$A$ reaction having equal energies of activation for forward and reverse reactions has

For a first-order reaction at $300 \, ^\circ C$,the activation energy is $35 \, kcal \, mol^{-1}$ and the frequency factor is $1.45 \times 10^{11} \, s^{-1}$. Calculate the rate constant.

The rate constant for a chemical reaction taking place at $500 \ K$ is expressed as $K = A \ e^{-1000}$. The activation energy of the reaction is:

For the reaction,$A \rightleftharpoons B$,$E_a = 50 \ kJ \ mol^{-1}$ and $\Delta H = -20 \ kJ \ mol^{-1}$. When a catalyst is added,$E_a$ decreases by $10 \ kJ \ mol^{-1}$. What is the $E_a$ for the backward reaction in the presence of the catalyst?

What is the value of the slope if $\log_{10} K$ ($y$-axis) is plotted versus $1/T$ ($x$-axis) for the Arrhenius equation?

Consider the following graph of the kinetic energy distribution among molecules at temperature $T.$ If the temperature is increased,how would the resulting graph differ from the one above $:-$