The elementary reaction $2SO_{2(g)} + O_{2(g)} \to 2SO_{3(g)}$ is carried out in a $1 \ dm^3$ vessel and a $2 \ dm^3$ vessel separately. The ratio of the reaction velocities will be

Fill in the blanks:
$(1)$ The time required to complete $99.9\%$ of a first-order reaction is ............ times the ${t_{1/2}}$.
$(2)$ The reaction in which the rate is given by $-\frac{d[R]}{dt} = k$ has an order of reaction equal to ........
$(3)$ For the reaction $[R] = [R]_0 e^{-kt}$,the order is .......

Which of the following relations is correct for the given reaction orders?

$A$ 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 catalyst for the hydrolysis of cane sugar is ........

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?