The energy profile diagram for a multi-step reaction,$A$ $\xrightarrow{1} B$ $\xrightarrow{2} C$ $\xrightarrow{3} D,$ is given below. The rate-determining step of the reaction is:

For reaction $A \to B$,rate constant $K_1 = A_1 e^{-E_{a_1}/RT}$ and for the reaction $X \to Y$,rate constant $K_2 = A_2 e^{-E_{a_2}/RT}$. If $A_1 = 10^8, A_2 = 10^{10}$ and $E_{a_1} = 600 \ cal \ mol^{-1}$,$E_{a_2} = 1800 \ cal \ mol^{-1}$,then the temperature at which $K_1 = K_2$ is (given: $R = 2 \ cal \ K^{-1} \ mol^{-1}$):

The decomposition of $A$ into product has a value of $k$ as $4.5 \times 10^{3} \, s^{-1}$ at $10^{\circ} C$ and an energy of activation of $60 \, kJ \, mol^{-1}$. At what temperature would $k$ be $1.5 \times 10^{4} \, s^{-1}$?

Write the Arrhenius equation representing the relationship between the rate constants $k_1$ and $k_2$ at two different temperatures $T_1$ and $T_2$.

When the temperature changes from $300 \ K$ to $310 \ K$,the rate of the reaction doubles. The activation energy of the reaction is ..... $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1} \text{ and } \log 2 = 0.301)$

For a reaction $E_a = 0$ and $k = 3.2 \times 10^8 \ s^{-1}$ at $300 \ K$. The value of frequency factor at $400 \ K$ would be