What is the activation energy $(kJ \, mol^{-1})$ for a reaction if its rate constant doubles when the temperature is raised from $300 \, K$ to $400 \, K$ ? $(R = 8.314 \, J \, mol^{-1} \, K^{-1})$

The rate constant for the reaction,$COCl_{2(g)} \longrightarrow CO_{(g)} + Cl_{2(g)}$ is given by $\ln[k / (min^{-1})] = -11067 / T(K) + 31.33$. The temperature at which the rate of this reaction will be doubled from that at $25^{\circ} C$ is $..... \, ^{\circ} C$.

For a reaction,the temperature coefficient is $2$. Calculate the activation energy $(E_a)$ in $kJ/mol$. (Assume the temperature range is $25^{\circ}C$ to $35^{\circ}C$)

The decomposition of ethane,$\frac{d[C_2H_6]}{dt} = k[C_2H_6]$,proceeds through a complex mechanism,which includes $5$ steps. The overall rate constant $(k)$ is expressed as $k = \frac{k_1 k_2 k_3}{k_2 k_5}$,where $k_1, k_2, k_3, k_4, k_5$ are the rate constants of the $5$ steps. If the activation energies of the steps are $E_1 = 1E, E_2 = 2E, E_3 = 3E, E_4 = 4E, E_5 = 5E$,where $E = 20 \ kJ/mol$,find the overall activation energy of the decomposition.

When the temperature changes from $300 \ K$ to $310 \ K$,the rate of the reaction doubles. The activation energy of the reaction is ..... $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1} \text{ and } \log 2 = 0.301)$

In a reaction,for every $10\,^{\circ}C$ rise of temperature,the rate is doubled. If the temperature is increased from $10\,^{\circ}C$ to $100\,^{\circ}C,$ the rate of the reaction will become $.......$ times.