation energies have been used to elucidate atomization mechanisms by extensive correlation of the experimental energy values with the literature values.

1. INTRODUCTION THE FORMATION of analyte atoms in graphite furnace atomizers has been discussed by

many workers [l-16]. In one popular hypothesis for atomization, the metal oxide is reduced, by the carbon of the furnace, to the free metal. CAMPBELL and OTTAWAY [l] have assumed that the reduction process is rapid and have correlated the appearance temperature with the temperature at which reduction of analyte oxides with solid carbon becomes thermodynamically favourable (AGfetiO,, 5 0). They applied this theory to 27 elements, and found agreement between these theoretically predicted temperatures and the experimentally observed temperatures for all but a few elements. STURGEON,CHAKRABAFUI and LANGFORD [2] have studied the mechanism of atom formation in a graphite furnace by using a combined thermodynamic and kinetic approach. They assumed that a condensed phase-gas-phase equilibrium for an analyte exists within the furnace and the production of observable atoms is characterized by a first-order rate constant, and a plot of the logarithm of the absorbance as a function of the inverse of the absolute temperature in the early part of the absorbance signal yields a straight line from which the activation energy, E,, can be obtained. However, these * Author to whom correspondence

should be addressed.

[l] W. C. CAMPBELLand J. M. (SITAWAY, T&n@ 21, 837 (1974). and C. H. LANGFORD, Anal. Chem. 48, 1792 (1976). [2] R. E. STURGEDN, C. L. WARTI 133 C. W. FULLER, Analyst 99, 739 (1974). [4] C. W. FULLER, Analyst 100,229 (1975). [5] C. W. FULLER, Proc. Anal. Diu. Chem. Sac. 13, 273 (1976). [6] C. W. PULLER, Analyst 101,798 (1976). [7] R. E. STURGEON and C. L. CX+NRABAR~, Anal. Chem. 49, 1100 (1977). [8] R. E. -GEON and C. L. CHAKRABAR~, Rag. Anal. Atom. Spectrosc. 1,1 (1978). [9] C. L. CHAKRABARTI,H. A. I-L+MED,C. C. WAN, W. C. LI, P. C. BERTELS,D. C. GREGO~REand S. LEE, Anal. Chem. 52, 167 (1980). [lo] c. L. WARTI, C. C. WAN, H. A. HAMED and P. C. BERTF?.LS. Can. Res. 13, 31 (1980). [ll] c. L. CHAKRAEIAR~,C. C. WAN, H. A. HAMED and P. C. BERTELS,Anal. Chem. 53, 444 (1981). C. C. WAN, H. A. HAMED and P. C. BERTELS,Nature 288, 246 (1980). Cl21 c. L. WARTI, [13] B. SMETS,Spectrochim. Acta 35B, 33 (1980). [14] B. V. L’vov, Proceedings of the Second International Atomic Absorption Conference, Sheffield, U.K. (1969). [15] W. M. G. T. VAN DEN BROEK and L. DE GALAN, Anal. Chem. 49, 2176 (1977). [16] B. V. L’vov, Atomic Absorption Spectrachemical Analysis. Adam Hilger Ltd., London (1970). 427

428

c.

L. CHAKRAFMRTI

et al.

approaches do not give any indication of absolute rates of analyte atom formation and consequently they cannot predict absorbance pulse shapes. Also, the model of atomization on which the above treatment has been based describes atomization in commercial graphite tube atomizers in which introduction of a sample into the analytical volume occurs by a process of accelerated vaporization of the sample due to the evaporation surface temperature increasing linearly with time. This has required the atomization time, or, to be defined by the following integral [5,8, 14, 161:

