Page 237 - Introduction to chemical reaction engineering and kinetics

8.7 Problems for Chapter 8 219

ing steps:

M + H+ + CH30Hz+(C); rapid (1)
A + CA CHaCOOCHs(E) + H,O+; slow (2)
M+HsO+s C + HzO(W); rapid (3)

Show that the rate law for this mechanism, with M present in great excess, is

where
L = cMK = c~c~/c~~~+. (5)

Assume all H+ is present in C and in HsO+.
(b) Show that the integrated form of equation (4) for a constant-volume batch reactor operat-
ing isothermally with a fixed catalyst concentration is

k = [(L + CAo) In (CAdcA) - (CA0 - CA)I/CHClLt.
This is the form used by Smith (1939) to calculate k and L.
(c) Smith found that L depends on temperature and obtained the following values (what are
the units of L?):
t/T: 0 20 30 40 50
L: 0.11 0.20 0.25 0.32 0.42
Does L follow an Arrhenius relationship?
8-3 Brijnsted and Guggenheim (1927) in a study of the mutarotation of glucose report data on the
effect of the concentration of hydrogen ion and of a series of weak acids and their conjugate
bases. The reaction is first-order with respect to glucose, and the rate constant (kobs) is given
by equation 8.2-9 (assume koH- = lo4 L mole1 min-‘). Some of their data for three separate
sets of experiments at 18°C are as follows:
(1) 103cnao,/molL-’ 1 9.9 20 40
103k,b,lmin-’ 5.42 6.67 8.00 11.26
(2) CHCO~N~ = 0.125 mol L-i (constant)

103cHco,H/mol L-’ 5 124 250
1 O3 k&mine l 7.48 7.86 8.50

(3) CHCO~H = 0.005 mOl L-i (ConSkUlt)
lo3 cHC02Na/mol L- ’ 40 60 100 125
lo3 k,Jmin-’ 6.0 6.23 6.92 7.48

Calculate: (a) k, and kH+ ; (b) kHA; (c) kA- .
Note that HC104 is a strong acid and that HCOzH (formic acid) is a weak acid (K, =
2.1 x 10-4). At 18°C K, = 1.5 X 10-14.
8-4 Repeat part (b) of Example 8-2 for a CSTR, and comment on the result.
8-5 Propose a rate law based on the Langmuir-Hinshelwood model for each of the following het-
erogeneously catalyzed reactions:
(a) In methanol synthesis over a Cu-ZnO-CrzOa catalyst, the rate-controlling process appears
to be a termolecular reaction in the adsorbed phase:

CO.s+2H.s + CH30H.s+2s