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The rate constant for the first order de...

The rate constant for the first order decompoistion of a certain reaction is described by the equation
`log k (s^(-1)) = 14.34 - (1.25 xx 10^(4)K)/(T)`
(a) What is the energy of activation for the reaction?
(b) At what temperature will its half-life periof be `256 min`?

Text Solution

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(i) `E_(a) =239.33" kJ/mol"` (ii) 669 K
(i) The Arrhenius equation is log k = log `A -(E_(a))/(2.303 RT)`
Comparing with the given equation : `1.25xx10^(4) =(E_(a))/(2.303 R) rArr E_(a) =239.33" kJ mol"^(-1)`
(ii) When half-life = 256 min, `k =("In 2")/(t_(1//2))=(0.693)/(256xx60) s^(-1) =4.5xx10^(-5) s^(-1)`
`rArr (1.25 xx 10^(4))/(T) =14.34 - log 4.5 xx10^(-5) =16.68 rArr T=(1.25xx10^(4))/(16.68) =669 K`
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