where ql(t) is the number of analyte atoms entering the analytical volume in unit time, and No is the number of analyte atoms in the sample. However, such a definition of r1 leaves much to be desired, since r1 so defined is not a characteristic time for the system-it is the time from the appearance time (i.e. the time at which the absorbance signal becomes barely detectable) to the time at which the signal reaches its peak [5,8, 14,161. FULLER[3-61 has described a kinetic approach to the atomization process. As an example, he has investigated the time-absorbance profiles at different temperatures, and has derived the rate equations that describe the variation of the amount of copper atoms in the furnace as a function of time. He has determined from the Arrhenius plot that the activation energy is 37 kcal mol-l, which reflects, as a probable mechanism, a slow first-order reaction involving reduction of copper oxide by carbon, followed by rapid vaporization of the copper atoms. The commercial electrothermal graphite tube atomizers have relatively low rates of heating and they are non-isothermal in time and along the length of the graphite tube, resulting in condensation of the analyte vapour at the cooler ends of the graphite tube and its subsequent re-evaporation producing unpredictable and erroneous results [2,8]. This paper describes the results of the capacitive discharge technique (CDT) with an anisotropic pyrolytic graphite tube atomizer. The technique allows for very much faster heating rates and provides an isothermal environment throughout the duration of atomization. Because the absorbance signal profile is almost entirely in the isothermal region, a purely kinetic treatment of the absorption pulse is possible. The use of an anisotropic pyrolytic graphite tube, which has high thermal conductivity in the adirection (in the direction along the graphite tube length) [9] promotes rapid distribution of heat uniformly along the graphite tube length. Since the atomization time in the CDT is much shorter than that in the conventional graphite furnace atomic absorption spectrometric technique, and since the atomization reactions occur either at the graphite surface or immediately after the analytes leave the graphite surface and have the surface temperature as they enter the gas phase, the analyte atomic vapour is assumed to have the surface temperature. It is therefore both important and reasonable to assume that the analyte atomic vapour temperature is equal to that of the graphite surface. Deviations from thermal equilibrium will cause large errors in the determination of rate constants and activation energies, particularly when activation energies of the order of 100 kcal mol-’ are involved. The characteristics of the transient signals are largely determined by kinetic parameters (rates of formation and loss of atoms). Hence, it is interesting to determine the kinetic parameters and establish the relationship of energy values that arise from those kinetic parameters to the nature of the atomization processes. This paper attempts to provide some direct evidences as to the nature of the major atomization processes for two elements (cadmium and lead) in an open-ended tube atomizer made of anisotropic pyrolytic graphite [9-121. 2.

THEORY

Previous workers [2,3,8, 13-161 have found that atom formation in graphite-furnace atomic absorption spectrometry may be described by a first-order rate process.

429

Mechanism of atomization at constant temperature

STURGEONet al. [2,8] have proposed four basic mechanism categories formation in the commercial, semi-enclosed, tube-type graphite atomizers. (1) Reduction of solid oxide by graphite surface; r------- _______________-__-_ reduction by C ,

MO(s) (2) Thermal decomposition

I&(I)

&M,(g) -

-

for atom

&p,

of solid oxide: MO(s) + M(g) + %-Mg)

(3) Dissociation

of oxide vapour:

O(g) MO@

MO(s) (4) Dissociation

+ M(g)

of halide vapour: M&(s)

-

M&(l) -

Mx(g) + X(g)

M(g)

X(g)

The mechanisms of loss of atomic vapour from a commerical semi-enclosed graphite tube atomizer have also been studied by STURGEON and CHAKRABAR~ [7]. They proposed four factors that may be looked upon as contributors to the loss of atomic vapour from the graphite tube atomizer: expulsion, diffusion, convection and chemical loss (loss due to formation of refractory compounds by analytes with other substances present in the atomizers)-the major factor contributing to loss of atomic vapour is diffusion to the cooler ends of the graphite tube where condensation occurs. This can be described as a first-order rate process. Consecutive first-order reactions that occur in an anisotropic pyrolytic graphite tube atomizer may be described by the following model:

where [A] represents the concentration of the pre-atomization analyte species; represents the concentration of the absorbing analyte atomic vapour formed; represents the concentration of the analyte atomic vapour that is lost from analytical volume; k, and k, are then identified as the first-order rate constants atom formation and loss, respectively. At all times the concentrations are related

[Al,+ [Bit+ [Cl,= [Alo where the subscripts t and 0 represent the time and the initial concentration, tively. The above model yields the differential equations (3) and (5).

