What is the relationship between the temperature $T$ and the activation energy $E_a$ in the Arrhenius equation?

Subtract $(i)$ $\ln \, k_1 = - \frac{E_a}{R T_1} + \ln A$ and $(ii)$ $\ln \, k_2 = - \frac{E_a}{R T_2} + \ln A$ and write the resulting equation.

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: $R = 8.314 \, J \, K^{-1} \, mol^{-1}$]

For the decomposition reaction of $N_2O_5$,the slope of the graph of $\log K$ versus $1/T$ is $-1.2 \times 10^4 \ K$. Calculate the activation energy $(E_a)$ of the reaction.

Calculate the activation energy of a reaction,whose rate constant doubles on raising the temperature from $300 \ K$ to $600 \ K$.

Based on the provided energy profile diagram,how many steps are in the mechanism of the reaction?