For a reaction taking place in three steps at the same temperature,the overall rate constant is $K = \frac{K_1 K_2}{K_3}$. If $E_{a1}$,$E_{a2}$,and $E_{a3}$ are $40 \ kJ/mol$,$50 \ kJ/mol$,and $60 \ kJ/mol$ respectively,the overall activation energy $E_a$ is . . . . . . $kJ/mol$.

The rate constant for a reaction can be increased by $\underline{a}$ the stability of the reactant or by $\underline{b}$ the stability of the transition state. Select the correct choice for $a$ and $b$.

In respect of the equation $k = A e^{-E_a/RT}$ in chemical kinetics,which one of the following statements is correct?

The minimum energy required for molecules to participate in a chemical reaction is called $.......$.

The rate constants of a reaction at $500 \, K$ and $700 \, K$ are $0.02 \, s^{-1}$ and $0.07 \, s^{-1}$ respectively. Calculate the values of $E_{a}$ and $A$.

For the reaction,$aA + bB \rightarrow cC + dD$,the plot of $\log k$ vs $\frac{1}{T}$ is given below. The temperature at which the rate constant of the reaction is $10^{-4} \ s^{-1}$ is ............... $K$. (Rounded-off to the nearest integer) [Given: The rate constant of the reaction is $10^{-5} \ s^{-1}$ at $500 \ K$.]