The Arrhenius equation for trans ispmerisation of `2`-butene and `2`-butene nitrile are given as follows:
(a) For `2`-butene `CH_(3)CH = CHCH_(3)K(S^(-1)) = 10^(13.8)`
(b) For `2`-butene nitrile `CH_(3)CH = CH.CNK'(S^(-1))`
`= 10^(11) exp^(-214.5 kJ "mol"-1//Rt)`
The temperature at which `K = K'`

Options

A. `913.87 K`
B. `533.43 K`
C. `1000.02 K`
D. `407.05 k`

Answer

A

Explanation

`because K = K'`
`10^(13.8)exp^(-263.5 "kJ mol"^(-1)//RT) = 10^(11) exp^(-214.5 "kJ mol"^(-1)//RT)`
or `10^(13.8-11) = exp([(-214.5) - (-263.5)]kJ mol^(-1))/(8.314 xx 10^(-3) kJ mol^(-1) K^(@) xx T)`
or `630.957 = exp(5.893 xx 10^(3))/(T)`
`:. 2.303 log 630.957 = (5.893 xx 10^(3))/(T)`
`:. T = (5.893 xx 10^(3))/(2.303 xx 2.8) = 913.87 K`