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The oxidation of aqueous sodium sulphite solutions
Chemical Engineering Science, 1966, Vol. 21, pp. 559-572.
Pergamon Press Ltd., Oxford.
Printed in Great Britain.
The oxidation of aqueous sodium sulphite solutions K. J. A. DE WAAL and J. C. OKESON Laboratorium
voor Fysische Technologie, Technische Hogeschool, Delft, The Netherlands
Abstract-A method is suggested for the determination of the interfacial area between a gas and a liquid and of the surface renewal rate of this interface. This method is based upon the oxidation of a concentrated aqueous sulphite solution with gaseous oxygen in the presence of cobaltous sulphate as a catalyst. The oxidation reaction is first-order and the reaction velocity constant can be varied between 50-10,000 set-1 by changing the catalyst concentration, thepn or the temperature. The energy of activation has been determined. The influence of some impurities and of some materials of construction has been investigated. The behaviour of copper as a catalyst is irregular; hence copper cannot be applied when the reaction is used for the determination of the contact area. Finally, some examples are given of the application of this method.
1. INTRODUCTION THE AIM of this investigation was to develop a method for the determination of the interfacial area between gas and liquid phases and the surface renewal rate of this interface. Gas absorption accompanied by a rather rapid chemical reaction is one possible technique. Consider for instance a gas A which dissolves in a liquid and then undergoes a first-order reaction with one of the liquid components. The penetration theory, based on stationary mass transfer perpendicular to the interface, yields the following equation :
2A 22, -$ = D, 2
“‘
-
krcA
,
with the initial and boundary conditions: t=o,
x20
:c*=o
t > 0,
x =o
: c, = c,*
t>o,
x=(x):c,=o
The mass flux of A at the interface will become ( DANCKWERTS [I]) : WAA
x=0
=
c: J[k,O,l( erfdCk,tl+ &)
time and then disappear into the bulk of the liquid. To describe this phenomenon, several models have been suggested. The models of WHITMAN [2] (filmmodel), HIGBIE [3] (all surface elements have the same age) and DANCKWERTS [4] (random surface renewal) are the best known. Although they differ in mathematical formulation, these models all give the same numerical results if proper values of the parameters (thickness of diffusion layer, mean contact time or surface renewal rate) are chosen [5-71. The description of the absorption process with any of them seems to be adequate. The surface renewal model of DANCKWERTS [4] proposes the following surface age distribution function : Assume a surface of which the age distribution (or the probability that the age of a surface element lies between t and t + dt) is represented by $(t)dt$ The fraction S, that is renewed per unit time is independent of the age of the surface elements. This leads to: $(t) = se-” (3) Combination of (2) and (3) gives: Q9,, = c,* *A- xkk, + s)D,l
(4)
so I
kt = ,/C(k, + W,l.
(*)
Generally, the liquid is in motion. Eddies are generated, come to the surface, remain there some t Present address: Mare Island Naval Ship Yard, Vallejo, California, U.S.A. 559
(5)
K. J. A. DE WAAL and J. C. OKESON
When the reaction is very fast, k, $ s, and kl, = xkD,l
(6)
The following systems of gas absorption accompanied by (rapid) first-order chemical reaction may be used: (1) Absorption of CO1 in NaOH or KOH solutions [6, 8, 9, 131. (2) Absorption of CO, in amine solutions [lo-121. Absorption of CO2 in carbonate/bicarbonate (3) buffer-solutions with arsenite ions as a catalyst [IO, 14, 151. (4) Absorption of O2 in ferrous salt solutions
order. Since the reaction velocity is strongly dependent on the pH, the solution must be buffered. The reaction is rapid at pH > 8 ; in this region however, ferrous hydroxyde precipitates. Hence, the system cannot be used. Note (5). This system is outlined below. The reaction velocity constant can be varied between 50-10,000 see-l. For small values of the surface renewal rate it is better to use the absorption of CO, in carbonate/bicarbonate buffer solutions. The physical properties of the liquid cannot be varied. 2. THE REACTION BETWEEN OXYGEN AND SULPHITE IoNs
1161.
of 0, in aqueous sodium (5) Absorption sulphite solutions with cobaltous ions as a catalyst. Note (1). The reaction between dissolved COz and hydroxyl ions is second-order and very rapid. At high hydroxyl ion concentrations the reaction is (pseudo) first-order. The reaction velocity constant cannot be varied. The absorption rate is rather large; in most cases pure COz must be used, in order to eliminate any gas phase resistance. Precautions must be made to remove the heat of reaction. Furthermore, the reaction remains pseudo first-order for only a limited time. Correction for the change in solubility of the CO* during reaction is also needed. The addition of glycerine or ethylalcohol has no influence on the reaction velocity constant; hence the viscosity and the surface tension of the liquid can be varied. Note (2). The amine solutions cannot be used because of the very rapid COz absorption rate; the pseudo first-order character is valid for a contact time of the order of 10e2 sec. Note (3). The reaction velocity constant of CO2 in a buffer solution of carbonate/bicarbonate can be varied between O-5and 26 set-‘. Hence, determination of interfacial area and of surface renewal rate is feasible with this system. For large values of the surface renewal rate, the concentration of the dissolving CO2 will no longer be negligible in the bulk of the liquid. Note (4). It is generally assumed that the reaction between dissolved oxygen and ferrous ions is second
General
In aqueous solution sulphite ions are oxidized by the absorbed oxygen according to the overall reaction equation: o2 + 2so;
--, 2so;
Although this oxidation has been the subject of numerous investigations for almost 70 years [17], the reaction mechanism is not yet clearly understood. It is certain that the reaction is generally first-order in oxygen and first-order in sulphite [18-201. Furthermore, traces of various materials influence the reaction velocity, e.g. the ions of heavy metals have a promoting effect [8]. In concentrated sulphite solutions the reaction must then be pseudo first-order and by varying the ion-concentration of a heavy metal, for example cobaltous ions, the reaction velocity may be changed. The system was investigated only so far as a knowledge of its properties is needed for its use in the determination of interfacial area and surface renewal rate. Experimental
For the experiments a wetted wall column was used and the absorption rate was determined by the soap film technique. A sulphite solution flows by gravity via a constant temperature bath, a needle valve and a rotameter to the wetted wall reactor. This reactor consists of a pipe and a distributor cap (both 560
The oxidation of aqueous sodium sulphite solutions
stainless steel) covering the upper part of the pipe. At the bottom of the pipe a Teflon collar is used, following a suggestion of DANCKWERTS [14]. The solution flows upwards inside the pipe, goes through the annulus between distributor cap and outer wall of the pipe, then contacts the oxygen while flowing down the pipe wall and leaves the reactor through three slits in the Teflon collar. The liquid then passes an overflow, with which the liquid in the reactor can be maintained at a desired level in the slits of the collar, and flows to the drain. Pure oxygen passes through a saturator, a constant temperature bath, a valve and rotameter and enters the reactor. It leaves the reactor via a gasburet into which a movable soap film can be introduced. Reactor, gasburet and the gas and liquid lines are jacketed and water of a constant temperature is circulated through the jackets. The measurements consisted of the determination of the absorbed volume of oxygen per unit time. Before each experiment, the reactor was purged with oxygen. When the gas and liquid had attained the desired temperature, a soap film was introduced by temporary shutting off the connection between reactor and gasburet with a soap solution. When the soap film reached the upper part of the gasburet, a valve in the oxygen supply line to the reactor was closed. The soap film descended and with a stopwatch the time required for a selected volume to be absorbed was measured. For the determination of a reaction velocity constant, about 40 1. of sulphite solution are needed. This solution is prepared as follows: 40 kg of water were drawn into a stainless steel bucket. About 4 1. were withdrawn from the bucket and saved for the cobalt catalyst. Exactly 4 kg of sodiumsulphitet are weighed and then slowly added (with rapid stirring) to the water in the bucket. The cobalt needed for an experiment is taken from a strong solution$ of known concentration (see t BASF, “pro photo” grade NazSOs oaq. $ As a catalyst, Merck analytical grade CoSO4 7 aq is used. It is not certain that the 7 aq form is stable under atmospheric conditions. Therefore, a concentrated solution of the catalyst is prepared. This solution must be diluted before it is added to the sulphite solution; otherwise, the solubility product of cobalt hydroxyde may be exceeded locally which results in the precipitation of the catalyst.
Appendix 1) and diluted with the reserved water. This solution is then slowly added with rapid stirring to the sulphite solution. Then the pH is adjusted to the desired values by the addition of 4N H,SO,. The sulphite solution is therefore 100 g/l. of water and the cobalt concentration is expressed in grammoles per liter of water. Measurements
1. Determination of the group ,/[k,D]/He. The mass transfer rate for rapid first order reactions is expressed by: (I),,,= J[k,ID]
- A. c02*.
(7)
If there is no gasphase resistance and if the ideal gas law and Henry’s law are valid: CO*
*
PO2
=HeRq*
(8)
Furthermore,
(9) The area exposed to the oxygen is: A = ndL.
WO
In this equation, d is the external diameter of the stainless steel tube plus twice the film thickness of the liquid. The film thickness can be calculated from the equation for laminar flow of liquid along a flat plate PO], and is constant for a given flowrate and temperature. Hence, the mass transfer rate becomes :
(11) In Fig. 1, QUis given as a function of L. A straight line fits the data satisfactorily, in agreement with Eq. (11). From the slope of the line, the value of ,/[k,D]/He is obtained. The temperature rise resulting from the heats of solution and reaction can be neglected, as is shown in Appendix. 2. $It has to be ascertained that the glass electrode is not influenced by large amounts of sodium ions.
561
K. J. A. DE WAAL and J. C. OKIZSON
FIG. 1.
