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:
For the cases
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 = raA = kaA CA θV
Rate of desorption of A = rdA = kdA θA
At equilibrium raA = rdA
Therefore,
kaA CAθV = kdAθA
θA = KA CAθV → 1where KA = kaA/kdA
Similarly, for B
θB = KB CBθV → 2 θV = fraction of unoccupied sites = 1 - θA - θBsubstituting for θA and θB from equn.1 and 2,
θV = 1 - KA CAθV - KB CBθVi.e.,
θV = 1 / (1 + KA CA + KB CB)Surface reaction:
A.s + B.s → C + 2s
-rA = k θAθB → 3
i.e., the overall rate equation is,
-rA = k KAKB CACB / (1 + KA CA + KB CB)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)
θA = KA CAθV θB = KB CBθV-rA = k θAθB → 4
and for the desorption of C:
rdC = kdC θC
adsorption of C:
raC = kaC CCθV
For equilibrium desorption of C,
rdC = raC
Therefore,
kdC θC = kaC CCθV
θC = KC CCθVwhere KC = kaC/kdC
Here, θV = 1 - θA - θB - θC
Therefore,
θV = 1 / (1 + KACA + KBCB + KCCC )and θA = KACA / (1 + KACA + KBCB + KCCC )
θB = KBCB / (1 + KACA + KBCB + KCCC )substituting for θA and θB in equn.4,
-rA = k KAKB CACB / (1 + KA CA + KB CB + KC CC)2
Last Modified on: 30-Apr-2024
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