Chapter 10: Catalysis and Catalytic Reactors
Deriving an Expression for rs
\( r_{AD} \sim \frac{k_A P_C}{K_A P_C} = C_{C \cdot S} = K_C P_C C_0 \)
\( r_D \sim \frac{k_D P_B C_0}{K_D} = C_{B \cdot S} = K_B P_B C_0 \)
\( r_S = C_0 k_S K_C \left[ P_C - \frac{P_B P}{K_C K_S} \right] \)
A site balance yields:
\( C_t = C_0 + C_{C \cdot S} + C_{B \cdot S} \)
\( C_t = \left( 1 + K_C P_C + K_B P_B \right) C_0 \)
Grouping the equilibrium constants together into one constant, \( K_P \):
\( K_P = \frac{K_C K_S}{K_B} \)
And grouping the remaining constants together as a single constant, \( k \):
\( r_S = \frac{k C_t K_C \left[ P_C - \frac{P_B P}{K_P} \right]}{1 + K_C P_C + K_B P_B} \)
We get:
\( r_S = \frac{k \left[ P_C - \frac{P_B P}{K_P} \right]}{1 + K_C P_C + K_B P_B} \)