Among the following statements,the correct statement about the half-life period for a first order reaction is

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 $(t)$ $\text{min}$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $\text{mol L}^{-1}$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first-order reaction as the concentration of $H_2O$ remains nearly constant $(54.2 \text{ mol L}^{-1})$ during the course of the reaction. What is the value of $k'$ in this reaction?

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 ......... $years$.

Consider the following reaction,the rate expression of which is given below:
$A + B \rightarrow C$
$\text{rate} = k[A]^{1/2}[B]^{1/2}$
The reaction is initiated by taking $1 \ M$ concentration of $A$ and $B$ each. If the rate constant $(k)$ is $4.6 \times 10^{-2} \ s^{-1}$,then the time taken for $A$ to become $0.1 \ M$ is . . . . . . . . . . $sec$. (nearest integer)

Half-life and rate constant for a first-order reaction are related by the equation:

The reaction $N_{2}O_{5} \longrightarrow 2NO_{2} + \frac{1}{2}O_{2}$ is first order in $N_{2}O_{5}$ having rate constant $6.2 \times 10^{-4} \ s^{-1}$. What is the value of rate of reaction when concentration of $N_{2}O_{5}$ is $1.25 \ mol \ L^{-1}$?