Ind. Eng. Chem. Fundam. 1905, 2 4 , 1-7
1
Concentration Dependence of Mutual Diffusion Coefficients in Regular Binary Solutions: A New Predictive Equation Francls A. L. Dulllen’ Department of Chemical Englneering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G 1
Abdul-Fattah A. Asfour Department of Chemical Engineering, University of Windsor, Windsor, Ontario, Canada
A new equation to predict the dependence of the mutual diffusiviiies on concentration has been proposed and tested on 16 different regular binary solutions. The equation predicts the experimental (Fickian)diffusion coefficient and does not need the tedious and somewhat uncertain correction for thermodynamic nonideality. The equation, which predicts that the logarithm of the quotient of the Fick diffusivii and viscosity is a linear function of the mole fraction, has been shown to be somewhat more accurate than either the Leffler-Cullinan or the Vignes equation for the
systems tested.
Introduction The prediction of the concentration dependence of the mutual diffusion coefficient D of binary solutions of nonelectrolytes has been a persistent problem. There is no equation or theory that would be able to predict this concentration dependence with satisfactory generality. Two existing correlations, the first due to Vignes (1966) and the second to Leffler and Cullinan (1970), have been frequently used to predict the concentration dependence of mutual diffusion coefficients with varying degrees of success. According to Vignes’ correlation the composition dependence of D l 0 2) is as follows 2)”
= (DO)”B(D”)”A
(1)
where 2)” is the expected value of 2) at xA, Do is the mutual diffusion coefficient at XB 1, D” is the mutual diffusion coefficient at xA 1,and B is the activity correction factor, defined as
/3
-+
(d In ai/d In xJTS
(2)
with ai the activity of component i at x i , T , and P. I t is evident that eq 1 predicts linear variation of the logarithm of the activity-corrected diffusivity with xA. Dillien (1971) carried out a statistical analysis of Vignes’ equation. While it was found to fit experimental data extremely well for ideal and some nearly ideal solutions, there were several instances were it was not accurate for nonideal, nonassociating solutions. Cullinan (1966) rationalized Vignes’ equation using Eyring’s absolute rate theory for diffusion. Cullinan and co-workers discussed this subject in a series of papers (Cullinan, 1967, 1968a,b; Cullinan and Cusick, 1967a,b). Leffler and Cullinan (1970) argued that although Vignes’ equation accounts for the solution thermodynamics in an appropriate way, it does not explicitly incorporate the effect of solution viscosity. Upon using the absolute rate theory interpretation of viscosity given by Eyring’s rate theory of viscosity (e.g., Glasstone et al., 1941), Leffler and Cullinan (1970) obtained the following “corrected” form of Vignes’ equation BLcq = (DovB)XB(D”qA)XA
(3)
0196-4313/85/ 1024-0001$01.50/0
where 2ILcis the expected value of B at X A , q is the absolute solution viscosity at xA,and q A and qB are the absolute viscosities of pure A and B, respectively. It is evident that eq 3 predicts linear variation of the logarithm of the product of activity-corrected diffusivity with viscosity as a function of x A . Leffler and Cullinan (1970) used data from various sources to substantiate their correlation and reported the percent maximum deviation between the predicted and the experimental diffusivities for each system. Comparing this value with the deviation calculated for the same system using Vignes’ equation, they concluded that their correlation improved the results in all cases, except for the system acetone-carbon tetrachloride. In the present paper the equations proposed by Vignes (1966) and by Leffler and Cullinan (1970) are examined for 16 regular solutions, and a new equation is proposed to predict the mutual diffusion coefficient D directly, rather than predicting the activity-corrected diffusion coefficient DIP, from which D must be calculated with the help of rather inaccurate values of /3 (Dullien, 1971). It is demonstrated in this paper that the new equation predicts values of D more accurately in the 16 binaries than either the equation of Vignes or the equation of Leffler and Cullinan.
