Page 114 - Introduction to chemical reaction engineering and kinetics

96 Chapter 5: Complex Systems

as obtained from equation 5.3-10 (rewritten to correspond to 5.3-11) by equating expo-
nents species by species. (n is not to be confused with reaction order itself.)
If we use 5.3-11 to eliminate k,(T) in equation 5.3-4, we obtain

r = kf(T)

If the effects of T and ci on r are separable, but the individual rate laws for rf and
r, are nof of the power-law form, equation 5.3-13 is replaced by the less specific form
(from 5.3-3),

r = kf(T) gf(ci) - J&l (53.14)
[ K,eJ” I

The value of IZ must be determined experimentally, but in the absence of such infor-
mation, it is usually assumed that n = 1.

The gas-phase synthesis of methanol (M) from CO and H, is a reversible reaction:

CO + 2H, + CH,OH
(a) If, at low pressure with a rhodium catalyst, rf = kfp,ig3p& and r,. =
krp$op&pM, what is the value of n in equation 5.3-12, and what are the values
of a’ and b’?
(b) Repeat (a) if r,. = k,pf.op~,p~5.

SOLUTION

(a) If we apply equation 5.3-12 to CH,OH, with c, c’ replacing (Yi, CX:, the exponents are
c = 0 and c’ = 1. Then
c
1-0
c’ -
n=-=-= 1
% 1
a’ = a + v&z = -0.3 - l(l) = -1.3
b’ = b + vHzn = 1.3 - 2(1) = -0.7

As a check, with n = 1, from equations 5.3-1 and -4

-1.3 -0.7
PM
Keq = kf = PC0 PHI PM =-
k
r PE;3Phf PCOP&