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 $R = 8.31 \ J \ K^{-1} \ mol^{-1}$]

The decomposition of formic acid on a gold surface follows first-order kinetics. If the rate constant at $300 \ K$ is $1.0 \times 10^{-3} \ s^{-1}$ and the activation energy $E_a = 11.488 \ kJ \ mol^{-1}$,the rate constant at $200 \ K$ is ............ $\times 10^{-5} \ s^{-1}$.
(Round off to the Nearest Integer).
(Given: $R = 8.314 \ J \ mol^{-1} K^{-1}$)

The temperature coefficient of a reaction is $2$. When the temperature is increased from $30^{\circ} C$ to $90^{\circ} C$,the rate of reaction is increased by: (in $times$)

For a chemical reaction,the rate of reaction doubles when the temperature increases by $10\,^oC$. If the temperature is increased from $10\,^oC$ to $100\,^oC$,the rate of reaction will increase by a factor of .....

What is Activation Energy $(E_a)$? Explain the reaction profile graph for activation energy and discuss the probability of effective collisions.

The rate of reaction becomes double when the temperature of the reaction is increased from $27\,^{\circ}C$ to $57\,^{\circ}C$. The activation energy of the reaction will be ....... $k\,cal$.