The rate constant of a reaction is increased by 4 times after addition of catalyst to the reaction mixture at the same temperature of $27^{\circ} \mathrm{C}$. The change in the activation energy of this reaction is (Take $\ln (1 / 4)=-1386, R=8.314$ )

Half-life periods for a reaction at initial concentrations of 0.1 M and 0.01 M are 5 and 50 minutes, respectively. The order of reaction is

If the definition of the temperature coefficient of the reaction holds good for a reaction between $27^{\circ} \mathrm{C}$ and $37^{\circ} \mathrm{C}$, the activation energy for the reaction in $\mathrm{kJ} \mathrm{mol}^{-1}$ is

The half-life of a first order reaction varies with temperature according to