The following equation is obtained for a first order reaction at $300 \ K$.
$\log_{10} \frac{k}{A} = 0.00174$
What is the activation energy (in $J \ mol^{-1}$) of the reaction?
$(R = 8.314 \ J \ mol^{-1} \ K^{-1})$

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 enthalpy $(H)$ of an elementary exothermic reaction,$A \rightleftharpoons B$ is schematically plotted against the reaction coordinate. The plots in the presence and absence of a catalyst are shown in dashed and solid lines,respectively. Identify the correct plot for the reaction.

Consider the following reaction that proceeds from $A$ to $B$ in three steps as shown in the energy profile diagram. Choose the correct values for the following parameters:
$1$. Number of intermediates
$2$. Number of activated complexes
$3$. Rate determining step

$A$ catalyst lowers the activation energy for a certain reaction from $83.314 \, kJ \, mol^{-1}$ to $75 \, kJ \, mol^{-1}$ at $500 \, K$. What will be the rate of reaction as compared to the uncatalysed reaction? Assume other things being equal.

$A$ rise in temperature increases the velocity of a reaction. It is because it results in