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Mechanism of Catalytic Reaction

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Develop the overall rate equation for the catalytic reaction A + B → C. The effect of diffusive mass transfer may be neglected. The following steps may be considered:

- Adsorption of A and B
- Surface reaction of adsorbed A and adsorbed B

For the cases

- The product C is not adsorbed
- The product C is adsorbed

Assume step (b) is the rate controlling step.

Calculations:

**(i) Product C is not adsorbed**:

Adsorption of A and B:

A + s → A.s

B + s → B.s

Where s is the vacant site.

Rate of adsorption of A = r_{aA} = k_{aA} C_{A} θ_{V}

Rate of desorption of A = r_{dA} = k_{dA} θ_{A}

At equilibrium r_{aA} = r_{dA}

Therefore,

k_{aA} C_{A}θ_{V} = k_{dA}θ_{A
}

θ_{A}* *= K_{A} C_{A}θ_{V} → 1
where K_{A} = k_{aA}/k_{dA}

Similarly, for B

θ_{B}* *= K_{B} C_{B}θ_{V} → 2
θ_{V} = fraction of unoccupied sites = 1 - θ_{A} - θ_{B}
substituting for θ_{A} and θ_{B} from equn.1 and 2,

θ_{V} = 1 - K_{A} C_{A}θ_{V} - K_{B} C_{B}θ_{V
}i.e.,

θ_{V} = 1 / (1 + K_{A} C_{A} + K_{B} C_{B})
Surface reaction:

A.s + B.s → C + 2s

-r_{A} = k θ_{A}θ_{B} → 3

i.e., the overall rate equation is,

-r_{A} = k K_{A}K_{B }C_{A}C_{B} / (1 + K_{A} C_{A} + K_{B} C_{B})^{2}

(ii) Product C is adsorbable:

*Adsorption of A and B:*

*
*A + s → A.s

B + s → B.s

Reaction between adsorbed A and adsorbed B:

A.s + B.s → C.s + s

Desorption of C:

C.s → C + s

For the above steps and some similarity to the part (i)

θ_{A}* *= K_{A} C_{A}θ_{V
}θ_{B}* *= K_{B} C_{B}θ_{V
}-r_{A} = k θ_{A}θ_{B }→ 4

and for the desorption of C:

r_{dC} = k_{dC} θ_{C}

adsorption of C:

r_{aC} = k_{aC} C_{C}θ_{V}

For equilibrium desorption of C,

r_{dC} = r_{aC}

Therefore,

k_{dC} θ_{C} = k_{aC} C_{C}θ_{V}

θ_{C} = K_{C} C_{C}θ_{V
}where K_{C} = k_{aC}/k_{dC}

Here, θ_{V} = 1 - θ_{A} - θ_{B} - θ_{C}

Therefore,

θ_{V} = 1 / (1 + K_{A}C_{A} + K_{B}C_{B} + K_{C}C_{C })
and θ_{A} = K_{A}C_{A} / (1 + K_{A}C_{A} + K_{B}C_{B} + K_{C}C_{C })

θ_{B} = K_{B}C_{B} / (1 + K_{A}C_{A} + K_{B}C_{B} + K_{C}C_{C })
substituting for θ_{A} and θ_{B} in equn.4,

-r_{A} = k K_{A}K_{B }C_{A}C_{B} / (1 + K_{A} C_{A} + K_{B} C_{B} + K_{C} C_{C})^{2}

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Last Modified on: 04-Feb-2022

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