Catalyst A reduces the activation energy for a reaction by 10 kJ mol1 at 300K. The ratio of rate constants, k T , C a t a l y s e d k T , U n c a t a l y s e d i s e x . The value of x is_________. (nearest integer) [Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 JK1 mol1]

K c a t = A e − ( E a ) c a t R T a n d K u n c a t = A e − ( E a ) u n c a t R T K c a t K u n c a t = e ( E a ) u n c a t − ( E a ) c a t R T = e 1 0 * 1 0 0 0 8 . 3 1 4 * 3 0 0 = e 4 . 0 0 9 = e x ∴ x = 4

Catalyst A reduces the activation energy for a reaction by 10 kJ mol1 at 300K. The ratio of rate constants, $\frac{k_{T}, C a t a l y s e d}{k_{T}, U n c a t a l y s e d} i s e^{x} .$ $\frac{_{}}{_{}}^{}$ The value of x is_________. (nearest integer)

[Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 JK1 mol1]

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Raj Pandey | Contributor-Level 9

5 months ago

$K_{c a t} = A e^{-} \frac{{(E a)}_{c a t}}{R T} a n d K_{u n c a t} = A e^{-} \frac{{(E a)}_{u n c a t}}{R T}$

$\frac{K_{c a t}}{K_{u n c a t}} = e^{\frac{{(E a)}_{u n c a t} - {(E a)}_{c a t}}{R T}} = e^{\frac{10 * 1000}{8.314 * 300}} = e^{4.009} = e^{x}$

$∴ x = 4$

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