CORRESPONDENCE MASS TRANSFER MODEL FOR KOLBE-SCHMITT CARBONATION OF 2-NAPHTHOL SIR: Phadtare and Doraiswamy ( 2 ) develop a rather complicated model to explain the kinetics of the carbonation of 2naphthol to 2,3-hydroxynaphthoic acid. I n their derivation, they incorrectly equate r / R , the ratio of the radius of unreacted sodium naphtholate to the initial naphtholate radius, to (1 x ) , the fraction of naphtholate unreacted. Actually, for spherical geometry, this relationship should read (7) :
0.7
0.6
0.5
Incorporation of this change into their model yields a final expression
. m
3
h
I
3
0.4
I 4
where 8 is reaction time and k , and A , are constants, in place of their Equation 18. Let us call the term in brackets f ( x ) ; then a plot of 8 / x us. f ( x ) / x should result in a straight line if Equation 2 holds. Unfortunately, their data do not correlate well with the amended equation. Actually, the function f ( x ) is the expected relationship to be obtained for spherical geometry if only diffusion through the solid product layer is controlling (7). However, their data show lack of correlation on this basis, too.
0.3
0.2
0.1
O n the other hand, recourse to a contracting sphere model for reaction-viz.,
k8
=
1 - (1
- x)'l3
0
(3)
where k is a constant, shows good correlation with their data as demonstrated in Figure 1. This correlation implies surface chemical reaction control (7), rather than diffusion limitation, exactly opposite to their conclusion. This result, of course, does not invalidate the authors' investigation of the reaction stoichiometry nor the experimental data obtained. I t is, however, an example of the danger of relying solely on kinetic correlations to characterize reaction mechanisms. Obviously, more work is needed to delineate the reaction model unequivocally.
SIR: The comments of Massoth suggest that chemical reaction might be the controlling step rather than diffusion through the product layer in the Kolbe-Schmitt carbonation of 2-naphthol. H e suggests that it is wrong to equate ratio r/R to the term (1 - x ) , the fraction of the naphtholate unreacted. I n the reference cited by him, this ratio should be (1 - x ) ' I a . I n a case like the present one, where several uncertain factors are involved, like the composition of the product crust, the compactness of the crust, and the actual relative magnitude of the chemical reaction in comparison with the rate of diffusion of CO2, we had taken r / R as roughly equal to 1 - x . Actually, the best method of proving or disproving the suggested model would be to compute A , and k, from direct experimental data from the defining equations for these constants as given by
: Minutes
Figure 1.
Surface reaction data correlation
literature Cited
Levenspiel, O., 346-50, Wiley, New (.2 .) Phadtare. P. G., DESIGNDEVELOP.4,
(1)
"Chemical Reaction Engineering," pp. York, 1962.
Doraiswamv. L.. INDENG.CHEM.PROCESS 274 (1965).' F. E. Massoth GulfResearch €3 Development Go. Pittsburgh, Pa.
Phadtare and Doraiswamy (7). If the values of the constants calculated show order of magnitude agreement with the statistically determined values from experimental data, it may provide fairly conclusive evidence of the correctness of the model. Work is in progress on the determination of A , and k, purely from their defining equations. Although conclusive data have not so far been obtained, present trends suggest that the independently determined values of A,n and k, would have the same order of magnitude as those calculated from the diffusion control equation using experimental conversion data. Another test of the model would be to carry out a similar reaction with a simpler starting material. Work is in progress on the carbonation of phenol, where the product crust can be more clearly defined. T h e preliminary experimental data VOL. 5
NO. 3
JULY 1966
351
