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 $R = 8.314 \ J \ mol^{-1} \ K^{-1}$)

For an endothermic reaction $X \rightarrow Y$,the activation energies for the forward and backward reactions are $E_f$ and $E_b$ respectively. Then,in general:

Which of the following would give a linear plot?
($k$ is the rate constant of an elementary reaction and $T$ is temperature in absolute scale)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: $A$ reaction can have zero activation energy.
Reason $R$: The minimum extra amount of energy absorbed by reactant molecules so that their energy becomes equal to threshold value,is called activation energy.
In the light of the above statements,choose the correct answer from the options given below:

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 $E_a$.

The rate law for the reaction $2NO + Cl_2 \rightarrow 2NOCl$ is given by $\text{rate} = k[NO]^2[Cl_2]$. Under what conditions will the value of the rate constant $k$ increase?