The rate constant for a first order reaction at $300\, ^\circ C$ for which $E_a$ is $35\, kcal\, mol^{-1}$ and frequency constant $(A)$ is $1.45 \times 10^{11} s^{-1}$ will be:

For an exothermic reaction $A \rightarrow B$,the activation energy of $A$ is $17 \, kJ/mol$. The heat of reaction is $40 \, kJ$. Calculate the activation energy for the reverse reaction $B \rightarrow A$.

According to the Arrhenius equation,which of the following statements are correct?
$(A)$ $A$ high activation energy usually implies a fast reaction.
$(B)$ Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
$(C)$ Higher the magnitude of activation energy,stronger is the temperature dependence of the rate constant.
$(D)$ The pre-exponential factor is a measure of the rate at which collisions occur,irrespective of their energy.

Assertion $(A)$ : $A$ catalyst increases the rate of a reaction.
Reason $(R)$ : In presence of a catalyst, the activation energy of the reaction increases.
The correct answer is

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 $E_a$.

For the reaction $A_2 + B_2 \rightleftharpoons 2AB$,the activation energies for the forward and backward reactions are $180 \, kJ \, mol^{-1}$ and $200 \, kJ \, mol^{-1}$ respectively. In the presence of a catalyst,the activation energy for both (forward and backward) reactions decreases by $100 \, kJ \, mol^{-1}$. What will be the enthalpy change $(\Delta H)$ for the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of a catalyst in $kJ \, mol^{-1}$?