At $25\,^{\circ}C$,the values of rate constant,activation energy and Arrhenius constant of a reaction are $3 \times 10^{-4}\, s^{-1}$,$129\, kJ/mol$ and $2 \times 10^{15}\, s^{-1}$ respectively. The value of rate constant as $T \to \infty$ is

$A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
The curves $M$ and $N$ represent the variation of energy with reaction coordinate for the reaction in absence and presence of catalyst.
Which value represents the activation energy $(E_a)$ for the backward reaction in the presence of catalyst?

The rate of a reaction doubles when its temperature changes from $300 \ K$ to $310 \ K$. The activation energy of such a reaction will be ........ $kJ/mol$.

For a first order reaction,the rate of reaction is $2.4 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$ at $27 \ ^\circ C$. The activation energy of the reaction is $24.942 \ kJ \ mol^{-1}$. The rate of reaction at $327 \ ^\circ C$ is ....... $mol \ L^{-1} \ s^{-1}$ [Take $e^5 = 150$,$e^{0.005} = 1$,$e^4 = 55$].

What is the activation energy $(kJ \, mol^{-1})$ for a reaction if its rate constant doubles when the temperature is raised from $300 \, K$ to $400 \, K$ ? $(R = 8.314 \, J \, mol^{-1} \, K^{-1})$

The rate of the chemical reaction doubles for an increase of $10 \text{ K}$ in absolute temperature from $298 \text{ K}$. What will be the activation energy?