Analysis of the Predictive Equations The reason for not trying to predict the experimentally measured binary mutual diffusion coefficient, D, directly and preferring instead to predict the activity-corrected diffusion coefficient DIP is that In (DIP) is expected to vary more linearly than In D when plotted vs. the mole fraction XA. Inspection of the plots in Figures 1-16 shows that the opposite is true in the majority of the systems; i.e., In a,deviates from linearity more strongly and more often than in 2). The fact is that the more nearly ideal the solution is, the more closely approximate linearity exists, both for In D and In 2) and for In 9. Remember that the factor 0 = d In ai/d In x i corrects only for the nonideality of the driving force for diffusion while the transport coefficient itself remains subject to the effects of the different interactions between molecules A-A, B-B, and A-B. These effects have been taken into account in the 0 1985 American Chemical Society
2
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985 n - HEXANE (A) -TOLUENE
IB)
30 20 W
2.6
’? N
24
;
-c 22 2.0
OaO
Os2
004
006
0.8
1.0
XA
Figure 3. Comparisons (as in Figure 1) for n-hexane-toluene. 2A CHLOROBENZENE (A) -8ROMOBENZENE IBI
BROMOSENZENEIAI-BE~ZENEI81
00.66 71i
; 0.56 -
22
nu 0.46
21
0)
:
x; 0
+m
c -
c -
0.3 6
20
0.26
19
0 I6 0.0
0.2
0.6
0.4
0.8
1.8 1.0
XA
Figure 2. Comparisons (as in Figure 1)for bromobenzene-benzene.
analysis of the composition dependence of viscosity (McAllister, 1960), and they should also be recognized when trying to understand the concentration dependence of D. That is, In D cannot be expected to be a linear function of xAany more than In 7 can. Vignes’ equation (eq 1) predicts that the logarithm of the activity-corrected diffusion varies linearly with x k It is because of the special significance of linearity that we chose to use the deviation of the experimental In 59 from In Dv, i.e., linearity, as the measure of accuracy of Vignes’ equation, rather than presenting a direct comparison between predicted and experimental diffusion coefficients. Accordingly, we let A In 2J In 2J - In D v (4) As In Bv is a linear function of xA (see eq l),A In D gives the deviation of the logarithm of the experimental D from linear variation with xA.
Figure 4. Comparisons (as in Figure 1) for chlorobenzene-bromobenzene.
Inspection of Figures 1 to 16 reveals that A In D is positive about twice as often as it is negative in the case of these binary solutions. It is practically zero for two systems only, i.e., chlorobenzene-bromobenzene and toluene-carbon tetrachloride. Leaving more sophisticated considerations aside, the basis of the Leffler-Cullinan equation probably is the expectation that whenever the viscosity, 7 , of a solution increases, D of the same solution decreases, and vice versa. Hence, the Dv produd is expected to vary less with xAthen either TJ or B. The more nearly constant a quantity, the easier it should be to predict it. Inspection of the graphs in Figures 1-16 shows that, as expected, for the majority of these systems, for an increase in 7 there corresponds a decrease in D,and vice versa. A more careful analysis of these curves will reveal, however, that this behavior does not guarantee accurate prediction of the experimental product by assuming that In Bq is linear in xA. As shown below, correct prediction of D by the Leffler-Cullinan equation (eq 3) depends on the
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985 1.6
DIETHYL ETHER (A1
~
CHLDROFORH (81
3
I.7 CHLOROFORM ( A I -BENZENE IBI
\ 1.5
0.7 0.0
0.2
0.6
0.4
0.8
0,O
1.0
0.2
1.0
0.8
XA
xA
Figure 5. Comparisons (as in Figure 1) for diebhylether-chloroform. IO0
006
0.4
BENZENE (AI
-
TOLUENE ( B l
Figure 7. Comparisons (as in Figure 1) for chloroform-benzene. I
1 1,80
I
1.00
c
\
0.85
0.2
41.65
i
t //
o.60 0.55
0.0
/
0.6
0.4
0.8
I .7l 1.0
0.0
0.2
0.4
06
08
1.0
xA
xA
Figure 6. Comparisons (as in Figure 1) for benzene-toluene.