[B] [C] the for by

(2) respec-

d[Al - = -k,[A]. dt

By solving equation

(3) one gets equation (4):

[Al = [Aloew C-k t> dCB1 - = k,[A] - k,[B]. dt

(4) (5)

In the limit, [A] tends to zero, which is identified with the exhaustion of the supply of the pre-atomization species A. At this point, equation (5) simplifies to:

4Bl - = - k,[B]. dt

(6)

430

C. L.

CHAKRAESARTI et at.

Since absorbance is proportional to the concentration of the absorbing species, B, the rate constant for atom loss, kt, can be determined from this part of the absorbance signal. A plot of the logarithm of absorbance vs time should be linear, yielding the rate constant k2 from the slope. Extrapolation of this line to the beginning of the absorption pulse would give the concentration of B necessary to produce the decay of the signal by diffusion process alone. However, equation (5) shows that the rate of formation of B is equal to the difference between the rate of conversion of species A into species B and the rate of loss of species B by diffusion. The difference between the extrapolated absorbance and the experimental absorbance at any time t is related to the concentration of the pre-atomization species A. Accordingly, equation (3) suggests that a plot of the natural logarithm of this difference vs time should be linear, with a slope equal to the rate constant for atom formation kl. If the kinetic parameters are evaluated, the shape of the absorption pulse may then be determined by solving equation (5). The use of the solution of equation (3) with the initial concentration of the species A as [A&, and with no B present initially, gives the following solution to equation (5): [B-j

-

[Al,k?(e-%*

_e-k,*)

‘--k,-k,

f

where [B], represents [B] at time t. [B], can be related to the measured absorbance by using a pre-exponential Absorbance = w

(eekzt - edkIt), 1

factor p: (8)

2

where p is a function of oscillator strength (a instant) of the atomic line and the efficiency with which the anaiyte atoms are produced. The efficiency with which the analyte atoms are produced is determined by the nature of the analyte species and the atomization temperature. The efficiency of atomization can be increased by forming the analyte species that is readily vaporized and atomized, and by use of high atomization temperature, since the atomization reactions are highly endothermic. The concentration of the pre-atom~ation species A decreases from the start of the atomization. The concentration of B, which is initially zero, at first increases, reaches a maximum when d[B]/dt is zero, and thereafter decreases exponentially with respect to time. When d[B]/dt is zero, the system is said to have reached a stationary state. At that instant and thereafter, we see from equations (5) and (4) that [B] = $ [A] = [A& $ exp (-k,t) 2

2

or [B] = kl

(10)

[Al kit’

Thus the con~ntrations of A and B both diminish e~nentially with respect to time while maintaining a constant ratio. On differentiating equation (7) we obtain the following expression for the time t,,, required for the attainment of the stationary state: kI exp (-k,t,,,)

= k2 exp (-k,t,,)

(11)

or 1

tmm=RlnG.

k,

The time tmaxis identified with the time required to attain the absorbance The maximum concentration of B is seen to be:

EL,,,, = IAl0expC-k2hd.

O-3

maximum. (13)

