Half life of a first order reaction is $900 \ \text{min}$ at $400 \ K$. Find its half life at $300 \ K$. Given: $\frac{E_a}{2.303 \ R} = 1.3056 \times 10^3 \ K$. (in $\text{min}$)

Consider the following plots of rate constant versus $\frac{1}{T}$ for four different reactions. Which of the following orders is correct for the activation energies of these reactions?

What does $P \cdot Z_{AB} \cdot e^{-\frac{E_a}{RT}}$ indicate in the rate equation?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: $A$ reaction can have zero activation energy.
Reason $R$: The minimum extra amount of energy absorbed by reactant molecules so that their energy becomes equal to threshold value,is called activation energy.
In the light of the above statements,choose the correct answer from the options given below:

For the reaction $X \rightleftharpoons Y$,the pre-exponential factors for the forward and backward reactions are equal. What will be the equilibrium constant of the reaction?

The rate of a reaction quadruples when the temperature changes from $293 \ K$ to $313 \ K$. Calculate the energy of activation of the reaction assuming that it does not change with temperature.