Write the Arrhenius equation in the form $\ln \, k = -\frac{E_a}{RT} + \ln \, A$.

Consider the following transformation involving first order elementary reactions in each step at constant temperature as shown below.
$A + B \underset{\text{Step } 3}{\overset{\text{Step } 1}{\rightleftharpoons}} C \xrightarrow{\text{Step } 2} P$
Some details of the above reaction are listed below.

Step	Rate constant $(s^{-1})$	Activation energy $(kJ \ mol^{-1})$
$1$	$k_1$	$300$
$2$	$k_2$	$200$
$3$	$k_3$	$Ea_3$

If the overall rate constant of the above transformation $(k)$ is given as $k = \frac{k_1 k_2}{k_3}$ and the overall activation energy $(E_a)$ is $400 \ kJ \ mol^{-1}$,then the value of $Ea_3$ is $\qquad$ $kJ \ mol^{-1}$ (nearest integer).

Which among the following equations represents the Arrhenius equation?

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:

For a first order reaction,a plot of $\ln k$ ($y$-axis) and $\frac{1}{T}$ ($x$-axis) gave a straight line with a slope equal to $-10^3 \ K$ and an intercept equal to $2.303$ (on $y$-axis). What is the activation energy ($E_a$ in $kJ \ mol^{-1}$) of the reaction? (Given $R = 8.314 \ J \ mol^{-1} \ K^{-1}$)

Which one of the following is true for an exothermic reaction $A \rightleftharpoons B$, if $E_f$ and $E_b$ are the activation energies of forward and backward reactions respectively?