Mechanism of atomization at constant temperature

431

It can be seen from equation 13 that [I%],=, =[A$, when kjlfmax<<1, i.e., for the highest sensitivity both k2 and tmaxmust be made as small as possible. The time tmaxis sensitive to both the heating rate and the temperature (i~the~~); generally, higher heating rates and higher temperatures yield smaller t,. However, the rate constant k2 for di~ion~ loss increases with higher temperature, ~though kZ is less sensitive to higher temperatures than k, because the diffusion coefficient is less strongly dependent on the temperat~e [16, pp. 287-2881. This technique yields kl >>kz, and hence, with the time t of the order of 40-100 ms, yields k,t >>k,t. Equation (8) is then reduced to: absorbance ==p[AJO,which results in large enhancement in the sensitivity [Q], for example, 27-fold enhancement for the Cu 324.7 nm line. Also, this technique is free from matrix interferences [10-121. 3. &PERIMENrAL 3.1. Apparatus. The details of the apparatus and accessories and their operation have been described in a previous paper [9] from this laboratory. 3.2. reagent. Stocksolutions of lead and cadmium were prepared separately by dissolving the appropriate mass of pure metals (99.9% pure) in UL,TRBX nitric acid (Baker Chemical Co.) and the solutions made up to 1000 pg ml-t with ultrapure water of resistivity 18.3 MIl cm obtained direct from a Milli-Q2 water purification system (Millipore Corporation). All test solutions were prepared by serial dilution of the above stock solutions with nltrapure water immediately prior to determination. 3.3. Procedure. Sample solutions (5.0~ low6 dm3) were injected into the atomizer by means of an Eppendorf syringe fitted with disposable plastic tips. The sequence of steps in the CDT heating program has been described in an earlier paper [9] from this laboratory. The atomizer temperature was set by adjusting the voltage of the temperature-control unit. The electrical energy from the capacitor bank was used for extremly fast heating of the atomizer to its maximum temperature; the atomization stage of the temperature control unit was used to maintain the temperature of the atomizer constant at some pre-selected value. Absorption and temperature profiles were recorded with a model 549 storage oscilloscope (Techtronix Inc.) fitted with a type lA7A hip-gain d~erenti~ plug-in. The absorbance signal traces were photo~aphed with a Polaroid camera (Techtronlx Inc.),

4. RESULTSand DISCUSSION In this study, cadmium and lead systems were chosen for the follow~g reasons. These systems can be investigated using relatively low atomization temperatures (1840-2540 K); these elements are unlikely to form carbides in a graphite atomizer; as used, in the nitrate form, the most stable species of these elements at the charring temperatures used are the solid oxides of these elements as will be explained later; and finally, this technique (CDT) has provided an opportunity to compare the atomisation mechanisms for these important elements using isothermal atomization at very high heating rates with those proposed by STURGEON et al. [Z, 81 for the commercial graphite tube atomizers in which the temperature increases linearly with time. 4.1 Cadmium Fig. 1 shows oscilloscopic traces of the surface temperature of the graphite tube and the absorbance signal from 5.0 x 10-l” kg of Cd (taken as cadmium nitrate in an aqueous solution) given by the Cd 228.8 nm line. It can be seen that the absorption pulse is located almost 90% within the isothermal region. In Fig. 2, the absorbance signal vs time was drawn using a logarithmic scale for the ordinate. The rate constant for cadmium atom loss ka was obtained from the slope of line B, which was drawn from the data from the tail of the experimental trace. The value of the slope of line B was calculated by least-squares linear regression involving the last few points on the decay part of the absorbance signal. The points of line A represent the ‘concentration’ of the pre-atom~ation species. Values are included only for those times at which the isothermal condition can be assumed from the temperature trace of Fig. 1. These data show a very good linear fit; hence, the rate constant k1 for the cadmium atom formation was calculated using least-squares linear regression over all of these points (line A).

432

C. L. CHAKRAESARTI et al.

Fig. 1. Oscilloscopic traces for cadmium atomized at a heating rate of 40 k rnssr and isothermal temperature of 1840 K. Cd A = 228.8 nm. The top trace is for 5.0 x lo-r4 kg of Cd (taken as nitrate in an aqueous solution). The middle trace is for the graphite surface temperature. The bottom trace is for ultrapure water. Vertical scale: 0.2 absorbance/scale division (for top trace). Horizontal scale: 50 mslscale division.

Fig. 3 compares the experimental absorbance-time signal with the theoretical mass of gaseous cadmium atoms that was calculated using equation (7). The ratio of these two curves is the p-factor of equation (g), which has dimensions of [absorbance masssl]. The agreement between the two curves is excellent, suggesting that the model of atomization described earlier represents correctly the physico-chemical processes involved in the atomization. Table 1 contains the rate constants, k, and kZ, for cadmium, determined at various temperatures from 1840 to 2220 K. Precision values are not shown since values of precision from least-squares regression calculations depend heavily on the number of points included, whereas the value of the rate constant itself does not. However, the

Fig. 2. Plots of absorbance (logarithmic scale) vs time (linear scale) for cadmium shown in Fig. 1. Curve A: cadmium atom formation, d[Cd(l)]/dt = -k,[Cd(l)]; slope = -k,. Curve B: cadmium atom loss, d[Cd(g)]/d t = - k,[Cd(g)]; slope = -k,.