% as a function of L. T = 30°C; [Co-] = 1O-3 kmol/m3 water; distilled water; one batch of sulphite. Slope =3.56 x 1O-6 ; ad = 5.5 x 1O-2 m; hence l/[krD]/He = 6.48 x 10-3 m/set.
2. Range of validity of first-order
model.
The
Figure 2 gives the results of such an experiment carried out at the highest reaction velocity to be used. It can be seen that the first order reaction is found at least up to the point where 50 per cent of the amount of sulphite originally present (which is 100 kg Na,S0,/m3 water) is oxidized. In Appendix 3 a method is described for estimating the time in which this decline takes place. If the sulphite concentration is too low, the re-
practical utility of this measuring technique depends upon the first-order approximation. It is therefore important to know over what parameter range this approximation is valid. The influence of the sulphite concentration was studied at constant catalyst concentration, pH, temperature and ionic strength (maintained by addition of analytical grade Na,SO,). In this way, a sulphite solution is simulated during oxidation in a practical experiment. _-
I
3;~ /-L
3
2
1
0 0
25
50
+ csoY3 kg1 75
[mawater
FIG. 2.
2/[krD]/He as a function of the sulphite concentration. T = 30°C; pi = 8.00; [CO++] = 10m3 kmol/m3 water; constant ionic strength. Distilled water, one batch of sulphite.
562
The oxidation of aqueous sodium sulphite soluttons
Fm. 3. z/[krD]/He as a function of the square root of the cobalt concentration for different values of the PH. T = 30°C; various types of water, various batches of sulphite. action becomes second-order and the absorption rate is also determined by the sulphite concentration and the first-order approximation is not valid. Furthermore, the catalyst precipitates as a hydroxyde at low sulphite concentrations. 3. Variation of the group ,/[k,D]/He. The value of the group ,/[k,D]/He is influenced by the catalyst concentration, the p,., of the solution and the temperature. In Fig. 3 J[k,D]/He is given as a function of the square root of the cobalt concentration, for
Fro. 4.
different values of the pH at 30°C. The relation between reaction velocity constant and cobalt concentration appears to be linear. Lowering of the pH reduces the reaction velocity constant. For p,., = 8.50, the linear relationship holds up to [Co’ “1 = 3 x 10S4 kmole/m’ water. A possible explanation of this behaviour will be given in the discussion. To be able to use the system at different temperatures, the group J[k,D]/He was also determined at 20°C and 33°C. Figure 4 shows the results for
d[k,D]/He as a function of the square root of the cobalt concentration for different eratures. p= = 8.50; various types of water, various batches of sulphite.
563
temp-
K. J. A.
DE WAAL
and J. C.
OKESON
10-i
Jk,ID Ci/d
t
10-3
10-4
FIG. 5.
pn = 8.50.
Log z/[&l)]
Similar
I
5
3.30 -
I
I
3,35
I
3,40
3.45
0 3.51
+ C'03"K-'1
as a function of l/T. PH = 8.50; various types of water, various batches of sulphite.
results
for pH = 7.50 and
(4 The absorption measurements were repeated
pH = 8.00 are given in Table 1.
in a glass reactor. Compared to the stainless steel reactor, no difference in the reaction velocity constant was found.
With these data it is possible to determine the specific absorption rate as a function of the temperature. The distribution coefficient, He, can be calculated according to the procedure given in Appendix 4. In Fig. 5 J[k,D] is plotted as a function of l/T at pH = 8.50. From the slope of the lines the apparent energy of activation can be calculated (8000 kcal/kmol). The energy of activation of ,/[O] is equal to 2100 kcal/kmol [8]. Hence it follows that the energy of activation of the reaction velocity constant, E, has the value E = 12,000 kcal/kmol. For pH = 7.50 and pH = 8.00 more or less the same value is found. This high value indicates that the chemical reaction is rate determining in the process. If we assume that the diffusion coefficient obeys the law of Nernst-Einstein (Appendix 5), the reaction velocity constant can be calculated. The resulting diffusion coefficients and reaction velocities are given in Table 1.
Q-4Different batches of sodium sulphite were used (all BASF grade). No influence was found except for pH = 7.50 at reaction velocity constants below 100 set-‘. Here, the absorption rate varies and extrapolation of the values of the reaction velocity constant, given in Table 1, are not reliable.
04 In a series of experiments distilled water, demineralized water and tap water were used in the preparation of the sulphite solution. With tap water, the reaction velocity constant was 5 to 6 per cent lower than with the other types of water.
(4 Dissolved iron and phenol have no influence. Copper ions however reduce the reaction velocity drastically. Because metallic copper dissolves in a sulphite solution (the copper test is positive, when the solution has been in contact with the metal), copper, brass and bronze must always be excluded.
Discussion
1. The influence of impurities. If the method is to be applied in production scale apparatus, it is quite important that the reaction is not unduly sensitive to the presence of impurities. The following tests were performed to elucidate the effects of various impurities.
Acceptable materials of constructions for the apparatus in which the sulphite system is to be used are: glass, steel, stainless steel, perspex, PVC and Teflon; epicoat resins can be used as a covering material.
564
The oxidation of aqueous sodium sulphite solutions
Table 1 pl3 = 150 D
He (& 15.0
625
[co++] 4[krDIIHe
PR
kr
x4krDIIHe
(m%ec)
(kmol/ms)
(lo-sm/sec)
(see-1)
1.36 x lo+’
3 x 10-5 1 x 10-4 2 x 10-4
0.41 0.61 0.85
64 106 209
1 0.61 1.17 1.78
(lOVm/sec) -
20.0
65
160
x 10-s
3 x 10-s 1 x 10-4 2 x 10-4
0.39 0.83 1.24
41 183 406
30.0
69
2.10 x 10-s
3 x 10-s 3 x 10-5 1 x 10-4 2 x 10-4 3x10-4 4 x 10-4 5 x 10-Q 1 x 10-3
0.75 1.39 2.06 3.30 -
128 440 965 2420 -
1.14 2.05 2.80 6.48
3 x 10-s 1 x 10-4 2 x 10-4
0.86 166 2.34
161 600 1220
1.17 2.22 3.22
33.0
70
Results.
2.25 x 10-a
-
All the measurements are carried out at a sulphite concentration
2. Limiting values of pH and catalyst concentration. Originally, the system was investigated without changing the pH. It was noted that at high cobalt
concentrations a brown precipitate was formed and that a black oily film floated on top of the solution. At lower concentrations the solution becomes turbid and green coloured during oxidation. This is due to the fact that locally the solubility product of cobalt hydroxyde is exceeded and precipitation takes place. Therefore, the pH was lowered and because the absorption rate depends on the pH [18, 22-241 this rate had to be determined for each pH separately. Above pH = 850 only low catalyst concentrations can be used and a slight decrease in sulphite concentration changes the absorption rate. Below pH = 7.50 large amounts of H,S04 are needed to lower the pH further and the influence of impurities in the sulphite becomes considerable. At pH = 8.50 the upper limit of the reaction velocity constant is about 5000 set -’ ; above this value precipitation of the catalyst may occur. In Fig. 3 the relation
=
plx= 850
8*00
kr
(set-1)
d/[krDIIHe (lOsm/sec)
(se%)
-
-
98 363 720
0.98 1.85 2.72
256 908 1960
295 955 1780 9510
0.45 1.43 2.14 390 4.13 5.20 5.80 -
46 465 1700 3460 5100 6350 7660 -
299 1070 2250
1.62 3.10 4.46
574 2100 4340
of 100 kg NasSOs/ms
water.
between reaction velocity constant and cobalt concentration is seen to deviate from linearity above k, = 5000 set- ‘. At k, = 50 see-’ the reaction is still insensitive to impurities. At pH = 8.00 the highest attained reaction velocity constant is about 10,000 set-‘. For the present purposes this is high enough. At pH = 7.50 the lower limit is 100 set-‘, most likely due to a greater influence of impurities. Summarizing: at pri = 8.50, k, can be varied between 50 to 5000 see- ’ ; at pH = 8.00 this interval is from say 100 to 10,000 set-’ ; at pH = 7.50 values above 100 set-’ can be used. As to the temperature, it is likely that any value can be used, as long as the upper limits of the reaction velocity constants given above are not exceeded. In a practical experiment the pH decreases as the oxidation proceeds. A correction with dilute sodium hydroxyde solution is necessary. This solution must be dilute, lest the solubility product of cobalt-hydroxyde be exceeded. 3. Variation of the physical properties of the
565
K. J. A.
DE
WAAL and J. C.
liquid. It is clear that the physical properties of gas
and liquid influence the size of the interfacial area and the value of the surface renewal rate. The influence of viscosity and surface tension of the sulphite solution were investigated by adding BIGELOW [17] predicts glycerine or ethanol. inhibition of the reaction by alcohols. The results of these experiments were negative indeed; the absorption rate was drastically reduced (by a factor 10 or more). Teepol and silicon oil have no influence on the reaction velocity; it is possible therefore to examine the influence of surfactants.
OKESON
reduced below 50 set-‘, low values of surface renewal rates cannot be determined accurately with this system. 3. APPLICATIONS 1. The interfacial area between gas and liquid
Conclusions
The oxidation of concentrated aqueous sodium sulphite solutions is first-order in oxygen. The reaction velocity constant can be changed from 50-10,000 see-‘. Hence it is possible to use this oxidation reaction for the determination of interfacial area and surface renewal rate in gas-liquid systems. Sodium sulphite is relatively cheap. In many cases the gas phase resistance is low enough to use air instead of pure oxygen. Therefore, the system is attractive for use in apparatuses of technical size. One drawback of this reactron is that the physical properties of the liquid cannot be changed. Since the reaction velocity constant cannot be
Two experiments were performed for which independent checks on the interfacial area were possible. A. The stagnant liquid surface in a bottle. A bottle is inserted in the place of the wetted wall reactor with which most of the above mentioned experiments were carried out. The bottle was placed in a constant temperature bath. Before beginning the experiment, the bottle was flushed with oxygen. A sulphite solution of the required temperature was introduced into the bottle and immediately thereafter the experiment was started. No stirring was employed. The absorption rate was determined during 150 min. Figure 6 gives the results of the experiment. The equation of the mass transfer rate is: @ =
value
X Meosurcd
FIG. 6.
z/[krD]/He
1
10
’
20
30
&O 50
He
Initially, the measured values are lower than theoretical value most probably because some was entrained during the introduction of sulphite solution. After purging with oxygen,
-Theoretical
oi0
.-&J)l
A
”
60
70
90
90 -
100 110 120 t [mid
measured in a stagnant liquid layer as a function T = 30°C; [Co*.] = 10e4 kmol/m* water.
