Chapter 10: Catalysis and Catalytic Reactors

Deriving an Expression for the Concentration of Species A on the Surface

Beginning with our expression for the rate of adsorption:

\( r_{AD} = k_A P C_t \left[ y A f_0 - \frac{f_{A \cdot S}}{P K_A} \right] \)

If the surface reaction is limiting, then:

\( \frac{r_{AD}}{k_A P C_t} \sim 0 = y A f_0 - \frac{f_{A \cdot S}}{P K_A} \)

\( y A f_0 = \frac{f_{A \cdot S}}{P K_A} \)

\( f_{A \cdot S} = y A f_0 P K_A \)

\( f_{A \cdot S} = f_0 P K_A \)

Recall that:

\( f_{A \cdot S} = \frac{C_{A \cdot S}}{C_t} \)

and

\( f_0 = \frac{C_0}{C_t} \)

Then:

\( \frac{C_{A \cdot S}}{C_t} = \frac{C_0 K_A P_A}{C_t} \)

Multiply both sides by \( C_t \) and we're left with:

\( C_{A \cdot S} = C_0 K_A P_A \)

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