433

Mechanismof atomization at constant temperature

^_^

0

I

I 50

I 100

I

I I50 Tm,

*Cc

I

I

250

303

ms

Fig. 3. Comparison of the absorbance-time profile for the atomization of cadmium obtained experimentally with the mass-time profile calculated using equation (7). O-measured absorbance of Cd(g), taken Cd 5.0 x lo-l4 kg (as nitrate) in an aqueous solution; A-calculated mass of Cd(g).

precision of any rate constant value can be no better than 10% R.S.D., as the absorbance values used in k, calculations have this order of relative precision. Fig. 4 shows the Arrhenius plot, the natural logarithm of the rate constant vs the reciprocal of the absolute temperature, drawn with the data of Table 1. The step yielding the absorbing cadmium vapour has an E, of 74 f 10 kJ mol-‘, as determined from the slope of this plot. The error in E, was calculated from the correlation coefficient obtained from the least-squares linear regression. 4.2 Lead Fig. 5 shows an oscilloscopic trace of the surface temperature superimposed on the atomic absorbance signal for 5.0 X lo-l3 kg of lead (taken as the nitrate in an aqueous solution) given by the 283.3 nm line. Again, over 90% of the signal is in the isothermal region. As with cadmium, the absorbance by lead was plotted vs time, using a logarithmic scale for the ordinate, as shown m Fig. 6. The tail part of this plot yields the rate constant kz for the loss of gaseous lead atoms. However, the difference between the extrapolated absorbance and the experimental absorbance vs time, plotted on the same axes, shows two intersecting straight lines of different slope. This corresponds to two distinct modes of loss of the pre-atomization species A. The straight line corresponding to earlier times and having the lower absolute slope, gives the value of the rate constant

Table 1. Rate constants for cadmium Rate constants (s-l) Temuerature 1840 1970 2120 2220

15 23 27 37

5.9 9.5 16 16

434

c.

L.

-ART1

et d.

Fig. 4. The Arrhenius plot for cadmium taken as nitrate dissolved in ultrapure water.

k, for the reaction: A&B. The straight line corresponding to later times and having the slightly steeper slope yields the sum of the rate constants for the two modes of decrease of the pre-atomization species A as shown below: AABk2.C k.

c

C' where C’ is the product of the other loss process of species A. Any A taking the path indicated by the arrow marked k, will not eventually yield an atomic absorption signal. The mathematical treatment adopted in the case of lead is admittedly a simplified treatment of a more complex process, but has the merit of showing the correct temperature dependence of the rate constants. However, where two straight-line segments are seen (as for lead) a more rigorous mathematical treatment is necessary if

Fig. 5. Oscilloscopic traces for lead atomized at a heating rate of 40 K ms-’ and a temperature of 2300 K. Pb A = 283.3 nm. The left trace is for the graphite surface temperature. The right trace is for 5.0~ lo-r3 kg of Pb (taken as nitrate in an aqueous solution). The bottom trace is for ultrapure water. Vertical scale-O.1 absorbance/scale division (for right and bottom traces; horizontal scale-50 ms/scale division.

435

Mechanism of atomization at constant temperature

\

\

\

\

A

\

‘\ \ \\ 00

0

\\ OOoo o o\

0

0

,c

B

0

\ \

0011

I loo

0

I 200

Time,

L 300

ms

Fig. 6. Plots of absorbance (logarithmic scale) vs time (linear scale) for lead shown in Fig. 5. Curve A: lead atom formation, d[Pb,(g)]/dt = -kJPb,(g)]; slope = -k,. Curve B: lead atom formation and loss of lead as lead dimer, d[Pb,(g)]/dt = -(k, + k,)[Pb,(g)]; slope - -(k, + k,) Curve C: loss of lead as monatomic lead, d[Pb(g)J/dt = - kJPb(g)]; slope = -k,.

