Activation energy $(E_a)$ and rate constants $(k_1)$ and $(k_2)$ of a chemical reaction at two different temperatures $(T_1)$ and $(T_2)$ are related by

The rate of a chemical reaction doubles for every $10^\circ \text{C}$ rise in temperature. If the temperature is increased by $50^\circ \text{C}$,the rate of reaction will increase by a factor of ........

Consider an endothermic reaction $X \to Y$ with the activation energies $E_b$ and $E_f$ for the backward and forward reactions,respectively. In general:

$A \rightarrow B$. 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). $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$

In the plot of $\ln k$ versus $\frac{1}{T}$,what do the slope and intercept represent?

Thermodynamic feasibility of the reaction alone cannot decide the rate of the reaction. Explain with the help of one example.