566
value
of contact
time. pH = 8.50;
(13)
the air the the
The oxidation of aqueous sodium sulphite solutions
theoretical and observed values of &k,D]/He agree. For contact times that exceed one hour, ,/[k,D]/He gradually decreases due to the fact that the reaction is no longer first-order. The maximum time of contact without surface renewal for which the reaction remains first-order is about four min, according to Eq. (20), Appendix 3. A possible explanation for this low estimate is that free convection plays a role, because the densities of Na2S03 and Na,SO, solutions differ (PNQSOS= 1085 kg/m3 at 30°C and pNalSo4= 1092 kg/m3 at 30°C). B. The surface of bubbles in a gaslift. A sulphite solution was transported by a regular stream of oxygen bubbles in a gaslift. The gaslift consisted of a glass tube (0.48 cm internal dia. and 88.0 cm length), a gas inlet section and a gas-liquid separator. Gaseous oxygen circulates in a closed system and entrains the sulphite solution at the inlet of the lift. Via the separator on top of the lift the liquid flows to the drain. The absorption rate is determined by means of a movable soap film in a gasburet which is connected to the oxygen line. The whole apparatus is operated at constant temperature. The bubbles were photographed and counted. From the shape of a bubble, the surface was calculated [25]. The total number of bubbles present in the lift was determined from the same photograph.
In Fig. 7 the theoretical absorption rate per bubble is compared with the measured rate per bubble for different bubble sizes. The theoretical absorption rate is calculated by multiplying the J[k,D]/He group of the solution and the photographically determined surface area of a bubble. For small bubbles the deviation of chemically determined areas from photographically determined ones may be attributable to volume change during the residence time of the bubble in the lift. The decrease due to oxygen loss is not compensated by the increase due to reducing hydrostatic pressure. From these two experiments it is clear that for the determination of the interfacial area the sulphite system is reliable and independent of the hydrodynamic conditions at the surface. 2. The interfacial area and the surface renewal rate in an agitated gas-liquid reactor Introduction. If the reaction is moderately fast, k, is dependent upon the age of the surface. As we have seen, the expression for kL is:
kL.= ,/C(k, +
WI
If the reaction velocity is so fast, that the oxygen concentration in the bulk of the liquid is zero, and if it is assumed that the gas phase resistance is negligible, then the mass transfer rate is:
L5
perbubbl [10-$]
to t
0.5-
OO
a5
1.0
115 -c
FIG. 7.
(5)
Bubbles,:
[10%]
Theoretical and measured absorption rates per bubble in a gaslift as a function of bubble length. T = 30°C; pi = 8.50; d[/+D]/He = 4.0 X 10m4m/set.
567
K. J. A. DE WAAL and
J. C. OKESON
Acsoy~ _ J[(k, + s)Dl-A.$$ F
By varying the reaction velocity constant in a series of experiments under the same hydrodynamic and aerodynamic conditions, it is possible to evaluate A and s. To test this, an agitated gas-liquid reactor was chosen. Experimental. A fully baffled vessel with a turbine impeller at one half of the height of the vessel was used. The gas distributor was placed directly below the impeller. The temperature was regulated by means of heating and cooling coils at the bottom of the vessel. Pure oxygen? was continuously fed to the gas distributor. One batch of sulphite solution was prepared according to the procedure mentioned in Section 2. Five 1. of it were brought into the reactor, the gas rate and impeller speed were adjusted to the desired value and the contents were heated to the desired temperature. As soon as steady state conditions were attained, the experiment started. At t = 0 (stopwatch) a sample of about 30 ml was drawn from the vessel. Immediately, 2 ml were pipetted (in duplicate) in an excess iodine solution. The rest of the sample was used for the determination of the pH and was finally replaced in the vessel. The slight decrease in pH during oxidation was corrected by the addition of some dilute NaOH solution and could be held constant to within +0*02 pH units. At regular time intervals this sampling and testing procedure was repeated. The iodine solutions were titrated with a standard thiosulphate solution. Results and discussion. The absorption rate is determined from the analysis of the sulphite concentration :
(15) According to Eq. (15) the concentration should be a linear function of time. The mass transfer is now expressed as: t Pure effect of bubbles. (Central
oxygen must be used in order to eliminate the different partial pressures of oxygen in the various The authors thank Mr. L. L. VAN DIERENWNCK Laboratory, State Mines, Geleen, The Netherlands)
for this suggestion based on experimental evidence.
-
(I6a)
or: 1 Acsos~ _ Zbt-&k,+s)Dl*S*~ HeRT
(16b)
In Eqs. (16a) and (16b) A or S and s are to be determined. Under similar aero- and hydrodynamic conditions these parameters are constant. The liquid volume participating in the reaction is known. The value of Acso,,,fAt is determined by chemical analysis. At the chosen temperature, the solubility and the diffusion coefficient are known. Since pure oxygen is used, po,/RT is likewise known. From Table 1, different values of k, are chosen. If
is plotted against k,, a straight line must appear. This is done in Fig. 8. It can be seen that the experiments are not in contradiction with the surface renewal model of DANCKWERTS; it is very difficult to sayiftheD~~~~WERTS model represents the physical reality, but it is satisfactory for design purposes. The line has a slope equal to S’D, and intersects the abscissa at -s. From the present experiment, it is calculated that S = 68*9m2/m3 and s = 110 s-‘. CALDERBANK [26] found for low stirring velocities or no stirring at all in a reactor of the same type: k, = 1.8 x 10w4m/s (bubble diameter <2 mm) to k, = 8.0 x IO-‘m/s (bubble diameter >2 mm) for the absorption of CO, in water. For physical absorption, the DANCKWERTS model leads to: k, = &-SD].
(17)
If a temperature of 30°C is assumed, this leads to k, = 5.7 x 10-4m/s which is in reasonable agreement with CALDERBANK. In the experiments, the gas hold-up was E = 0.02. If we assume that the gas is divided in n bubbles/m3 of the same diameter db, it can be derived that mrd2, = 68.9 m2/m3 and
568
1 n7rd,3 = 0.02 6
The oxidation of aqueous sodium sulphite solutions
FIG. 8. Evaluation of surface area and surface renewal PR = 8.50 height of the vessel * d-r of the vessel = 1; superficial gas velocity is
rate in an agitated gas-liquid reactor. T = 30°C; diameter impeller = 0.4; n = 5 revolutions/set; diameter vessel 11.7 X 10-3 mlsec.
this follows db = I.75 mm and II = 7.2 x lo6 bubbles/m3. These values seem reasonable.
is determined by the sensitivity of the galvanometer.
APPENDIX1
APPENDIX2
From
1 mgCo++
= 0.01695 ml NK,Fe(CN)6
Determination of the cobalt concentration
The temperature effect of the reaction
The concentration of the cobaltous sulphate solution is determined by a dead-stop titration of the cobalt with potassium ferricyanide. (For the dead-stop technique see e.g. [27].) In an Erlenmeyer flask of 500 ml a sample of the solution is added to 200 ml 3N NH,OH + O*lN KNOJ. Two platinum wires are immersed in the solution, a stabilized potential of 250 mV is applied and the current is read on a galvanometer. Because oxygen interferes with the measurement, nitrogen or carbondioxide is bubbled through the solution. The solution must be well stirred. 0.05 N potassium ferricyanide solution is added from a microburette. The end point of the titration is indicated by a sudden commencement of flow of current; the titration is continued for a while. In a graph the number of ml of ferricyanide added is plotted as a function of the galvanometer reading; the experimental points are grouped on two straight lines. The equivalence point of the titration is at the intersection of the lines. The lowest amount of cobalt that can be analysed
DANCKWERTS [28] treated the problem of the rise in temperature at the interface due to gas absorption with first-order chemical reaction. The following expression was derived with the assumptions he made : (18)
with :
569
H, = 3.8 x lo3 ~CWi kcal H z = 132.6 x lo3 Ee
p= 10853; cp =
1 kcal kg”C;
a = 144 X 10-7$c.
c291;
K. J. A. DE
WAAL
This leads to: AT = 3.74 x 10’ * c* * ,/k$]
. J[t]
(19),
Example: At T = 30°C and k, = 10,000 set-’ and the use of pure oxygen, the temperature rise of the surface of a stagnant solution after a contact time of O-1 set amounts to 0.35”C. The temperature effect can be important at high reaction velocities since the reaction velocity constant depends on temperature: a temperature rise of 1°C increases the reaction velocity constant with 5.5 per cent.
