The activation energys of two reaction are $E_1 and E_2 (E_1 \gt E_2)$ . If the temperature of the system is increased from $ T_1 to T_2 $ , the rate constant of the reaction changes from $K_1 to K_2^1 $ in the first reaction and $ K_2 to K_2^1$ in second reaction, predict which of the following expression is correct ?
$ { K_1 ^ 1 \over K_1 } \gt { K_2 ^1 \over K_2 } $ $ log { K_1 ^1 \over K_1 } = { E_1 \over 2.303 R } \left[ { T_2 -T_1 \over T_1 T_2 } \right] , log { K_2^1 \over K_2 } = { E_2 \over 2.303 R } [ {T_2 - T_1 \over T_1 T_2 } ] $ $ Since E_1 \gt E_2 $ $ \therefore log { K_1 ^1 \over K_1 } \div log { K_2 ^1 \over K_2 } \gt 1 or { K_1^1 \over K_1 } \gt { K_2 ^1 \over K_2 }$