Figure 8. Comparisons (as in Figure 1) for chloroform-toluene.
extent and the sign of the deviations of both In a) and In q from linearity when plotting these functions vs. xA. Comparing eq 1 and 3, after taking logarithms In BLC = In a), In qp - In 7
is more accurate than Vignes’ equation when A In a) and A In q have opposite signs, unless IA In qI 1 2lA In 21.On the other hand, when A h a) and Aln 7 have the same sign, the Leffler-Cullinan equation is always less accurate than the Vignes equation. Inspection of Figures 1to 16 reveak that for these binary solutions the signs of A In a) and A In q are sometimes the same. Whenever this is the case, the assumption of linear variation of In (a)/?) with XA would stand a better chance than the Leffler-Cullinan equation to yield accurate predictions of a). An additional observation is that in more than half of the 16 solutions In and In D deviate from linearity in the opposite sense; Le., negative deviations of In B are accompanied by positive deviations of In D, and vice versa. For all of these systems In D and In q deviate from the straight line in the same sense. This observation led to the idea (Asfour, 1979) of trying a new predictive equation in which it is assumed that In ( D / q ) is a linear function of xA,i.e.
+
= In
A In q
(5)
vP = In qB + xA(ln q A - In qB)
(6)
a), -
where In
is the logarithm of the predicted solution viscosity if linear variation of In q with xA is assumed. Aln q gives the deviation of the logarithm of the experimental viscosity from linear variation with xk The deviation of In a)=C from In a), i.e., Aln BLc,can thus be written as A In a)LcE In - In 3ILc = (In B - In a),) + A In q = A In a) + A In q (7) It is evident from eq 7 that the Leffler-Cullinan equation
(DAD/‘I)= ( D o / d X B ( D ” / ~ ~ ) ” *
(8)
4
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985 0.8 BENZENE ( A I - CARBON TETRACHLORIDE 1Bl
o.2
t
t
0.0
0,2
i
I
I
0.4
0.6
0.8
11.6 1.0
xA
Figure 9. Comparisons (as in Figure 1)for benzene-carbon tetrachloride.
0.0
0.2
0.4
0.6
0.8
1.0
xA
Figure 11. Comparisons (as in Figure 1) for cyclohexane-carbon tetrachloride.
OMCTS IA, - C A m TETRACHLORIDE I B I
n-HEXANE IAl -CARBON TETRACHLORIDEIBI
1
h
0 03.10.0
2.2
1::
1,7 0,O
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
1.0
XA
1.0
Figure 12. Comparisons (as in Figure 1)for n-hexene-carbon tetrachloride.
XA
Figure 10. Comparisons (as in Figure 1) for OMCTS-carbon tetrachloride.
lY/
TOLUENE (A)-CARBON TETRACHLORIDE I B I
Were eq 8 accurate, then D m would be equal to D, the measured value of the mutual diffusion coefficient. By comparing eq 8 and 1, after taking logarithms, we can write In DAD = In Bv + In 7 - In qp = In Bv + A In 7 (9) where In qp is given by eq 6. The error of In DAD is A In D ,
= In D - In Dm
= In D - In Bv - A In 7
= A In D - A In q
(10)
A In D = In D - In Bv
(11)
where In eq 11, A In D is the deviation of In D from the straight line if plotted against XA. Equation 8 depends for accurate prediction of D on both A In D and A In q having the same
I
0.0
0,2
1
0.6
0.4
I
0.8
1.6 LO
XA
Figure 13. Comparisons (as in Figure 1)for toluene-carbon tetrachloride.