and J. C. OKESON The maximum allowable contact time without surface renewal is then t = 37 sec. Had air been used with a reaction velocity constant k, = 50 set-‘, then t would have been 16.7 h. APPENDIX4 The determination of the distribution coeficient
Because of the reactivity, the solubility of oxygen cannot be determined directly in sulphite solutions. Therefore, the solubility was calculated in the following way : The solubility of oxygen in pure water at different temperatures is known [31]. With the equation of VANKREVELENand HOFTIJZER[32]:
APPENDIX3 Calculation of the maximum contact time, without renewal, during which the reaction remains first-order
In Fig. 2 is shown that the reaction remains first-order up to the point where the sulphite concentration is reduced to half its original value. It is of importance to know in what time this decrease takes place. For the reaction velocities used, the thickness of the layer in which the reaction takes place is 7 x 10e6 to 4 x lo-‘m. It may be assumed, therefore, that the reaction proceeds at the interface and that the liquid is of infinite depth. Mass transport (by diffusion) of sulphite ions to the reaction plane where these ions are consumed by the reaction is analogous to heat transport in a semi-infinite solid with a constant flux of heat at the boundary. For this problem the temperature at the boundary as a function of time is given by CARSLAWand JAEGER [30]. The concentration of sulphite ions at the interface as a function of time is then: cso4-
(20)
The maximum allowable decrease in cSOJ,, is 0.4 kmole/m3 ; if DsOJ,, = Do,, Eq. (20) becomes: 0.125 ’ = Cc*]‘. k, *
(21)
Example: In an experiment the temperature is 3O”C, pure oxygen is applied and k, = 10,000 see-‘.
log cc,*l
= - KOt_CCiZi2 CC**Ler
(23)
the equilibrium concentration in the electrolyte solution is calculated. The ratio of the oxygen concentration in the gas and in the sulphite solution is defined as the distribution coefficient He. The constant K, is composed of three factors. K. = i+ + i- + i,
(24)
with i+ = O-094 (sodium ions) i- = 0.021 (sulphate ions; it is assumed that sulphite ions have the same value) The temperature i, = 0.033 (oxygen at 15’C) dependence of ie = O-019 (oxygen at 25°C) is supposed to be I linear [32]. The calculated values of He are given in Table 1. APPENDIX5 Determination of the dijiision coeficient
The value of the diffusion coefficient of oxygen in water at 22°C [33] is: Do, = 2.4 x 10-gm2/sec. With the equation of Nernst-Einstein :
Drl - = constant, T
(22)
the diffusion coefficient can be determined at other viscosities and temperatures. At the temperatures in the experiments, the kinematic viscosity and density of a sulphite solution were determined. The calculated values of the diffusion coefficient are given in Table 1. 570
The oxidation of aqueous sodium sulphite solutions APPENDIX
A
6
CA
The application
of copper as a catalyst
Interfacial area Concentration of component
m2 A in the liquid
kmol/m3 Equilibrium concentration of component A in the kmol/m* liquid Concentration of component A in the bulk of the cA, liquid kmol/ms kions/m3 Ionic concentration ci kmol/m* Initial concentration co kcal/kg”K Specific heat at constant pressure CP d Diameter of the wetted wall column DA Diffusion coefficient of component A in the liquz mZ/sec DA 1 kcal/kmol E Energy of activation kcal/kmol HI Heat of solution kcal/kmol HZ Heat of reaction He Distribution coefficient [kmol/m3]B,,/[kmol/m3]li,uia m/set kr. Mass transfer coefficient in the hquid W-1 first-order reaction velocity constant see-’ k:: Frequency factor m L Length of the wetted wall atm. PO2 Partial pressure of oxygen R Gas constant atm.ms/kmol “K or kcal/kmol “K set-’ Surface renewal rate mz/ms ; Specific interfacial area set Time “K ; Temperature X Distance perpendicular to the interface (x = 0 at m the interface) Valency of ionic species N sec/ms Viscositv kmol/sec Absorption rate of component A kmol/m%ec Mass flux of component A ma/set Volumetric absorption rate Surface age distribution function CA*
We have investigated extensively the behaviour of copper as a catalyst. The reaction velocity constant has been determined in a gaslift at 2O”C, 3O”C, 40°C and 50°C. The value is low: at 30°C the reaction velocity constant is 56 set- ’ and the energy of activation is 14,000 kcal/kmole. The absorption rate is dependent upon the hydrodynamic conditions at the interface. It must be concluded that copper can not be used as a catalyst for the evaluation of the contact area. Although it has been widely used as a catalyst, the results obtained with it are questionable. Acknowledgements-The authors thank ir. H. KRAMERSand Prof.dr.ir. W. J. BEEK for their stimulating discussions and their interest in this investigation. One of the authors (J. C. 0.) was holder of a Fulbright Scholarship and a grant from the United States Navy. Ir. J. SCHERMERHORN performed the experiments in the agitated gas-liquid reactor and investigated the behaviour of copper as a catalyst. Ir. J. GLASSperformed the experiments in the gaslift.
NOTATION a
Thermal diffusivity
mZ/sec
REFERENCES DANCKW~RTSP. V. Trans. Faraaby Sec. 1950 46 300. WHITMANW. G. and LEWISW. K. Znd. Engng Chem. 1924 16 1215. HIGBIE R. W. Trans. Am. Znstn. them. Engrs. 1935 31 365. DANCKWERTSP. V. Znd. Engng Chem. 195143 1460. DANCKWERT~P. V. and KENNEDYA. M. Trans. Znstn. Chem. Engrs. 1954 32 S49. YOSHIDAF. and MIURA Y. A.Z.Ch.E.JI. 19639 331. DANCKWERTSP. V., KENNEDYA. M. and ROBERTSD. Chem. Engng Sci. 1963 18 63. WESTERTERP K. R. Doctoral Thesis T.H. Delft 1962. HOFTIJZERP. J. and VAN KREVELEND. W. Trans. Znstn. them. Engrs. 1954 32 MO. SHARMAM. M. and DANCKWERTSP. V. Trans. Faraday Sot. 1963.59 386. ASTARITAG., MARRUCIG. and GIOIA F. Chem. Emma Sci. 1964 19 95. CLARKEJ. K. A. Znd. Engng Chem. Fundamentals l?& 3 239. YOSHIDAF. and MIVRA Y. Znd. Engng. Chem. Process Design and Development 1963 2 263. ROBERTSD. and DANCKWERTSP. V. Chem. Engng Sci. 196217 1961. RICHARDSC. M., RATCLIFFC. A. and DANCKWERTSP. V. Chem. Engng Sci. 1964 19 325. LERK C. F. Doctoral Thesis T.H. Delft 1965. BIGELOWS. L. Z. phys. Chem. 1898 26 493. FULLERE. C. and_CRrsT R. H. J. Am. them. Sot. 1941 63 1644. CALLOWD. S., GILLETW. A. and PIRT S. J. Chemy. Znd. 1957 418 YAGI S. and INOUEH. Chem. Engng Sci. 1962 17 411. BIRD R. B., STEWARTW. E. and LIGHTFOOTE. N. Transport Phenomena, Wiley, New York, 2nd Ed. 1962, p. 37. REINDERSW. and VLES S. Reck Trav. them. Pavs-Bus 1925 44 249. HABERF. Naturwissensch. 1931 19 450.
571
K. J, A. DE WAAL and J. C. OKESON [24] (251 1261 [27j 1281 [29]
[30] [31] [32] [33]
ROX~URGHJ. M. Can. Chem. Engng 1962 48 127. Bsa~ W. J. and VAN I-Is~vtr~ J. W. Chem. Engng Sci. 1963 18 377. CALDERBANK P. H. Trans. Znstn. them Enars. 1959 37 173. VOOELA. I. Quantitative Znorganic Analyiis Longmans, London, 2nd Ed., 1951, p. 692. DANCKWERT~P. V. Appl. Scient. Res. 1953 A3 385. RO~%NIF. D. Selected Values of Chemical Thermodynamic Properties U.S. Government Printing Office, Washington D.C. 1952. CARSLAWH. S. and JAEGERJ. C. Conduction of Heats in Solids Clarendon Press, Oxford, 2nd Ed. 1959 p. 75. S~IDELLA. Solubilities of Organic and Inorganic Compounds Van Nostrand, Princeton, 1952. VAN KREXEL~ND. W. and HOFI~JZERP. J. Chim. Znd. XXI-ere Congrds Znt. Chim. Znd. 1948 168. EMMERTR. E. and PIGFORDR. L. Chem. Engng Prog. 1954 50 87.
R&sum&On propose une methode pour la dktermination de la surface interfaciale gaz-liquide et du renouvellement de l’interface. Cette methode est bas& sur l’oxydation par l’oxygene dune solution concent& aqueuse de sulfite de sodium en presence de sulfate de cobalt comme catalyseur. La reaction d’oxydation est d’un ordre pseudo 1 et on peut modifier la constante de vitesse de 50 a 10.000 se& par changement de concentration du catalyseur, dupn et de la temperature. L’energie d’activation a et6 d&erminb. On a ttudi6 l’intluence de quelques impure@ et de la nature des materiaux de construction de l’appareil. 11 est difficile de predire l’activitt catalytique du cuivre; aussi son utilisation comme catalyseur n’est pas possible si on veut utiliser cette reaction pour la determination de la surface interfaciale gaz-liquide. Finalement quelques exemples de l’application de cette methode sont dom&
dem nachfolgenden Artikel wird eine Methode zur Bcstimmung der G&se der Grenz!Xche zwischen Gas und Fliissigkeit und der Grenzflachenemeuerung gegeben. Dieses ist die Oxydierung (mit gasfiirmigen Sauerstoff) von konzentrierten wlissrigen Sulfrtliisungen mit Kobaltsulfat als Katalysator. Die Reaktion ist erster Ordnung und die Reaktionsgeschwindigkeitskonstante kann man durch Anndenmg der Katalysatormenge, des PA, oder der Temperatur variieren zwischen 50 bis 10,000 se@. Die Aktivierungsenergie wird bestimmt. Ausserdem wird der Einfluss einiger Verunreinigungen und Mate&lien untersucht. Die katalytische Wirkung von Kupfer ist unregelmassig; deshalb kamr dieses nicht gebraucht werden, wear die Reaktion zur Bestimmung der KontaktoberlXche benutzt werden ~011. Schliesslich werden einige Beispiele gegeben ftir die Anwendung dieser Methode. Zussammenfassung--In
572
Pergamon Press Ltd., Oxford.
