The rate constant of a reaction at $25\,^oC$ is $1 \times 10^{-3}\,s^{-1}$. If the rate of the reaction doubles when the temperature is increased to $35\,^oC$,the activation energy of the reaction is .......... $kJ\, mol^{-1}$.

$A \rightarrow B$. The molecule $A$ changes into its isomeric form $B$ following first-order kinetics at a temperature of $1000 \ K$. If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \ kJ \ mol^{-1}$ and the frequency factor is $10^{20} \ s^{-1}$,the time required for $50 \%$ of molecules of $A$ to become $B$ is $..............$ picoseconds (nearest integer). $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$

The time required for $10 \%$ completion of a first order reaction at $298 \,K$ is equal to that required for its $25 \%$ completion at $308 \,K$. If the value of $A$ is $4 \times 10^{10} \,s^{-1}$,calculate $k$ at $318 \,K$ and $E_a$.

Plots showing the variation of the rate constant $k$ with temperature $T$ are given below. The plot that follows Arrhenius equation is

The rate constant of a reaction is given by $k = P Z e^{-E_{a} / R T}$ under standard notation. In order to speed up the reaction,which of the following factors has to be decreased?

For the reaction $C_2H_5I + OH^- \rightarrow C_2H_5OH + I^-$,the rate constants at $30^\circ C$ and $60^\circ C$ are $0.325$ and $6.735 \ L \ mol^{-1} \ s^{-1}$ respectively. The value of activation energy $(E_a)$ is .......... calories.