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

For a reaction,the rate constant is expressed as,$K = A \cdot e^{-40000/T}$. The energy of activation is ....... $cal$.

$A$ catalyst:

According to the Arrhenius equation,a plot of the logarithm of the rate constant $(\log \, k)$ versus which of the following yields a straight line?

The rate coefficient $(k)$ for a particular reaction is $1.3 \times 10^{-4} \ M^{-1} \ s^{-1}$ at $100 \ ^oC$ and $1.3 \times 10^{-3} \ M^{-1} \ s^{-1}$ at $150 \ ^oC$. What is the energy of activation $(E_a)$ (in $kJ \ mol^{-1}$) for this reaction? $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

For the reaction $A \rightarrow B$,the rate constant $k$ (in $s^{-1}$) is given by $\log_{10} k = 20.35 - \frac{2.47 \times 10^{3}}{T}$. The energy of activation in $kJ \, mol^{-1}$ is ..... . (Nearest integer) [Given: $R = 8.314 \, J \, K^{-1} \, mol^{-1}$]