Printed in Great Britain.
The oxidation of aqueous sodium sulphite solutions K. J. A. DE WAAL and J. C. OKESON Laboratorium
voor Fysische Technologie, Technische Hogeschool, Delft, The Netherlands
Abstract-A method is suggested for the determination of the interfacial area between a gas and a liquid and of the surface renewal rate of this interface. This method is based upon the oxidation of a concentrated aqueous sulphite solution with gaseous oxygen in the presence of cobaltous sulphate as a catalyst. The oxidation reaction is first-order and the reaction velocity constant can be varied between 50-10,000 set-1 by changing the catalyst concentration, thepn or the temperature. The energy of activation has been determined. The influence of some impurities and of some materials of construction has been investigated. The behaviour of copper as a catalyst is irregular; hence copper cannot be applied when the reaction is used for the determination of the contact area. Finally, some examples are given of the application of this method.
1. INTRODUCTION THE AIM of this investigation was to develop a method for the determination of the interfacial area between gas and liquid phases and the surface renewal rate of this interface. Gas absorption accompanied by a rather rapid chemical reaction is one possible technique. Consider for instance a gas A which dissolves in a liquid and then undergoes a first-order reaction with one of the liquid components. The penetration theory, based on stationary mass transfer perpendicular to the interface, yields the following equation :
2A 22, -$ = D, 2
“‘
-
krcA
,
with the initial and boundary conditions: t=o,
x20
:c*=o
t > 0,
x =o
: c, = c,*
t>o,
x=(x):c,=o
The mass flux of A at the interface will become ( DANCKWERTS [I]) : WAA
x=0
=
c: J[k,O,l( erfdCk,tl+ &)
time and then disappear into the bulk of the liquid. To describe this phenomenon, several models have been suggested. The models of WHITMAN [2] (filmmodel), HIGBIE [3] (all surface elements have the same age) and DANCKWERTS [4] (random surface renewal) are the best known. Although they differ in mathematical formulation, these models all give the same numerical results if proper values of the parameters (thickness of diffusion layer, mean contact time or surface renewal rate) are chosen [5-71. The description of the absorption process with any of them seems to be adequate. The surface renewal model of DANCKWERTS [4] proposes the following surface age distribution function : Assume a surface of which the age distribution (or the probability that the age of a surface element lies between t and t + dt) is represented by $(t)dt$ The fraction S, that is renewed per unit time is independent of the age of the surface elements. This leads to: $(t) = se-” (3) Combination of (2) and (3) gives: Q9,, = c,* *A- xkk, + s)D,l
(4)
so I
kt = ,/C(k, + W,l.
(*)
Generally, the liquid is in motion. Eddies are generated, come to the surface, remain there some t Present address: Mare Island Naval Ship Yard, Vallejo, California, U.S.A. 559
(5)
K. J. A. DE WAAL and J. C. OKESON
When the reaction is very fast, k, $ s, and kl, = xkD,l
(6)
The following systems of gas absorption accompanied by (rapid) first-order chemical reaction may be used: (1) Absorption of CO1 in NaOH or KOH solutions [6, 8, 9, 131. (2) Absorption of CO, in amine solutions [lo-121. Absorption of CO2 in carbonate/bicarbonate (3) buffer-solutions with arsenite ions as a catalyst [IO, 14, 151. (4) Absorption of O2 in ferrous salt solutions
order. Since the reaction velocity is strongly dependent on the pH, the solution must be buffered. The reaction is rapid at pH > 8 ; in this region however, ferrous hydroxyde precipitates. Hence, the system cannot be used. Note (5). This system is outlined below. The reaction velocity constant can be varied between 50-10,000 see-l. For small values of the surface renewal rate it is better to use the absorption of CO, in carbonate/bicarbonate buffer solutions. The physical properties of the liquid cannot be varied. 2. THE REACTION BETWEEN OXYGEN AND SULPHITE IoNs
1161.
of 0, in aqueous sodium (5) Absorption sulphite solutions with cobaltous ions as a catalyst. Note (1). The reaction between dissolved COz and hydroxyl ions is second-order and very rapid. At high hydroxyl ion concentrations the reaction is (pseudo) first-order. The reaction velocity constant cannot be varied. The absorption rate is rather large; in most cases pure COz must be used, in order to eliminate any gas phase resistance. Precautions must be made to remove the heat of reaction. Furthermore, the reaction remains pseudo first-order for only a limited time. Correction for the change in solubility of the CO* during reaction is also needed. The addition of glycerine or ethylalcohol has no influence on the reaction velocity constant; hence the viscosity and the surface tension of the liquid can be varied. Note (2). The amine solutions cannot be used because of the very rapid COz absorption rate; the pseudo first-order character is valid for a contact time of the order of 10e2 sec. Note (3). The reaction velocity constant of CO2 in a buffer solution of carbonate/bicarbonate can be varied between O-5and 26 set-‘. Hence, determination of interfacial area and of surface renewal rate is feasible with this system. For large values of the surface renewal rate, the concentration of the dissolving CO2 will no longer be negligible in the bulk of the liquid. Note (4). It is generally assumed that the reaction between dissolved oxygen and ferrous ions is second
General
In aqueous solution sulphite ions are oxidized by the absorbed oxygen according to the overall reaction equation: o2 + 2so;
--, 2so;
Although this oxidation has been the subject of numerous investigations for almost 70 years [17], the reaction mechanism is not yet clearly understood. It is certain that the reaction is generally first-order in oxygen and first-order in sulphite [18-201. Furthermore, traces of various materials influence the reaction velocity, e.g. the ions of heavy metals have a promoting effect [8]. In concentrated sulphite solutions the reaction must then be pseudo first-order and by varying the ion-concentration of a heavy metal, for example cobaltous ions, the reaction velocity may be changed. The system was investigated only so far as a knowledge of its properties is needed for its use in the determination of interfacial area and surface renewal rate. Experimental
For the experiments a wetted wall column was used and the absorption rate was determined by the soap film technique. A sulphite solution flows by gravity via a constant temperature bath, a needle valve and a rotameter to the wetted wall reactor. This reactor consists of a pipe and a distributor cap (both 560
The oxidation of aqueous sodium sulphite solutions
stainless steel) covering the upper part of the pipe. At the bottom of the pipe a Teflon collar is used, following a suggestion of DANCKWERTS [14]. The solution flows upwards inside the pipe, goes through the annulus between distributor cap and outer wall of the pipe, then contacts the oxygen while flowing down the pipe wall and leaves the reactor through three slits in the Teflon collar. The liquid then passes an overflow, with which the liquid in the reactor can be maintained at a desired level in the slits of the collar, and flows to the drain. Pure oxygen passes through a saturator, a constant temperature bath, a valve and rotameter and enters the reactor. It leaves the reactor via a gasburet into which a movable soap film can be introduced. Reactor, gasburet and the gas and liquid lines are jacketed and water of a constant temperature is circulated through the jackets. The measurements consisted of the determination of the absorbed volume of oxygen per unit time. Before each experiment, the reactor was purged with oxygen. When the gas and liquid had attained the desired temperature, a soap film was introduced by temporary shutting off the connection between reactor and gasburet with a soap solution. When the soap film reached the upper part of the gasburet, a valve in the oxygen supply line to the reactor was closed. The soap film descended and with a stopwatch the time required for a selected volume to be absorbed was measured. For the determination of a reaction velocity constant, about 40 1. of sulphite solution are needed. This solution is prepared as follows: 40 kg of water were drawn into a stainless steel bucket. About 4 1. were withdrawn from the bucket and saved for the cobalt catalyst. Exactly 4 kg of sodiumsulphitet are weighed and then slowly added (with rapid stirring) to the water in the bucket. The cobalt needed for an experiment is taken from a strong solution$ of known concentration (see t BASF, “pro photo” grade NazSOs oaq. $ As a catalyst, Merck analytical grade CoSO4 7 aq is used. It is not certain that the 7 aq form is stable under atmospheric conditions. Therefore, a concentrated solution of the catalyst is prepared. This solution must be diluted before it is added to the sulphite solution; otherwise, the solubility product of cobalt hydroxyde may be exceeded locally which results in the precipitation of the catalyst.
Appendix 1) and diluted with the reserved water. This solution is then slowly added with rapid stirring to the sulphite solution. Then the pH is adjusted to the desired values by the addition of 4N H,SO,. The sulphite solution is therefore 100 g/l. of water and the cobalt concentration is expressed in grammoles per liter of water. Measurements
1. Determination of the group ,/[k,D]/He. The mass transfer rate for rapid first order reactions is expressed by: (I),,,= J[k,ID]
- A. c02*.
(7)
If there is no gasphase resistance and if the ideal gas law and Henry’s law are valid: CO*
*
PO2
=HeRq*
(8)
Furthermore,
(9) The area exposed to the oxygen is: A = ndL.
WO
In this equation, d is the external diameter of the stainless steel tube plus twice the film thickness of the liquid. The film thickness can be calculated from the equation for laminar flow of liquid along a flat plate PO], and is constant for a given flowrate and temperature. Hence, the mass transfer rate becomes :
(11) In Fig. 1, QUis given as a function of L. A straight line fits the data satisfactorily, in agreement with Eq. (11). From the slope of the line, the value of ,/[k,D]/He is obtained. The temperature rise resulting from the heats of solution and reaction can be neglected, as is shown in Appendix. 2. $It has to be ascertained that the glass electrode is not influenced by large amounts of sodium ions.
561
K. J. A. DE WAAL and J. C. OKIZSON
FIG. 1.
% as a function of L. T = 30°C; [Co-] = 1O-3 kmol/m3 water; distilled water; one batch of sulphite. Slope =3.56 x 1O-6 ; ad = 5.5 x 1O-2 m; hence l/[krD]/He = 6.48 x 10-3 m/set.
