Page 115 - Introduction to chemical reaction engineering and kinetics

5.3 Reversible Reactions 97

(b)

a’ = -0.3 - l(O.5) = -0.8
b’ = 1.3 - 2(0.5) = 0.3

5.3.3 Determination of Rate Constants
The experimental investigation of the form of the rate law, including determination of
the rate constants kf and k,, can be done using various types of reactors and methods,
as discussed in Chapters 3 and 4 for a simple system. Use of a batch reactor is illustrated
here and in Example 5-4, and use of a CSTR in problem 5-2.
Consider the esterification of ethyl alcohol with formic acid to give ethyl formate (and
water) in a mixed alcohol-water solvent, such that the alcohol and water are present in
large excess. Assume that this is pseudo-first-order in both esterification (forward) and
hydrolysis (reverse) directions:

%HCOOCzHs(D) + H,O(large excess)
C,H,OH(large excess) + HCOOH(A) 7

For the reaction carried out isothermally in a batch reactor (density constant), the val-
ues of kf and k, may be determined from experimental measurement of cA with respect
to t, in the following manner.
The postulated rate law is

r, = (-IA) = kfcA - krcD (5.3-15)

= kfc,,U - f~) - krCAofA (5.3-15a)
(5.3-16)
= +A,[1 - (1 + %,e,).f~l

from equation 5.3-11 (with n = l), which is 5.3-19 below. From the material balance
for A,

(-rA) = C,,d f,ldt
Combining equations 2.2-4 and 5.3-16, we obtain the governing differential equation:

% = kf[l - (1 + lK,,,)f~l (5.3-17)

The equivalent equation in terms of CA is

- - - (5.3-17a)
dCA - kfcA - krcD = kfCA - kr(CAo - CA)
dt
Integration of equation 5.3-17 with fA = 0 at t = 0 results in

In (5.3-18)