Activation energy is given by the formula

Activation energy is defined as:

The half-life periods of a first order reaction at $300 \ K$ and $400 \ K$ are $50 \ s$ and $10 \ s$ respectively. The activation energy of the reaction in $kJ \ mol^{-1}$ is $(\log 5 = 0.70)$

For a reaction,the temperature increases from $10\,^\circ\text{C}$ to $50\,^\circ\text{C}$. The rate of the reaction will increase by a factor of ........

It has been found that for a chemical reaction with a rise in temperature by $9 \, K$,the rate constant gets doubled. Assuming a reaction to be occurring at $300 \, K$,the value of activation energy is found to be $...... \, kJ \, mol^{-1}$. [nearest integer]
(Given $\ln 10 = 2.3, R = 8.3 \, J \, K^{-1} \, mol^{-1}, \log 2 = 0.30$ )

The rate of a chemical reaction doubles for every $10\,^{\circ}C$ rise of temperature. If the temperature is raised by $50\,^{\circ}C,$ the rate of the reaction increases by about ......... times.