2. Range of validity of first-order
model.
The
Figure 2 gives the results of such an experiment carried out at the highest reaction velocity to be used. It can be seen that the first order reaction is found at least up to the point where 50 per cent of the amount of sulphite originally present (which is 100 kg Na,S0,/m3 water) is oxidized. In Appendix 3 a method is described for estimating the time in which this decline takes place. If the sulphite concentration is too low, the re-
practical utility of this measuring technique depends upon the first-order approximation. It is therefore important to know over what parameter range this approximation is valid. The influence of the sulphite concentration was studied at constant catalyst concentration, pH, temperature and ionic strength (maintained by addition of analytical grade Na,SO,). In this way, a sulphite solution is simulated during oxidation in a practical experiment. _-
I
3;~ /-L
3
2
1
0 0
25
50
+ csoY3 kg1 75
[mawater
FIG. 2.
2/[krD]/He as a function of the sulphite concentration. T = 30°C; pi = 8.00; [CO++] = 10m3 kmol/m3 water; constant ionic strength. Distilled water, one batch of sulphite.
562
The oxidation of aqueous sodium sulphite soluttons
Fm. 3. z/[krD]/He as a function of the square root of the cobalt concentration for different values of the PH. T = 30°C; various types of water, various batches of sulphite. action becomes second-order and the absorption rate is also determined by the sulphite concentration and the first-order approximation is not valid. Furthermore, the catalyst precipitates as a hydroxyde at low sulphite concentrations. 3. Variation of the group ,/[k,D]/He. The value of the group ,/[k,D]/He is influenced by the catalyst concentration, the p,., of the solution and the temperature. In Fig. 3 J[k,D]/He is given as a function of the square root of the cobalt concentration, for
Fro. 4.
different values of the pH at 30°C. The relation between reaction velocity constant and cobalt concentration appears to be linear. Lowering of the pH reduces the reaction velocity constant. For p,., = 8.50, the linear relationship holds up to [Co’ “1 = 3 x 10S4 kmole/m’ water. A possible explanation of this behaviour will be given in the discussion. To be able to use the system at different temperatures, the group J[k,D]/He was also determined at 20°C and 33°C. Figure 4 shows the results for
d[k,D]/He as a function of the square root of the cobalt concentration for different eratures. p= = 8.50; various types of water, various batches of sulphite.
563
temp-
K. J. A.
DE WAAL
and J. C.
OKESON
10-i
Jk,ID Ci/d
t
10-3
10-4
FIG. 5.
pn = 8.50.
Log z/[&l)]
Similar
I
5
3.30 -
I
I
3,35
I
3,40
3.45
0 3.51
+ C'03"K-'1
as a function of l/T. PH = 8.50; various types of water, various batches of sulphite.
results
for pH = 7.50 and
(4 The absorption measurements were repeated
pH = 8.00 are given in Table 1.
in a glass reactor. Compared to the stainless steel reactor, no difference in the reaction velocity constant was found.
With these data it is possible to determine the specific absorption rate as a function of the temperature. The distribution coefficient, He, can be calculated according to the procedure given in Appendix 4. In Fig. 5 J[k,D] is plotted as a function of l/T at pH = 8.50. From the slope of the lines the apparent energy of activation can be calculated (8000 kcal/kmol). The energy of activation of ,/[O] is equal to 2100 kcal/kmol [8]. Hence it follows that the energy of activation of the reaction velocity constant, E, has the value E = 12,000 kcal/kmol. For pH = 7.50 and pH = 8.00 more or less the same value is found. This high value indicates that the chemical reaction is rate determining in the process. If we assume that the diffusion coefficient obeys the law of Nernst-Einstein (Appendix 5), the reaction velocity constant can be calculated. The resulting diffusion coefficients and reaction velocities are given in Table 1.
Q-4Different batches of sodium sulphite were used (all BASF grade). No influence was found except for pH = 7.50 at reaction velocity constants below 100 set-‘. Here, the absorption rate varies and extrapolation of the values of the reaction velocity constant, given in Table 1, are not reliable.
04 In a series of experiments distilled water, demineralized water and tap water were used in the preparation of the sulphite solution. With tap water, the reaction velocity constant was 5 to 6 per cent lower than with the other types of water.
(4 Dissolved iron and phenol have no influence. Copper ions however reduce the reaction velocity drastically. Because metallic copper dissolves in a sulphite solution (the copper test is positive, when the solution has been in contact with the metal), copper, brass and bronze must always be excluded.
Discussion
1. The influence of impurities. If the method is to be applied in production scale apparatus, it is quite important that the reaction is not unduly sensitive to the presence of impurities. The following tests were performed to elucidate the effects of various impurities.
Acceptable materials of constructions for the apparatus in which the sulphite system is to be used are: glass, steel, stainless steel, perspex, PVC and Teflon; epicoat resins can be used as a covering material.
564
The oxidation of aqueous sodium sulphite solutions
Table 1 pl3 = 150 D
He (& 15.0
625
[co++] 4[krDIIHe
PR
kr
x4krDIIHe
(m%ec)
(kmol/ms)
(lo-sm/sec)
(see-1)
1.36 x lo+’
3 x 10-5 1 x 10-4 2 x 10-4
0.41 0.61 0.85
64 106 209
1 0.61 1.17 1.78
(lOVm/sec) -
20.0
65
160
x 10-s
3 x 10-s 1 x 10-4 2 x 10-4
0.39 0.83 1.24
41 183 406
30.0
69
2.10 x 10-s
3 x 10-s 3 x 10-5 1 x 10-4 2 x 10-4 3x10-4 4 x 10-4 5 x 10-Q 1 x 10-3
0.75 1.39 2.06 3.30 -
128 440 965 2420 -
1.14 2.05 2.80 6.48
3 x 10-s 1 x 10-4 2 x 10-4
0.86 166 2.34
161 600 1220
1.17 2.22 3.22
33.0
70
Results.
2.25 x 10-a
-
All the measurements are carried out at a sulphite concentration
2. Limiting values of pH and catalyst concentration. Originally, the system was investigated without changing the pH. It was noted that at high cobalt
concentrations a brown precipitate was formed and that a black oily film floated on top of the solution. At lower concentrations the solution becomes turbid and green coloured during oxidation. This is due to the fact that locally the solubility product of cobalt hydroxyde is exceeded and precipitation takes place. Therefore, the pH was lowered and because the absorption rate depends on the pH [18, 22-241 this rate had to be determined for each pH separately. Above pH = 850 only low catalyst concentrations can be used and a slight decrease in sulphite concentration changes the absorption rate. Below pH = 7.50 large amounts of H,S04 are needed to lower the pH further and the influence of impurities in the sulphite becomes considerable. At pH = 8.50 the upper limit of the reaction velocity constant is about 5000 set -’ ; above this value precipitation of the catalyst may occur. In Fig. 3 the relation
=
plx= 850
8*00
kr
(set-1)
d/[krDIIHe (lOsm/sec)
(se%)
-
-
98 363 720
0.98 1.85 2.72
256 908 1960
295 955 1780 9510
0.45 1.43 2.14 390 4.13 5.20 5.80 -
46 465 1700 3460 5100 6350 7660 -
299 1070 2250
1.62 3.10 4.46
574 2100 4340
of 100 kg NasSOs/ms
water.
between reaction velocity constant and cobalt concentration is seen to deviate from linearity above k, = 5000 set- ‘. At k, = 50 see-’ the reaction is still insensitive to impurities. At pH = 8.00 the highest attained reaction velocity constant is about 10,000 set-‘. For the present purposes this is high enough. At pH = 7.50 the lower limit is 100 set-‘, most likely due to a greater influence of impurities. Summarizing: at pri = 8.50, k, can be varied between 50 to 5000 see- ’ ; at pH = 8.00 this interval is from say 100 to 10,000 set-’ ; at pH = 7.50 values above 100 set-’ can be used. As to the temperature, it is likely that any value can be used, as long as the upper limits of the reaction velocity constants given above are not exceeded. In a practical experiment the pH decreases as the oxidation proceeds. A correction with dilute sodium hydroxyde solution is necessary. This solution must be dilute, lest the solubility product of cobalt-hydroxyde be exceeded. 3. Variation of the physical properties of the
565
K. J. A.
DE
WAAL and J. C.
liquid. It is clear that the physical properties of gas
and liquid influence the size of the interfacial area and the value of the surface renewal rate. The influence of viscosity and surface tension of the sulphite solution were investigated by adding BIGELOW [17] predicts glycerine or ethanol. inhibition of the reaction by alcohols. The results of these experiments were negative indeed; the absorption rate was drastically reduced (by a factor 10 or more). Teepol and silicon oil have no influence on the reaction velocity; it is possible therefore to examine the influence of surfactants.
OKESON
reduced below 50 set-‘, low values of surface renewal rates cannot be determined accurately with this system. 3. APPLICATIONS 1. The interfacial area between gas and liquid
Conclusions
The oxidation of concentrated aqueous sodium sulphite solutions is first-order in oxygen. The reaction velocity constant can be changed from 50-10,000 see-‘. Hence it is possible to use this oxidation reaction for the determination of interfacial area and surface renewal rate in gas-liquid systems. Sodium sulphite is relatively cheap. In many cases the gas phase resistance is low enough to use air instead of pure oxygen. Therefore, the system is attractive for use in apparatuses of technical size. One drawback of this reactron is that the physical properties of the liquid cannot be changed. Since the reaction velocity constant cannot be
Two experiments were performed for which independent checks on the interfacial area were possible. A. The stagnant liquid surface in a bottle. A bottle is inserted in the place of the wetted wall reactor with which most of the above mentioned experiments were carried out. The bottle was placed in a constant temperature bath. Before beginning the experiment, the bottle was flushed with oxygen. A sulphite solution of the required temperature was introduced into the bottle and immediately thereafter the experiment was started. No stirring was employed. The absorption rate was determined during 150 min. Figure 6 gives the results of the experiment. The equation of the mass transfer rate is: @ =
value
X Meosurcd
FIG. 6.
z/[krD]/He
1
10
’
20
30
&O 50
He
Initially, the measured values are lower than theoretical value most probably because some was entrained during the introduction of sulphite solution. After purging with oxygen,
-Theoretical
oi0
.-&J)l
A
”
60
70
90
90 -
100 110 120 t [mid
measured in a stagnant liquid layer as a function T = 30°C; [Co*.] = 10e4 kmol/m* water.
