Page 188 - Introduction to chemical reaction engineering and kinetics

170 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws

Similarly, from 7.3-9 and -13,

kcM “P2 CM(kCMT)2 (7.3-14)
CP, = 1 + kCMT = (1 + kCMT)2

Proceeding in this way, from 7.3-10, we obtain in general:

CM( kc&-l
CP, = = cM[l + (kcM+l]l-’ (7.3-15)
(1 + kCMT)‘-l
Thus, the product distribution (distribution of polymer species P,) leaving the CSTR
can be calculated, if cMO, k, and T are known.
For a BR or a PFR in steady-state operation, corresponding differential equations
can be established to obtain the product distribution (problem 7-15).

7.4 PROBLEMS FOR CHAPTER 7

7-1 The rate of production of urea, (NH&CO, from ammonium cyanate increases by a factor of
4 when the concentration of ammonium cyanate is doubled. Show whether this is accounted
for by the following mechanism:

NH,+ + CNO- SNHa + HNCO; fast
NH~ + HNCO A(NH,)~co; ~10~

Note that ammonium cyanate is virtually completely dissociated in solution.
7-2 What rate law (in terms of ro,) is predicted for the reaction

from the following mechanism:

0+0~+0
1
0’ + 033202

Clearly state any assumption(s) made.
7-3 The gas-phase reaction between nitric oxide and hydrogen, which can be represented stoi-
chiometrically by

2N0 + 2H2 = N2 + 2H20

is a third-order reaction with a rate law given by

(-rN0) = kioC;oC~2

(a) If the species (NO)2 and Hz02 are allowed as reactive intermediates, construct a reaction
mechanism in terms of elementary processes or steps. Clearly indicate any features such
as equilibrium, and “fast” and rate-determining (“slow” ) steps. Use only bimolecular
steps.
(b) Derive the rate law from the mechanism constructed to show that it is consistent with the
observed order of reaction.
(c) Express kNo in terms of the constants in the rate law derived.