the mechanism is as shown; the slower must be treated like B above, then the faster extracted from the differences. Table 2 shows the kinetic parameters kl, k2 and k, determined at various temperatures from 2050 to 2540 K. As expected for the highly endothermic reactions involved, the rate constant for atom formation kl increases rapidly with the increasing temperature, compared with the slower increases of both the rate constant k, for the loss of Pb monomer, and the rate constant k, for the loss of Pbz dimer. The values of the rate constants k2 and k, for the loss of Pb monomer and Pbz dimer, respectively, are similar in magnitude-this is to be expected if the loss of both species is solely by a first-order difisional process. The diffusion coefficients of Pb and Pbz depend only to a small extent on the mass of the diffusing species according to the equation given by L’vov [16]. The activation energy for Pb, determined in the same manner as in the case of cadmium, was 125 f 7 kJ mol-‘. The Arrhenius plot for lead is shown in Fig. 7. The kl values are inversely proportional to the time for the reaction involved; hence, this time is a characteristic time for the system, unlike the 71 value of the earlier model for atomization [5,8,14,16]. For example, the half-life, tllZ, for any first-order reaction is related to kl value by the equation: t,,* = 0.693/k1. Hence, the time derived from the kl value for a first-order reaction is a characteristic time-this is an important contribution of the model for atomization presented in this paper. Table 2. Rate constants for lead Rate Constants (s-l) Temperature (K)

k,

k,

k,

2050 2120 2300 2420 2540

12 17 25 39 52

11 12 15 15 17

10 12 11 15 16

C. L. CHAKRABARnet al.

436

IO4

K/T

Fig. 7. The Arrhenius plot for lead taken as nitrate dissolved in ultrapure water.

4.3 Mechanisms

In the case of cadmium, CdO(s) is formed by the decomposition of Cd(NO& at the charring stage. It has been found from thermodynamic calculation [17,18], that the carbon reduction of CdO(s) to Cd is not favourable (AG>O) at the appearance temperature of Cd. AGGEXTand SPROTT[19] have also shown that there is no signifiaint difference in the atomization behaviour of cadmium between carbon and tantalum atomizers. Hence, the vapour-phase cadmium atoms may be accounted for only by thermal decomposition of the oxide, with subsequent production of the gaseous cadmium atoms by vaporization of liquid cadmium as follows: +0,(g) / CdO(s) \

~!W??_%J_?~!z~ Cd(l) 7

cd(g) k,

OUT

In the case of lead, PbO(s) is formed at the charring temperature as a product of either decomposition or hydrolysis of lead compounds. Thermodynamic calculation [S] shows that reduction of PbO to Pb by carbon at the appearance temperature of lead (1040 K) is thermodynamically favourable. STURGEONet al. [2,8], SEDYKHet al. [20], and others [21,22] have shown that liquid lead is vaporized to either the monatomic or the diatomic gaseous lead species. Although STURGEONet al. [2,8] have observed two distinct values of activation energies for lead, the present authors have found only one, 125 *7 kJ mol-l, over the range 2050-2520 K. The diatomic lead vapour can account for the alternative mode of loss of the pre-atomization species A (the reaction with rate [17] I. BARIN and 0. KNACKE, Thermochemical Properties of Inorganic Substances. Springer, New York (1973). [18] I. BARIN, 0. KNACKEand 0. KUBASCHEWSIU, Thermochemical Properties of Inorganic Substances (Supplement), Springer, New York (1977). [19] J. AGGEXTand A. J. SPROT~,Anal. Chim. Acta 72, 49 (1974). [20] E. M. SEDYKH,Yu. I. BELYAEVand P. I. OZHEGOV,Zh. Anal. Khim. 34, 1984 (1979). [21] K. A. GINGERICH, D. L. COCKEand F. J. MILLER,Chem. Phys. 64, 4027 (1976). [22] R. E. HONIG,J. Chem. Phys. 21, 573 (1953).