566
value
of contact
time. pH = 8.50;
(13)
the air the the
The oxidation of aqueous sodium sulphite solutions
theoretical and observed values of &k,D]/He agree. For contact times that exceed one hour, ,/[k,D]/He gradually decreases due to the fact that the reaction is no longer first-order. The maximum time of contact without surface renewal for which the reaction remains first-order is about four min, according to Eq. (20), Appendix 3. A possible explanation for this low estimate is that free convection plays a role, because the densities of Na2S03 and Na,SO, solutions differ (PNQSOS= 1085 kg/m3 at 30°C and pNalSo4= 1092 kg/m3 at 30°C). B. The surface of bubbles in a gaslift. A sulphite solution was transported by a regular stream of oxygen bubbles in a gaslift. The gaslift consisted of a glass tube (0.48 cm internal dia. and 88.0 cm length), a gas inlet section and a gas-liquid separator. Gaseous oxygen circulates in a closed system and entrains the sulphite solution at the inlet of the lift. Via the separator on top of the lift the liquid flows to the drain. The absorption rate is determined by means of a movable soap film in a gasburet which is connected to the oxygen line. The whole apparatus is operated at constant temperature. The bubbles were photographed and counted. From the shape of a bubble, the surface was calculated [25]. The total number of bubbles present in the lift was determined from the same photograph.
In Fig. 7 the theoretical absorption rate per bubble is compared with the measured rate per bubble for different bubble sizes. The theoretical absorption rate is calculated by multiplying the J[k,D]/He group of the solution and the photographically determined surface area of a bubble. For small bubbles the deviation of chemically determined areas from photographically determined ones may be attributable to volume change during the residence time of the bubble in the lift. The decrease due to oxygen loss is not compensated by the increase due to reducing hydrostatic pressure. From these two experiments it is clear that for the determination of the interfacial area the sulphite system is reliable and independent of the hydrodynamic conditions at the surface. 2. The interfacial area and the surface renewal rate in an agitated gas-liquid reactor Introduction. If the reaction is moderately fast, k, is dependent upon the age of the surface. As we have seen, the expression for kL is:
kL.= ,/C(k, +
WI
If the reaction velocity is so fast, that the oxygen concentration in the bulk of the liquid is zero, and if it is assumed that the gas phase resistance is negligible, then the mass transfer rate is:
L5
perbubbl [10-$]
to t
0.5-
OO
a5
1.0
115 -c
FIG. 7.
(5)
Bubbles,:
[10%]
Theoretical and measured absorption rates per bubble in a gaslift as a function of bubble length. T = 30°C; pi = 8.50; d[/+D]/He = 4.0 X 10m4m/set.
567
K. J. A. DE WAAL and
J. C. OKESON
Acsoy~ _ J[(k, + s)Dl-A.$$ F
By varying the reaction velocity constant in a series of experiments under the same hydrodynamic and aerodynamic conditions, it is possible to evaluate A and s. To test this, an agitated gas-liquid reactor was chosen. Experimental. A fully baffled vessel with a turbine impeller at one half of the height of the vessel was used. The gas distributor was placed directly below the impeller. The temperature was regulated by means of heating and cooling coils at the bottom of the vessel. Pure oxygen? was continuously fed to the gas distributor. One batch of sulphite solution was prepared according to the procedure mentioned in Section 2. Five 1. of it were brought into the reactor, the gas rate and impeller speed were adjusted to the desired value and the contents were heated to the desired temperature. As soon as steady state conditions were attained, the experiment started. At t = 0 (stopwatch) a sample of about 30 ml was drawn from the vessel. Immediately, 2 ml were pipetted (in duplicate) in an excess iodine solution. The rest of the sample was used for the determination of the pH and was finally replaced in the vessel. The slight decrease in pH during oxidation was corrected by the addition of some dilute NaOH solution and could be held constant to within +0*02 pH units. At regular time intervals this sampling and testing procedure was repeated. The iodine solutions were titrated with a standard thiosulphate solution. Results and discussion. The absorption rate is determined from the analysis of the sulphite concentration :
(15) According to Eq. (15) the concentration should be a linear function of time. The mass transfer is now expressed as: t Pure effect of bubbles. (Central
oxygen must be used in order to eliminate the different partial pressures of oxygen in the various The authors thank Mr. L. L. VAN DIERENWNCK Laboratory, State Mines, Geleen, The Netherlands)
for this suggestion based on experimental evidence.
-
(I6a)
or: 1 Acsos~ _ Zbt-&k,+s)Dl*S*~ HeRT
(16b)
In Eqs. (16a) and (16b) A or S and s are to be determined. Under similar aero- and hydrodynamic conditions these parameters are constant. The liquid volume participating in the reaction is known. The value of Acso,,,fAt is determined by chemical analysis. At the chosen temperature, the solubility and the diffusion coefficient are known. Since pure oxygen is used, po,/RT is likewise known. From Table 1, different values of k, are chosen. If
is plotted against k,, a straight line must appear. This is done in Fig. 8. It can be seen that the experiments are not in contradiction with the surface renewal model of DANCKWERTS; it is very difficult to sayiftheD~~~~WERTS model represents the physical reality, but it is satisfactory for design purposes. The line has a slope equal to S’D, and intersects the abscissa at -s. From the present experiment, it is calculated that S = 68*9m2/m3 and s = 110 s-‘. CALDERBANK [26] found for low stirring velocities or no stirring at all in a reactor of the same type: k, = 1.8 x 10w4m/s (bubble diameter <2 mm) to k, = 8.0 x IO-‘m/s (bubble diameter >2 mm) for the absorption of CO, in water. For physical absorption, the DANCKWERTS model leads to: k, = &-SD].
(17)
If a temperature of 30°C is assumed, this leads to k, = 5.7 x 10-4m/s which is in reasonable agreement with CALDERBANK. In the experiments, the gas hold-up was E = 0.02. If we assume that the gas is divided in n bubbles/m3 of the same diameter db, it can be derived that mrd2, = 68.9 m2/m3 and
568
1 n7rd,3 = 0.02 6
The oxidation of aqueous sodium sulphite solutions
FIG. 8. Evaluation of surface area and surface renewal PR = 8.50 height of the vessel * d-r of the vessel = 1; superficial gas velocity is
rate in an agitated gas-liquid reactor. T = 30°C; diameter impeller = 0.4; n = 5 revolutions/set; diameter vessel 11.7 X 10-3 mlsec.
this follows db = I.75 mm and II = 7.2 x lo6 bubbles/m3. These values seem reasonable.
is determined by the sensitivity of the galvanometer.
APPENDIX1
APPENDIX2
From
1 mgCo++
= 0.01695 ml NK,Fe(CN)6
Determination of the cobalt concentration
The temperature effect of the reaction
The concentration of the cobaltous sulphate solution is determined by a dead-stop titration of the cobalt with potassium ferricyanide. (For the dead-stop technique see e.g. [27].) In an Erlenmeyer flask of 500 ml a sample of the solution is added to 200 ml 3N NH,OH + O*lN KNOJ. Two platinum wires are immersed in the solution, a stabilized potential of 250 mV is applied and the current is read on a galvanometer. Because oxygen interferes with the measurement, nitrogen or carbondioxide is bubbled through the solution. The solution must be well stirred. 0.05 N potassium ferricyanide solution is added from a microburette. The end point of the titration is indicated by a sudden commencement of flow of current; the titration is continued for a while. In a graph the number of ml of ferricyanide added is plotted as a function of the galvanometer reading; the experimental points are grouped on two straight lines. The equivalence point of the titration is at the intersection of the lines. The lowest amount of cobalt that can be analysed
DANCKWERTS [28] treated the problem of the rise in temperature at the interface due to gas absorption with first-order chemical reaction. The following expression was derived with the assumptions he made : (18)
with :
569
H, = 3.8 x lo3 ~CWi kcal H z = 132.6 x lo3 Ee
p= 10853; cp =
1 kcal kg”C;
a = 144 X 10-7$c.
c291;
K. J. A. DE
WAAL
This leads to: AT = 3.74 x 10’ * c* * ,/k$]
. J[t]
(19),
Example: At T = 30°C and k, = 10,000 set-’ and the use of pure oxygen, the temperature rise of the surface of a stagnant solution after a contact time of O-1 set amounts to 0.35”C. The temperature effect can be important at high reaction velocities since the reaction velocity constant depends on temperature: a temperature rise of 1°C increases the reaction velocity constant with 5.5 per cent.
