The rate constant of a reaction at temperature $200 \ K$ is $10$ times less than the rate constant at $400 \ K.$ What is the activation energy $({E_a})$ of the reaction ($R = $ gas constant) (in $R$)?

Which of the following statements is in accordance with the Arrhenius equation?

The time required for $10 \%$ completion of a first order reaction at $298 \,K$ is equal to that required for its $25 \%$ completion at $308 \,K$. If the value of $A$ is $4 \times 10^{10} \,s^{-1}$,calculate $k$ at $318 \,K$ and $E_a$.

The rate of reaction becomes double when the temperature of the reaction is increased from $27\,^{\circ}C$ to $57\,^{\circ}C$. The activation energy of the reaction will be ....... $k\,cal$.

For a reaction having three steps, the overall rate constant is $K = \frac{k_1 k_2}{k_3}$. The values of $E_{a1}$, $E_{a2}$ and $E_{a3}$ (activation energies for each step) are $40$, $50$ and $60 \text{ kJ mol}^{-1}$ respectively. The overall activation energy $E_a$ of the reaction is:

Which statement is true with respect to a catalyst?