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985 5
Table I. Sources of Data system 1. OMCTS-benzene 2. bromobenzene-benzene 3. n-hexane-toluene 4. chlorobenzene-bromobenzene 5. diethyl ether-chloroform 6. benzene-toluene 7. chloroform-benzene 8. chloroform-toluene 9. benzene-carbon tetrachloride 10. OMCTS-carbon tetrachloride 11. cyclohexane-carbon tetrachloride 12. n-hexane-carbon tetrachloride 13. toluene-carbon tetrachloride 14. chloroform-carbon tetrachloride 15. n-hexane-benzene 16. cyclohexane-benzene
viscosity
diffusivity data Marsh (1968) Marsh (1968) International Critical Tables (1929) Miller and Carman (1959) Ghai (1973) Ghai (1973) Caldwell &d Babb (1956) Caldwell and Babb (1956) Anderson and Babb (1961) Anderson and Babb (1961) Asfour (1979) Asfour (1979) Asfour (1979) Sanni and Hutchison (1973) Asfour (1979) Asfour (1979) Grunberg (1954) Caldwell and Babb (1956) Marsh (1968) Marsh (1968) Kulkarni et al. (1965) Kulkarni et al. (1965)
vapor-liquid equilib data Marsh (1968) McGlashan and Wingrove (1956) Funk and Prausnitz (1970) Bourrely and Chevalier (1968) Dolezalek and Schulze (1913) Bell and Wright (1927) Campbell et al. (1966) Rao et al. (1956) Christian et al. (1960) Marsh (1968) Scatchard et al. (1939)
Bidlack and Anderson (1964) Ghai (1973) Kelly et al. (1971)
Bidlack and Anderson (1964) Christian et al. (1960) Ghai (1973) Wang et al. (1970) Kelly et al. (1971) McGlashan et al. (1954)
Asfour (1979) Grunberg (1954)
Harris et al. (1970) Sanni (1973) 0.90 -
Funk and Prausnitz (1970) Funk and Prausnitz (1970) CYCLOHEXANE (AI
~
BENZENE I B I
- 2.20
0.8
m N
2.0 g
5 - 0.6 t m
nu
e
0
'? N
+
I2
-e
0.4
1.8
0.2 0.0
0.2
0.6
0.4
0.8
1.6 1.0
'k
Figure 14. Comparisons (as in Figure 1) for chloroform-carbon tetrachloride.
1' 7 1
n -HEXANE (AI
].9
~
BENZENE I61
- 1.75 040
0.2
0.4
0.6
0.8
LO
'A
Figure 16. Comparisons (as in Figure 1)for cyclohexane-benzene.
for 14 of the 16 binary solutions.
0.0
0.2
0.4
0.6
0.8
1.0
'k
Figure 15. Comparisons (as in Figure 1) for n-hexane-benzene.
sign and the same magnitude. Inspection of Figures 1to 16 reveals that A In D and A In q have the same sign, at least over a portion of the complete concentration range,
Detailed Comparison of the Performance of the Three Predictive Equations A detailed discussion of the experimental and predicted diffusivities and viscosities of the 16 binary solutions reveals a number of interesting features. At the end of the discussion of each system the three predictive equations (i.e., V = Vignes, LC = Leffler-Cullinan, AD = AsfourDullien) are ranked in the order of their predictive value. When examining the diagrams it will be noted that In 2)Lc and In D m are situated on opposite sides of the straight line that is In 2)" and are mirror images of each other. Whether In DLc or In D m is above the straight line depends on whether Aln q is negative or positive, respectively. It should be also borne in mind that In Dvand In DLCare to be compared with In D,whereas In DADis to be compared with In D. The sources of the data used are listed in Table I. Figure 1: OMCTS-Benzene. In D, In D,and In q all give S-shaped curves, each of which exhibits deviations from the straight line in the same sense. In Dm is also an S-shaped curve in the same sense as In D. In DE,however,
6
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985
gives an S-shaped curve in the opposite sense as In B (AD: 1; v: 2; LC: 3). Figure 2: Bromobenzene-Benzene. Both In D and In B plot as highly irregular curves which criss-cross the straight line. The two curves are practically indistinguishable. Aln q is negative throughout the whole composition range (AD, LC, V: 1). Figure 3: n -Hexane-Toluene. Throughout the entire range of xA, In D and In D show pronounced negative and positive deviations, respectively, from the straight line. In q exhibits more moderate negative deviations throughout the whole range. A In B (see eq 4) being large and positive and A In q (see eq 5) moderately negative, A In 21Lc is moderately positive. With A In D (see eq 10) large and negative, A In Dm becomes moderately negative (AD, LC: 1; V 2). Figure 4: Chlorobenzene-Bromobenzene. Throughout the entire composition range In D and In B exhibit slight positive and negative deviations, respectively. In q shows slight positive deviations throughout the range. In Dm and In BLcalso exhibit slight positive and negative deviations, respectively, from the straight