Under identical reaction conditions,for a reactant with an initial concentration of $1.386 \, M$,the time taken for the concentration to become half is $40 \, s$ for a first-order reaction and $20 \, s$ for a zero-order reaction. The ratio of the rate constant of the first-order reaction $(K_1)$ to the rate constant of the zero-order reaction $(K_0)$ is ......... $mol \, L^{-1}$.

Given below are two statements: $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$ and $1 \text{ cal} = 4.2 \text{ J}$.
Statement $I$: When $E_a = 12.6 \text{ kcal/mol}$,the room temperature rate constant is doubled by a $10 \text{ }^\circ\text{C}$ increase in temperature ($298 \text{ K}$ to $308 \text{ K}$).
Statement $II$: For a first-order reaction $A \to B$,the graph of half-life $(t_{1/2})$ versus initial concentration $[A]_o$ is a straight line passing through the origin.
In the light of the above statements,choose the correct answer from the options given below:

For the following parallel chain reaction,what will be the value of the overall half-life of $A$ in minutes?
Given that $\frac{[B]_t}{[C]_t} = \frac{16}{9}$
$A \xrightarrow{k_1 = 2 \times 10^{-3} \ s^{-1}} 4B$
$A \xrightarrow{k_2} C$

In the phenomenon of autocatalysis,......

An endothermic reaction with a high activation energy for the forward reaction is represented by the diagram:

The effect of $pH$ on the rate constant for the hydrolysis of an ester is given by: