Hydrolysis of $DDT$ is a first order reaction,its half-life is $10 \ years$. Time required to hydrolyse $10 \ g$ of $DDT$ to half is ......... $years$.

$A$ first-order reaction starts with a decimolar solution of the reactant. After $8$ minutes,its concentration becomes $M/100$. Calculate the rate constant of the reaction.

Which of the following graphs represents a first-order reaction?

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below:

Time $(t)$ $(\min)$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $(M)$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first order reaction as the concentration of $H_{2}O$ remains nearly constant $(55 \ mol \ L^{-1})$ during the course of the reaction. What is the value of $k^{\prime}$ in this reaction?

The reaction $A + B \xrightarrow{k}$ product is first order with respect to $A$ and zero order with respect to $B$. If $a_0$ and $a_t$ are the concentrations of $A$ at $t = 0$ and after time $t \, sec$ respectively,then select the correct relationship -

Calculate the rate constant of a first-order reaction $A \rightarrow B$ having a rate of $5.4 \times 10^{-6} \text{ mol dm}^{-3} \text{ s}^{-1}$ and concentration $[A] = 0.3 \text{ M}$.