Under identical reaction conditions,the concentration of a substance is $1.386 \ mol \ m^{-3}$. It is halved in $40 \ s$ and $20 \ s$ by first-order and zero-order kinetics,respectively. The ratio of the rate constants for the first-order $(k_1)$ and zero-order $(k_0)$ reactions,$\left( \frac{k_1}{k_0} \right)$,is ............ $m^3 \ mol^{-1}$.

$A$ substance $S$ undergoes two reactions under similar reaction conditions:
$\mathop S\limits_{(2.0 \ M)} \xrightarrow{K_0} X$ (zero order)
$\mathop S\limits_{(2.0 \ M)} \xrightarrow{K_2} Y$ (second order)
The time taken for the concentration of $S$ to become half is $40 \ s$ and $10 \ s$ for the zero-order and second-order reactions,respectively. What is the value of the ratio $K_0 / K_2$?

The hydrolysis of an ester was carried out separately with $0.1 \ N$ $HCl$ and $0.1 \ N$ $H_2SO_4$. Then for the rate of reaction $(R)$ in the presence of acid,which of the following relations is true?

Determine whether the following statements are True or False:
$(a)$ The rate of reaction can be decreased by decreasing the concentration of reactant.
$(b)$ Graphite quickly changes to Diamond.
$(c)$ The rate of corrosion of iron is fast.
$(d)$ The meaning of kinesis in Greek is movement.

Match the rate expressions in List-$I$ for the decomposition of $X$ with the corresponding profiles provided in List-$II$. $X_s$ and $k$ are constants having appropriate units.

Which of the following statement$(s)$ is (are) correct?