Page 236 - Introduction to chemical reaction engineering and kinetics

218 Chapter 8: Catalysis and Catalytic Reactions

integral in 8.5-22 as: /
v
kc,
= j”‘*’
[
“O-v
dCA
0 The integral may be evaluated either numerically by means of E-Z Solve, or analytically
1 + 2KBch + (KA - ~KB)CA
0
I
by means of the substitution x = 1 + 2KBcA, + (KA - 2KB)cA. The latter results in
CAS )2 [WA - %kAs + (1 + 2KBc,)ln
(-rA)intdcA = (KA -k2K
I0 B
3.8 x 1O-4 {[340 - 2(4.2 x 106)]0.012 +
= [340 - 2(4.2 x 106)12

1 + 2(4.2 X 106)0.012 = 1
[l + 2(4.2 x 106)0.012] In 1 + 340(0.012) } 4.8 X lo-r2mo12 LP2 s-l

From the LH rate expression and the stoichiometry, since CA = cAs,

kCAS k C AS
( - rA)intlc,, =
1 + KACA$ + ~KB(C& - c&) = l+KAcA,
= 3.8 X 10-4(0.012) = 9.0 X 10P7mol L-r s-r
1 + 340(0.012)

Substitution of numerical values in 8.5-22 gives

0.7(9.0 x 10-7)
‘G = [2(0.10)4.8 x 10-‘2]“2 = o’64

(b) From Figure 8.11,
7 = 0.85 to 0.90

which implies a slight but significant effect of diffusional resistance on the process.
(C) (-rA)& = ?-/-YA)~~~ = 8 x lo-71-f101L-1 S-l.

8.7 PROBLEMS FOR CHAPTER 8
0 8-1 The hydrolysis of ethyl acetate catalyzed by hydrogen ion,
v
7O-v
CH3COOC2H5(A) + Hz0 + CH$OOH + CzH50H

in dilute aqueous solution, is first-order with respect to ethyl acetate at a given pH. The ap-
parent first-order rate constant, k( = k~c$+), however, depends on pH as indicated by:

PH 3 2 1
104kls-’ 1.1 11 110
What is the order of reaction with respect to hydrogen ion H+, and what is the value of the
rate constant kA, which takes both CA and cn+ into account? Specify the units of kA.
8-2 (a) The Goldschmidt mechanism (Smith, 1939) for the esterification of methyl alcohol
(M) with acetic acid (A) catalyzed by a strong acid (e.g., HCl), involves the follow-