The rate of a reaction quadruples when temperature changes from $27^{\circ} C$ to $57^{\circ} C$. Calculate the energy of activation.
Given $R=8.314 \ J \ K^{-1} \ mol^{-1}, \log 4=0.6021$

For the reaction $A_2 + B_2 \rightleftharpoons 2AB$,the activation energies for the forward and backward reactions are $180 \, kJ \, mol^{-1}$ and $200 \, kJ \, mol^{-1}$ respectively. In the presence of a catalyst,the activation energy for both (forward and backward) reactions decreases by $100 \, kJ \, mol^{-1}$. What will be the enthalpy change $(\Delta H)$ for the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of a catalyst in $kJ \, mol^{-1}$?

$A$ chemical reaction was carried out at $300 \, K$ and $280 \, K$. The rate constants were found to be $K_1$ and $K_2$ respectively. The energy of activation is $1.157 \times 10^4 \, cal \, mol^{-1}$ and $R = 1.987 \, cal \, K^{-1} \, mol^{-1}$. Then:

The rate constant of a reaction at temperature $200 \ K$ is $10$ times less than the rate constant at $400 \ K.$ What is the activation energy $({E_a})$ of the reaction ($R = $ gas constant) (in $R$)?

In a multistep reaction such as $A + B$ $\longrightarrow Q$ $\longrightarrow C$,the potential energy diagram is shown below. What is $E_{a}$ for the reaction $Q \longrightarrow C$?

The rate of a reaction doubles when its temperature changes from $300 \, K$ to $310 \, K.$ Activation energy of such a reaction will be .......... $kJ \, mol^{-1}$. $(R= 8.314 \, J \, K^{-1} \, mol^{-1}$ and $\log 2=0.301)$