For the reaction $A \to B$,$K_1 = 10^8 \, e^{-6000/8.34T}$ and for the reaction $P \to Q$,$K_2 = 10^{10} \, e^{-8000/8.34T}$. At what temperature $T$ will $K_1 = K_2$ (in $K$)?

For the equilibrium $A_{(g)} \rightleftharpoons B_{(g)}$,$\Delta H$ is $-40 \ kJ/mol$. If the ratio of the activation energies of the forward $(E_f)$ and reverse $(E_b)$ reactions is $\frac{2}{3}$,then:

What is the role of a catalyst in a catalytic reaction?

The variation of the rate constant with temperature is given by the Arrhenius equation $k = A e^{-E_a / (RT)}$. If $T \to \infty$,the rate constant $k$ will be equal to:

The activation energy for a reaction at the temperature $T \ K$ was found to be $2.303 \ RT \ J \ mol^{-1}$. The ratio of the rate constant to the Arrhenius factor is

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)