In the reaction of decomposition of reactant $A$ into product,the rate constant is $4.5 \times 10^{-3} \ s^{-1}$ at $283 \ K$ temperature and energy of activation is $60 \ kJ \ mol^{-1}$. At which temperature will the value of rate constant $K$ be $3 \times 10^{10} \ s^{-1}$ (in $K$)?

If the rate constants of a reaction at $500 \ K$ and $700 \ K$ are $0.002 \ s^{-1}$ and $0.06 \ s^{-1}$,respectively,the value of activation energy is $(R=8.314 \ J \ mol^{-1} \ K^{-1}, \log 3=0.477)$.

The rate constant for the decomposition of hydrocarbons is $2.418 \times 10^{-5} \, s^{-1}$ at $546 \, K$. If the energy of activation is $179.9 \, kJ / mol$,what will be the value of the pre-exponential factor?

At $27^{\circ}C$ in the presence of a catalyst, the activation energy of a reaction is lowered by $10 \ kJ \ mol^{-1}$. The logarithm ratio of $\frac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is .... (Consider that the frequency factor for both the reactions is the same)

Catalyst $A$ reduces the activation energy for a reaction by $10 \ kJ \ mol^{-1}$ at $300 \ K$. The ratio of rate $\frac{k_{T, \text{Catalysed}}}{k_{T, \text{Uncatalysed}}}$ is $e^{x}$. Find the value of $x$ [nearest integer].
[Assume that the pre-exponential factor is same in both the cases.
Given $R = 8.31 \ J \ K^{-1} \ mol^{-1}$]

Which of the following graphs between the rate constant $(k)$ and temperature $(T)$ represents the Arrhenius equation?