Page 129 - Introduction to chemical reaction engineering and kinetics

5.7 Problems for Chapter 5 111

(a) Consider EA to be defined by EJ, = RT2d In kldT, where k is the overall rate constant.
(b) Consider EA to be defined by k = A exp( -EiIRT), where A is the overall pre-exponential
factor.
(c) If there is any difference between EL and Ei, how are they related?
5-10 For the kinetics scheme A 3 B -% C, each step being first-order, for reaction occurring in a
constant-volume batch reactor (only A present initially),
(a) At what time, 2, in terms of kl and k2, are CA and cn equal (other than t + to), and what
is the condition for this to happen?
(b) What is the value oft,,, when kl = k2?
(c) Show that cn has an inflection point at 2t,,,.
(d) Calculate kl t,,, and CB,,,~~/CA~ for each of the cases (i) K = kzlkl = 10, (ii) K = 1, and
(iii) K = 0.1.
(e) From the results in (d), describe how t,,, and CB,&CA~ change with decreasing K.
5-11 The following liquid-phase reactions take place in a CSTR operating at steady state.

2A + B +C; rc = klci
A + B + 2D; ro = 2k2cAcg

The inlet concentration of A is 2.50 mol L-l. The outlet concentrations of A and C are respec-
tively 0.45 mol L-l and 0.75 mol L-l. Assuming that there is no B, C, or D in the feed, and
that the space time (7) is 1250 s, calculate:
(a) The outlet concentrations of B and D; and
(b) kl and k2.
5-12 The following data are for the kinetics scheme:

A + B + C+E;(-Yn) = klCACB; kl = ?
A + C -+ D + E; rn = k2cAcc; k2 = 3.0 X 10m3 L mol-’ rnin-’

tlmin Concentration/m01 L-’

CA CB cc CD CE
0 5.0 0.040 ? 0 0
23 - 0.020 ? - -
M - 0 0 0.060 ?

Assuming that the reactions occur at constant Tin a constant-volume batch reactor, calculate:
(a) The concentration of C at time zero and the concentration of E at time m;
(b) The second-order rate constant kl; and
(c) The concentration of C at time 23 min.

5-13 Consider a liquid-phase reaction taking place in a CSTR according to the following kinetics
scheme:

A + B + C; rn = klCA
A + C + 2D; rn = 2k2CACc
The inlet concentration of A is CA0 = 3 mol L-l, and there is no B, C, or D in the feed. If, for a
space time r = 10 min, the outlet concentrations of A and B are CA = 1.25 and cn = 1.50 mol
L-’ at steady-state, calculate the values of (a) kl, (b) k2, (c) CC, and (d) co (not necessarily in
the order listed). Include the units of kl and k2 in your answer.