$A$ first order reaction is $50\%$ completed in $20\, \text{minutes}$ at $27\, ^oC$ and in $10\, \text{minutes}$ at $47\, ^oC$. The energy of activation of the reaction is ....... $Kcal$.

At $298 \text{ K}$ temperature,the activation energy for the reaction $x_2 + y_2 \rightarrow 2xy + 20 \text{ kJ}$ is $15 \text{ kJ}$. What will be the activation energy for the reaction $2xy \rightarrow x_2 + y_2$?

Calculate the rate constant of a first-order reaction having a pre-exponential factor $A = 1.6 \times 10^{13} \ s^{-1}$ and $\frac{E_a}{2.303 RT} = 21$.

At what temperature does the rate become double that at $300 \, K$ (in $, K$)? Given $\ln k = 10 - \frac{69 \, kJ}{RT}$.

The plot of $\log k_f$ versus $1 / T$ for a reversible reaction $A_{(g)} \rightleftharpoons P_{(g)}$ is shown. Pre-exponential factors for the forward and backward reactions are $10^{15} \ s^{-1}$ and $10^{11} \ s^{-1}$,respectively. If the value of $\log K$ for the reaction at $500 \ K$ is $6$,the value of $|\log k_b|$ at $250 \ K$ is $\qquad$ $[K = \text{equilibrium constant of the reaction}, k_f = \text{rate constant of forward reaction}, k_b = \text{rate constant of backward reaction}]$

The velocity of the chemical reaction doubles every $10^\circ C$ rise of temperature. If the temperature is raised by $50^\circ C$,the velocity of the reaction increases to about .......... times.