line (AD, LC, v: 1). Figure 5: Diethyl Ether-Chloroform. A In D and A in D (see eq 10 and 4) have large positive and negative values, respectively, throughout the entire composition range. A In q (see eq 5) is moderately positive throughout the range. As a result, Aln DAD and A In DLcare moderately positive and negative, respectively, throughout (AD, LC: 1; v: 2). Figure 6: Benzene-Toluene. A In D is moderately negative throughout the whole range of xA; A In B, however, is strongly positive up to about X A = 0.56, whereas over the rest of the range it is small and negative. A In q is slightly negative throughout the whole range. Consequently, A In DAD turns out to be slightly negative throughout and A In B u is moderately positive over more than half of the range, whereas over the rest of it, it is moderately negative (AD: 1;LC: 2; V: 3). Figure 7: Chloroform-Benzene. A In D is slightly negative, A In B is strongly negative throughout the entire range, and Aln q is also slightly negative up to about X A = 0.66 from which point on it is slightly positive. As a result, A In Dm is practically zero, whereas A In 21Lc is strongly negative throughout (AD: 1; V: 2; LC: 3). Figure 8: Chloroform-Toluene. A In D is slightly negative, A In B is very large and negative, whereas A In q is moderately large and positive. Consequently, A In Dm is large and negative but A In DLc is even much larger and negative. On the other hand, the trend of In Dw is similar to that of In B , whereas In DAD and In D have opposite trends (AD, LC: 1, V: 2). Figure 9: Benzendarbon Tetrachloride. In D , In SLc, In DAD,and In q all are practically linear, whereas In 2l exhibits pronounced positive deviations (AD: 1; LC, V 2). Figure 10 OMCTS-Carbon Tetrachloride. A In D is large and positive over the entire range; A In is moderately positive over the first half of the range and is practically zero in the remaining half. As A In q is strongly positive throughout, A In Dm is moderately positive and A In S L c is more strongly positive. Whereas the trends of In D and In DAD are similar, those of In B and In BLc are opposite (AD: 1; V: 2; LC: 2). Figure 11: Cyclohexandarbon Tetrachloride. A In D is slightly negative, A In B is strongly positive, and A In 7 is even larger and negative. On the balance, A In B L c is slightly negative and A In DAD strongly positive.
The trend of In BLCfollows closely that of In B , and In D m has a similar trend as In D (LC: 1; AD, V: 2). Figure 12: n -Hexanexarbon Tetrachloride. A In D is slightly positive, A In D is more significantly positive, and Aln q is negative to about the same degree. Consequently, A In DLCis almost zero and A In DAD is moderately positive (LC: 1; V: 2; AD: 3). Figure 13: Toluene-Carbon Tetrachloride. All quantities deviate from linearity only very slightly (AD, LC, v: 1). Figure 14: Chloroform-Carbon Tetrachloride. A In D and A In q are nagative to about the same extent, whereas A In D is smaller and it changes sign at about x A = 0.5. As a result, A In D m is practically zero, whereas A In DLCis negative throughout (AD: 1; V: 2; LC: 3). Figure 15: n-Hexane-Benzene. A In D and A In q are negative to about the same extent, whereas A In B is at first zero and later it is much more strongly positive over most of the range. Consequently, A In Dm is practically zero, and A In DLc is at first negative and then strongly positive (AD: 1; LC, V 2). Figure 16: Cyclohexane-Benzene. A In D and A In B are strongly negative and positive, respectively. With A In q similarly large and negative, A In Dm and A In BLC both are of comparable size. Both In Dm and In SLC have the correct trend (AD, LC: 1; V: 2). The tally of the above results shows that the new predictive equation occupied first place in 14 cases, and second and third place each in one case. The Leffler-Cullinan equation was first in nine cases, and second and third in four and three cases, respectively. The Vignes equation was first in three cases, second in 12 cases, and third in one case. These results indicate that the new equation is at least as good and probably better than the other two equations in predicting diffusion coefficients of binary regular solutions of nonelectrolytes. Its great advantage lies in the fact that it predicts directly the experimental (Fickian) diffusion coefficient and, therefore, it obviates the need to use activity coefficient data in order to obtain the diffusion Coefficient.
