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 $35^{\circ}C$)

Which of the following statements is correct regarding the Arrhenius equation and reaction kinetics?

At $27^{\circ}C$ in the presence of a catalyst, the activation energy of a reaction is lowered by $10 \ kJ \ mol^{-1}$. The logarithm ratio of $\frac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is .... (Consider that the frequency factor for both the reactions is the same)

The rate constant $(K')$ of one reaction is double the rate constant $(K'')$ of another reaction. What is the relationship between the corresponding activation energies of the two reactions (${E_a}'$ and ${E_a}''$)?

Activation energy is given by the formula

For two reactions,the values of the pre-exponential factor are the same. However,the difference between their activation energy values is $24.9 \, kJ \, mol^{-1}$. The ratio of their rate constants at $300 \, K$ is ....