and J. C. OKESON The maximum allowable contact time without surface renewal is then t = 37 sec. Had air been used with a reaction velocity constant k, = 50 set-‘, then t would have been 16.7 h. APPENDIX4 The determination of the distribution coeficient
Because of the reactivity, the solubility of oxygen cannot be determined directly in sulphite solutions. Therefore, the solubility was calculated in the following way : The solubility of oxygen in pure water at different temperatures is known [31]. With the equation of VANKREVELENand HOFTIJZER[32]:
APPENDIX3 Calculation of the maximum contact time, without renewal, during which the reaction remains first-order
In Fig. 2 is shown that the reaction remains first-order up to the point where the sulphite concentration is reduced to half its original value. It is of importance to know in what time this decrease takes place. For the reaction velocities used, the thickness of the layer in which the reaction takes place is 7 x 10e6 to 4 x lo-‘m. It may be assumed, therefore, that the reaction proceeds at the interface and that the liquid is of infinite depth. Mass transport (by diffusion) of sulphite ions to the reaction plane where these ions are consumed by the reaction is analogous to heat transport in a semi-infinite solid with a constant flux of heat at the boundary. For this problem the temperature at the boundary as a function of time is given by CARSLAWand JAEGER [30]. The concentration of sulphite ions at the interface as a function of time is then: cso4-
(20)
The maximum allowable decrease in cSOJ,, is 0.4 kmole/m3 ; if DsOJ,, = Do,, Eq. (20) becomes: 0.125 ’ = Cc*]‘. k, *
(21)
Example: In an experiment the temperature is 3O”C, pure oxygen is applied and k, = 10,000 see-‘.
log cc,*l
= - KOt_CCiZi2 CC**Ler
(23)
the equilibrium concentration in the electrolyte solution is calculated. The ratio of the oxygen concentration in the gas and in the sulphite solution is defined as the distribution coefficient He. The constant K, is composed of three factors. K. = i+ + i- + i,
(24)
with i+ = O-094 (sodium ions) i- = 0.021 (sulphate ions; it is assumed that sulphite ions have the same value) The temperature i, = 0.033 (oxygen at 15’C) dependence of ie = O-019 (oxygen at 25°C) is supposed to be I linear [32]. The calculated values of He are given in Table 1. APPENDIX5 Determination of the dijiision coeficient
The value of the diffusion coefficient of oxygen in water at 22°C [33] is: Do, = 2.4 x 10-gm2/sec. With the equation of Nernst-Einstein :
Drl - = constant, T
(22)
the diffusion coefficient can be determined at other viscosities and temperatures. At the temperatures in the experiments, the kinematic viscosity and density of a sulphite solution were determined. The calculated values of the diffusion coefficient are given in Table 1. 570
The oxidation of aqueous sodium sulphite solutions APPENDIX
A
6
CA
The application
of copper as a catalyst
Interfacial area Concentration of component
m2 A in the liquid
kmol/m3 Equilibrium concentration of component A in the kmol/m* liquid Concentration of component A in the bulk of the cA, liquid kmol/ms kions/m3 Ionic concentration ci kmol/m* Initial concentration co kcal/kg”K Specific heat at constant pressure CP d Diameter of the wetted wall column DA Diffusion coefficient of component A in the liquz mZ/sec DA 1 kcal/kmol E Energy of activation kcal/kmol HI Heat of solution kcal/kmol HZ Heat of reaction He Distribution coefficient [kmol/m3]B,,/[kmol/m3]li,uia m/set kr. Mass transfer coefficient in the hquid W-1 first-order reaction velocity constant see-’ k:: Frequency factor m L Length of the wetted wall atm. PO2 Partial pressure of oxygen R Gas constant atm.ms/kmol “K or kcal/kmol “K set-’ Surface renewal rate mz/ms ; Specific interfacial area set Time “K ; Temperature X Distance perpendicular to the interface (x = 0 at m the interface) Valency of ionic species N sec/ms Viscositv kmol/sec Absorption rate of component A kmol/m%ec Mass flux of component A ma/set Volumetric absorption rate Surface age distribution function CA*
We have investigated extensively the behaviour of copper as a catalyst. The reaction velocity constant has been determined in a gaslift at 2O”C, 3O”C, 40°C and 50°C. The value is low: at 30°C the reaction velocity constant is 56 set- ’ and the energy of activation is 14,000 kcal/kmole. The absorption rate is dependent upon the hydrodynamic conditions at the interface. It must be concluded that copper can not be used as a catalyst for the evaluation of the contact area. Although it has been widely used as a catalyst, the results obtained with it are questionable. Acknowledgements-The authors thank ir. H. KRAMERSand Prof.dr.ir. W. J. BEEK for their stimulating discussions and their interest in this investigation. One of the authors (J. C. 0.) was holder of a Fulbright Scholarship and a grant from the United States Navy. Ir. J. SCHERMERHORN performed the experiments in the agitated gas-liquid reactor and investigated the behaviour of copper as a catalyst. Ir. J. GLASSperformed the experiments in the gaslift.
NOTATION a
Thermal diffusivity
mZ/sec
REFERENCES DANCKW~RTSP. V. Trans. Faraaby Sec. 1950 46 300. WHITMANW. G. and LEWISW. K. Znd. Engng Chem. 1924 16 1215. HIGBIE R. W. Trans. Am. Znstn. them. Engrs. 1935 31 365. DANCKWERTSP. V. Znd. Engng Chem. 195143 1460. DANCKWERT~P. V. and KENNEDYA. M. Trans. Znstn. Chem. Engrs. 1954 32 S49. YOSHIDAF. and MIURA Y. A.Z.Ch.E.JI. 19639 331. DANCKWERTSP. V., KENNEDYA. M. and ROBERTSD. Chem. Engng Sci. 1963 18 63. WESTERTERP K. R. Doctoral Thesis T.H. Delft 1962. HOFTIJZERP. J. and VAN KREVELEND. W. Trans. Znstn. them. Engrs. 1954 32 MO. SHARMAM. M. and DANCKWERTSP. V. Trans. Faraday Sot. 1963.59 386. ASTARITAG., MARRUCIG. and GIOIA F. Chem. Emma Sci. 1964 19 95. CLARKEJ. K. A. Znd. Engng Chem. Fundamentals l?& 3 239. YOSHIDAF. and MIVRA Y. Znd. Engng. Chem. Process Design and Development 1963 2 263. ROBERTSD. and DANCKWERTSP. V. Chem. Engng Sci. 196217 1961. RICHARDSC. M., RATCLIFFC. A. and DANCKWERTSP. V. Chem. Engng Sci. 1964 19 325. LERK C. F. Doctoral Thesis T.H. Delft 1965. BIGELOWS. L. Z. phys. Chem. 1898 26 493. FULLERE. C. and_CRrsT R. H. J. Am. them. Sot. 1941 63 1644. CALLOWD. S., GILLETW. A. and PIRT S. J. Chemy. Znd. 1957 418 YAGI S. and INOUEH. Chem. Engng Sci. 1962 17 411. BIRD R. B., STEWARTW. E. and LIGHTFOOTE. N. Transport Phenomena, Wiley, New York, 2nd Ed. 1962, p. 37. REINDERSW. and VLES S. Reck Trav. them. Pavs-Bus 1925 44 249. HABERF. Naturwissensch. 1931 19 450.
571
K. J, A. DE WAAL and J. C. OKESON [24] (251 1261 [27j 1281 [29]
[30] [31] [32] [33]
ROX~URGHJ. M. Can. Chem. Engng 1962 48 127. Bsa~ W. J. and VAN I-Is~vtr~ J. W. Chem. Engng Sci. 1963 18 377. CALDERBANK P. H. Trans. Znstn. them Enars. 1959 37 173. VOOELA. I. Quantitative Znorganic Analyiis Longmans, London, 2nd Ed., 1951, p. 692. DANCKWERT~P. V. Appl. Scient. Res. 1953 A3 385. RO~%NIF. D. Selected Values of Chemical Thermodynamic Properties U.S. Government Printing Office, Washington D.C. 1952. CARSLAWH. S. and JAEGERJ. C. Conduction of Heats in Solids Clarendon Press, Oxford, 2nd Ed. 1959 p. 75. S~IDELLA. Solubilities of Organic and Inorganic Compounds Van Nostrand, Princeton, 1952. VAN KREXEL~ND. W. and HOFI~JZERP. J. Chim. Znd. XXI-ere Congrds Znt. Chim. Znd. 1948 168. EMMERTR. E. and PIGFORDR. L. Chem. Engng Prog. 1954 50 87.
R&sum&On propose une methode pour la dktermination de la surface interfaciale gaz-liquide et du renouvellement de l’interface. Cette methode est bas& sur l’oxydation par l’oxygene dune solution concent& aqueuse de sulfite de sodium en presence de sulfate de cobalt comme catalyseur. La reaction d’oxydation est d’un ordre pseudo 1 et on peut modifier la constante de vitesse de 50 a 10.000 se& par changement de concentration du catalyseur, dupn et de la temperature. L’energie d’activation a et6 d&erminb. On a ttudi6 l’intluence de quelques impure@ et de la nature des materiaux de construction de l’appareil. 11 est difficile de predire l’activitt catalytique du cuivre; aussi son utilisation comme catalyseur n’est pas possible si on veut utiliser cette reaction pour la determination de la surface interfaciale gaz-liquide. Finalement quelques exemples de l’application de cette methode sont dom&
dem nachfolgenden Artikel wird eine Methode zur Bcstimmung der G&se der Grenz!Xche zwischen Gas und Fliissigkeit und der Grenzflachenemeuerung gegeben. Dieses ist die Oxydierung (mit gasfiirmigen Sauerstoff) von konzentrierten wlissrigen Sulfrtliisungen mit Kobaltsulfat als Katalysator. Die Reaktion ist erster Ordnung und die Reaktionsgeschwindigkeitskonstante kann man durch Anndenmg der Katalysatormenge, des PA, oder der Temperatur variieren zwischen 50 bis 10,000 se@. Die Aktivierungsenergie wird bestimmt. Ausserdem wird der Einfluss einiger Verunreinigungen und Mate&lien untersucht. Die katalytische Wirkung von Kupfer ist unregelmassig; deshalb kamr dieses nicht gebraucht werden, wear die Reaktion zur Bestimmung der KontaktoberlXche benutzt werden ~011. Schliesslich werden einige Beispiele gegeben ftir die Anwendung dieser Methode. Zussammenfassung--In
572