Conclusions (1)A new equation, eq 8 for the prediction of the dependence of mutual (Fickian) diffusion coefficient on composition has been proposed and tested. The equation, which predicts the experimental diffusion coefficient directly and does not require the customary activity correction for the thermodynamic nonideality, proved to be more successful than either the equation of Leffler and Cullinan or that of Vignes in predicting the concentration dependence of the diffusion coefficients in regular solutions. The equation is not recommended for estimation of diffusion coefficienls in systems consisting of n-alkanes and in solutions containing a polar component exhibiting stronger A-A-type than A-B-type interactions. (2) The logarithm of the activity-corrected diffusion coefficient is a linear function of the mole fraction, in general, only in ideal solutions. In nonideal solutions, linearity of the logarithm of the activity-corrected diffusion coefficient is no more likely to exist than linearity of the logarithm of the solution viscosity. (3) Linearity of the logarithm of the activity-corrected diffusivity-viscosity product in the mole fraction exists if there are deviations from linearity of about equal size but of opposite sign of the logarithm of the activity-corrected diffusivity and the logarithm of the solution viscosity, respectively. This behavior, however, has not been generally observed. In fact, the signs of these two kinds of deviations have often been found to be the same, resulting
7
Ind. Eng. Chem. Fundam. 1985, 24, 7-11
in pronounced nonlinear behavior of the logarithm of the activity corrected diffusivity-viscosity product as a function of the mole fraction. (4) The logarithm of the quotient of the experimental (Fickian) diffusivity and the viscosity is a straight line if the logarithm of the Fickian diffusivity deviates from linearity to the same extent and in the same sense as the logarithm of the solution viscosity. Both the logarithm of the Fickian diffusivity and the logarithm of the viscosity were found to exhibit deviations of the same sign, over at least a portion of the composition range, in 14 of the 16 systems examined in this work. Acknowledgment The authors wish to thank the Natural Sciences and Engineering Council of Canada for the financial support of this work. Nomenclature ai= activity of component i D = experimental (Fick) mutual-diffusion coefficient D = activity-corrected mutual-diffusion coefficient, equal to DIP Do = limiting mutual-diffusion coefficient when xA 0 D” = limiting mutual-diffusion coefficient when xA 1 xi = mole fraction of component i; i = A, B Greek Letters P = activity correction factor (eq 2) 9 = absolute viscosity Subscripts AD = refers to Asfour-Dullien A, B = refers to components of mixture LC = refers to Leffler-Cullinan V = refers to Vignes
--
Literature Cited Anderson, D. K.; Babb, A. L. J . Phys. Chem. 1961, 65, 1281. Asfour, A. A. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., Canada, 1979. Bell, T.; Wright, R. J . Phys. Chem. 1927, 37, 1885. Bdlack, D. L.; Anderson, D. K. J . Phys. Chem. 1964, 68,3790. Bourrely. J.; Chevalier, V. J . Chim. Phys. 1966, 65, 1961. Caklwell. C. S.; Bab, A. L. J . Phys. Chem. 1956, 60,51. Campbell. A. N.; Kartzmark, E. M.; Chatterjee, R. M. Can. J . Chem. 1966, 4 4 , 1183. Christian, S. D.; Naparko, E.; Affsprung, H. E. J . Phys. Chem. 1960, 6 4 , 442. Cullinan, H. T. Ind. Eng. Chem. Fundam 1966, 5 , 281. Cullinan, H. T. Can. J . Chem. Eng. 1967, 4 5 , 377. Cullinan, H. T.; Cusick, M. R. AIChE J . 19678, 73, 1171. Cullinan, H. T. Ind. Eng. Chem. Fundam. l966a, 7 , 177. Cullinan, H. T. Ind. Eng. Chem. Fundam. 1968b, 7 , 331. Doiezalek, F.; Schulze, 2. Phys. Chem. 1913, 83,45. Dullien. F. A. L. Ind. Eng. Chem. Fundam. 1971, 10, 41. Funk, E. W.; Prausnitz, J. M. Ind. Eng. Chem. 1970, 62(9),8. -1, R. K. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., Canada, 1973. Glasstone, S.; Laidler. K. J.; Eyrlng, H. “Theory of Rate Processes”; McGrawHill: New York, 1941. Grunberg, L. Trans. Faraday SOC.1954, 5 0 , 1293. Harris. K. R.; Pua, C. K. N.; Dunlop, P. J. J . Phys. Chem. 1970, 7 4 , 3518. “International Crkical Tables”, Vol. 5; McGraw-Hill: New York, 1929; p 43. Kelly, C. M.; Wlrth, G. B.; Anderson, D. K. J . Phys. Chem. 1971 7 5 , 3293. Kulkarni, M. V.: Allen, G. F.; Lyons, P. A. J . Phys. Chem. 1965, 69, 2491. Leffler, J.; Cullinan, H. T. Ind. Eng. Chem. Fundam. 1970a, 9 , 84. Marsh, K. N. Trans. Faraday SOC. 19888, 6 4 , 894. Marsh, K. N. Trans. Faraday SOC. 1966b,6 4 , 883. McAiilster, R. A. AIChE. J . 1960, 6 , 427. McGlashan, M. L.; Wingrove, M. Trans. Faraday SOC.1956, 5 2 , 470. McGiashan, M. L.; Prue, J. E.: Sainsbury, I. E. J. Trans. Faraday Soc. 1954, 50, 1284. Mlller, L.; Carman, P. C. Trans. Faraday SOC. 1959, 55, 1831. Rao, R. M.; Sitapethy, R.; Anjaneyulu, N. S. R.; Raju, G. J. V.; Rao, C. V. J . Sci. Ind. Res. 1956, 75B, 556. Sannl, S. A.; Hutchison, H. P. J . Chem. Eng. Date 1973, 78,317. Scatchard, G.; Wood, S. E.; Mochel, J. M. J . Am. Chem. SOC. 1939, 6 1 , 3206. Vlgnes, A. Ind. Eng. Chem. Fundam. 1966, 5 , 189. Wang, J. L. H.; Boublikova, L.; Lu, B. C. Y. J . Appl. Chem. 1970, 20, 172.
Received for review November 21, 1983 Revised manuscript received April 16, 1984 Accepted May 11, 1984
SO2 Absorption into NaOH and Na,SO, Aqueous Solutionst ChungShlh Chang’ and Gary T. Rochelle Department of Chemical Engineering, The Universtty of Texas at Austin, Austin, Texas 78712
The chemical absorption of sulfur dioxide into aqueous sodium sulfite and sodium hydroxide solutions is modeled by simultaneous mass transfer and multiple instantaneous reversible reactions. Experiments on the absorption of dilute sulfur dioxide into aqueous sodium hydroxide solutions were carried out in a stirred vessel with a plane gas-liquid interface. An approximation method based on film theory is used to estimate surface renewal theory solutions for mass transfer enhancement factors. Predictions by the present model are compared with those by a previous irreversible model over a wMe range of SO2 partial pressure in the gas phase.
Scope Because of its relevance to pollution abatement, SO2 absorption into NaOH or N@03 solution has been studied by several investigators. Goettler (1967) investigated the simultaneous absorption of SO2 and C02 into NaOH solution flowing over a single sphere. The absorption rates were modeled by film theory with the assumption that
* Acurex Corporation, P.O. Box 13109,Research Triangle Park, NC 27709.
Presented at the AIChE 88th National Meeting, Philadelphia, June 8-12,1980. 01984313/85/1024-0007$01.50/0
dissolved sulfur dioxide and hydroxide ion participate in a two-step instantaneous irreversible reaction and two reaction planes are formed within the liquid phase. Hikita et al. (1972) derived the solution of the penetration theory using the model of two reaction planes. Onda et al. (1971) studied the behavior of reaction plane movement by absorbing sulfur dioxide into agar gel containing sodium hydroxide or sodium sulfite solution. The experimental results for the sulfur dioxide-sodium hydroxide system were found to agree with penetration theory based on the two-reaction-plane model. Hikita et a1 (1977) measured the absorption rate of pure sulfur dioxide into aqueous sodium bisulfite, sodium hydroxide, and sodium sulfite 0 1985 American Chemical Society
