The rate of surface reaction is
Since we cannot readily measure the concentrations of the adsorbed species, we must utilize the adsorption and desorption steps to eliminate CC · S and CB · S from this equation.
From the adsorption rate expression in Equation (10-25) and the condition that kA and kD are very large by comparison with kS when surface reaction is limiting (i.e., rAD/kA ≃ 0),12 we obtain a relationship for the surface concentration for adsorbed cumene:
CC · S = KCPCCυ
In a similar manner, the surface concentration of adsorbed benzene can be evaluated from the desorption rate expression [Equation (10-29)] together with the approximation:
Substituting for CB · S and CC · S in Equation (10-26) gives us
where the thermodynamic equilibrium constant was used to replace the ratio of surface reaction and adsorption constants, i.e.,
The only variable left to eliminate is Cυ:
Ct = Cυ + CB · S + CC · S
Substituting for concentrations of the adsorbed species, CB · S, and CC · S yields
The initial rate of reaction is
Figure 10-16 shows the initial rate of reaction as a function of the initial partial pressure of cumene for the case of surface reaction limiting.
Figure 10-16. Surface-reaction-limited.
At low partial pressures of cumene
and we observe that the initial rate will increase linearly with the initial partial pressure of cumene:
At high partial pressures
and Equation (10-45) becomes
and the initial rate is independent of the initial partial pressure of cumene.
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