Problem Set 4

1. The presence of substance C seems to increase the rate of reaction of A and B, A + B → AB

We suspect that C acts catalytically by combining with one of the reactants to form an intermediate, which then reacts further. From the rate data in Table 4.1 suggest a mechanism and rate equation for this reaction. [k1 = 1; k2 = 100]

[A] [B] [C] rAB 1 3 0.02 9 3 1 0.02 5 4 4 0.04 32 2 2 0.01 6 2 4 0.03 20 1 2 0.05 12

2. Gaseous reactant A diffuses through a gas film and reacts on the surface of a solid according to a reversible first-order rate,

−r”A = k” (CAs – CAe)

where CAe is the concentration of A in equilibrium with the solid surface. Develop an expression for the rate of reaction of A accounting for both the mass transfer and reaction steps. [−r”A = k(CAs – CAe) for k−1 = k”−1 + kg

−1]

3. In slurry reactors, pure reactant gas is bubbled through liquid containing suspended catalyst particles. Let us view these kinetics in terms of the film theory, as shown in Fig. 1. Thus, to reach the surface of the solid, the reactant which enters the liquid must diffuse through the liquid film into the main body of liquid, and then through the film surrounding the catalyst particle. At the surface of the particle, reactant yields product according to first-order kinetics. Derive an expression for the rate of reaction in terms of these resistances. [−r = k CAi ; k−1 = (kil·ai)−1 + (kls·as)−1 + ks

−1]

Fig. 1

4. Consider the autocatalytic reaction

A → B k1

B + A → C + A k2

Assuming that the steady state approximation is valid and that the initial concentration of A is [A0] and that those of B and C are zero, develop expressions for [B], [A], and [C].