431

Mechanism of atomization at constant temperature

constant k3) via diffusion out of the open ends of the graphite tube. This is consistent with the following mechanism: AH+=125+7Wmol-' r_________________~

PbO(s) C

Pb(1) -

&bb,(g) 7

+b(g) 7

OUT

k. I OUT The species left by Cd(N03)* and Pb(NO& on termal decomposition in the graphite atomizer below their appearance temperatures (720 K for Cd and 1040 K for Pb [2,8n have been shown above as CdO(s) and PbO(s), respectively, on the following grounds. The partial pressure of CO molecules which ultimately determines the partial pressure of free atomic oxygen in the graphite tube atomizer depends on the temperature. Also, the reaction C + 0 + CO becomes thermodynamically more favourable than the competing reaction M + 0 + MO (where C, M and 0 represent carbon, analyte metal and oxygen, respectively) only at relatively high temperatures-the higher the temperature, the more favourable the former reaction; the reaction M+O * MO becomes increasingly less favourable (thermodynamically) with increasing temperature [23]. Hence, the species CdO(s) and PbO(s) can and do exist at relatively low temperatures (
C. L.

438

CHAKRABARTI

et al.

Table 3. AHe for metal sublimation, carbon reduction of the oxide and dissociation of the oxide compared with the experimental activation energy AH’ (kJ mot-‘) 1291

Element

M(s) -+ M(g)

M(l) --, M(g)

MO(s)+C+ M(g) + CO

MO(g)+ M(g) + G(g)

Cd Pb

106 183

99 178

251 291

<368 378

&M,(g) + M(g)

Experimental E, (W mol-‘)

5.7 118 [2211

74*10 125rt7

wavelength of lead analysis line (283.3 nm) suggests the absence of any interfering molecular species of lead, the mechanisms of atomization proposed earlier seem reasonable. Table 3 presents the literature values of AhHe for various possible reactions from mechanism categories I-III. Because the reactions are highly endothermic it is reasonable to treat E, = AH’. It can be readily seen that the experimenta E, values agree with the literature AH* values for the atomization mechanisms proposed earlier. 4.4 Absorbance

maximum

The time required for attaining the absorbance maximum of cadmium and lead are: for cadmium:

tmax,od=

In k,-ln k2 k _k 1

tmax,Pb =

for lead:

2

In ( kl + kJ - In k2 kl+k3-k2

.

Table 4 presents values of t,, both calculated, as above, and measured from the oscilloscopic traces; the agreement between them is good for Cd but not so good for Pb. The lack of good agreement for Pb is due to the equation for fmaX,rbbeing an approximation (as explained earlier). The equation gives undue weight to kJ, making the loss factor larger than it really is; hence, for lead, the calculated tmaXat both temperatures is shorter than the measured t,,,,,. However, the agreement for Cd and Pb, in general, is close enough to indicate that the model for atomi~tion presented in this paper correctly represents the physic-chemica1 principles involved in the atomization. The results of Fig. 3 lend further support to this conclusion. Table 4. Time to reach the absorption pulse peak

t,, (ms) EIement

‘I’(R)

Calculated

Observed

Cd Cd Pb Pb

1840 1970 2050 2300

103 65 63 42

110 70 95 65

One of the sig~ficant features of this model for atomization is that it has done away with the empirical atomization time 71 of the earlier model [5,8,14,163 and replaced it with the rate constant k, which is inversely proportional to the characteristic time for the system. The new model, with the empiricism removed, is not only more capable of predicting correctly the shape of the absorption pulse, but also provides better knowledge of atomization mechanisms. Acknowledgements-The authors thank Dr. C. H. LANGFORD, Dr. D. R. WILES, and Dr. P. KRLJUSfor helpful discussions and suggestions. R.J.T. thanks the Natural Sciences and Engineering Research Council of Canada for a summer undergraduate research fellowship. H.A.H. thanks the Government of Iraq for a postgraduate scholarship. This research was supported by grants from the Natural Sciences and Engineering Research Council of Canada. [29] R. C.

WEAST (Editor), ~affdboQ~ of C~~~s~

and Physics, 60th edition. C.R.C. Press (1980).