For a reaction,$A \rightarrow B$,the average energies of $A$ and $B$ are $30 \ kcal/mol$ and $60 \ kcal/mol$ respectively. The energy of activation for the backward reaction is $93 \ kcal/mol$. The energy of activation for the forward reaction is:

The number of given statement/s which is/are correct is $.....$.
$(A)$ The stronger the temperature dependence of the rate constant,the higher is the activation energy.
$(B)$ If a reaction has zero activation energy,its rate is independent of temperature.
$(C)$ The stronger the temperature dependence of the rate constant,the smaller is the activation energy.
$(D)$ If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.

The rate constant of a reaction increases by five times on increase in temperature from $27^{\circ} C$ to $52^{\circ} C$. The value of activation energy in $kJ \, mol^{-1}$ is $....$ . (Rounded-off to the nearest integer) $[R = 8.314 \, J \, K^{-1} \, mol^{-1}]$

The rate constant of a reaction is given by $k = P Z e^{-E_{a} / R T}$ under standard notation. In order to speed up the reaction,which of the following factors has to be decreased?

The rate constants of a reaction at $500 \, K$ and $700 \, K$ are $0.02 \, s^{-1}$ and $0.07 \, s^{-1}$ respectively. Calculate the values of $E_{a}$ and $A$.

The activation energy of one of the reactions in a biochemical process is $532611 \, J \, mol^{-1}$. When the temperature falls from $310 \, K$ to $300 \, K$,the change in rate constant observed is $k_{300} = x \times 10^{-3} \, k_{310}$. The value of $x$ is $.....$ [Given: $\ln 10 = 2.3$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$]