The equilibrium constant at $27\,^{\circ}C$ and $127\,^{\circ}C$ is $30$ and $40$ respectively. What will be the ratio of activation energy $(E_{a})_{f} / (E_{a})_{b}$?

For a reaction,given below is the graph of $\ln k$ vs $\frac{1}{T}$. The activation energy for the reaction is equal to $...... \ cal \ mol^{-1}$. (Nearest integer). (Given : $R = 2 \ cal \ K^{-1} \ mol^{-1}$)

For a reaction,the value of rate constant at $300 \ K$ is $6.0 \times 10^5 \ s^{-1}$. The value of Arrhenius factor $A$ at infinitely high temperature is

For a certain reaction,consider the plot of $\ln k$ versus $1/T$ given in the figure. If the rate constant of this reaction at $400 \ K$ is $10^{-5} \ s^{-1}$,then the rate constant at $500 \ K$ is:

The time taken for half of the initial amount of $N_2O_5$ to decompose is $12 \ min$ at $310 \ K$ and $2 \ hrs$ at $300 \ K$. The activation energy of the reaction in $kJ \ mol^{-1}$ is $\left(R=8.3 \ J \ K^{-1} \ mol^{-1}\right)$

For the reaction $A \rightleftharpoons B$,if $E_a$ is the activation energy of the forward reaction,then the activation energy of the backward reaction is: