The rate constant for the decomposition of a hydrocarbon is given as $K = (4.5 \times 10^{11} \ s^{-1}) e^{-(28000 \ K) / T}$. The activation energy of the reaction (in $J/mol$) is:

For a reaction,given below is the graph of $\ln k$ vs $\frac{1}{T}$. The activation energy for the reaction is equal to $...... \ cal \ mol^{-1}$. (Nearest integer). (Given : $R = 2 \ cal \ K^{-1} \ mol^{-1}$)

For reaction $A \to B$,the rate constant $k_1 = A_1 e^{-E_{a_1} / (RT)}$ and for the reaction $X \to Y$ the rate constant $k_2 = A_2 e^{-E_{a_2} / (RT)}$. If $A_1 = 10^8$,$A_2 = 10^{10}$ and $E_{a_1} = 600 \ cal/mol$,$E_{a_2} = 1800 \ cal/mol$,then the temperature at which $k_1 = k_2$ is (Given : $R = 2 \ cal/K \cdot mol$)

According to the Arrhenius equation,which of the following statements are correct?
$(A)$ $A$ high activation energy usually implies a fast reaction.
$(B)$ Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
$(C)$ Higher the magnitude of activation energy,stronger is the temperature dependence of the rate constant.
$(D)$ The pre-exponential factor is a measure of the rate at which collisions occur,irrespective of their energy.

The rate of the chemical reaction doubles for an increase of $10 \, K$ in absolute temperature from $298 \, K$. Calculate $E_{a}$.

The specific rate constant of a $1^{st}$ order reaction depends on the