Mechanism of Catalytic Reaction

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:

1. Adsorption of A and B
2. Surface reaction of adsorbed A and adsorbed B

For the cases

1. The product C is not adsorbed
2. 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_Aθ_V = k_dAθ_A

θ_A = K_A C_Aθ_V → 1

where K_A = k_aA/k_dA

Similarly, for B

θ_B = K_B C_Bθ_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_Aθ_V - K_B C_BθV

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_Aθ_B → 3

i.e., the overall rate equation is,

-r_A = k K_AK_B C_AC_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_AθV

θ_B = K_B C_BθV

-r_A = k θ_Aθ_B → 4

and for the desorption of C:

r_dC = k_dC θ_C

adsorption of C:

r_aC = k_aC C_Cθ_V

For equilibrium desorption of C,

r_dC = r_aC

Therefore,

k_dC θ_C = k_aC C_Cθ_V

θ_C = K_C C_CθV

where K_C = k_aC/k_dC

Here, θ_V = 1 - θ_A - θ_B - θ_C

Therefore,

θ_V = 1 / (1 + K_AC_A + K_BC_B + K_CC_C )

and θ_A = K_AC_A / (1 + K_AC_A + K_BC_B + K_CC_C )

θ_B = K_BC_B / (1 + K_AC_A + K_BC_B + K_CC_C )

substituting for θ_A and θ_B in equn.4,

-r_A = k K_AK_B C_AC_B / (1 + K_A C_A + K_B C_B + K_C C_C)²