The rate constant of a reaction increases by five times on

Question

The rate constant of a reaction increases by five times on increase in temperature from 27

^\circ

C to 52

^\circ

C. The value of activation energy in kJ mol^{$-$ 1} is _________. (Rounded off to the nearest integer)

[R = 8.314 J K^{$-$ 1}mol^{$-$ 1}]

DivineJEE · Accepted Answer

T_(1) = (273 + 27) = 300 K, T_(2) = (273 + 52) = 325 KGiven, temperature coefficient of the reaction,alpha _T = K_325 / K_300 = 5log K_T_2 / K_T_1 = E_a / 2.303R x ( T_2 - T_1 / T_1T_2 )log K_325 / K_300 = E_a / 2.303 x 8.314( 325 - 300 / 300 x 325 )log 5 = E_a / 2.303 x 8.319 x 25 / 300 x 325E_(a) = 52194.78 J mol^(-)= 52.194 kJ mol^(-1) = 52 kJ mol^(-1)

Explanation

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