Acid hydrolysis of ester is a first order reaction and the rate constant is given by, $\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{{\mathrm{V}}_{\infty }-{\mathrm{V}}_{\circ }}{{\mathrm{V}}_{\infty }-{\mathrm{V}}_{\mathrm{t}}}$

where, ${\mathrm{V}}_0, {\mathrm{V}}_{\mathrm{t}}$ and ${\mathrm{V}}_{\infty }$ are the volume of standard $\mathrm{NaOH}$ required to neutralise an acid present. At any given time, if ester is $50\%$ neutralised at time $\mathrm{t}$, then

$3\mathrm{A}⟶2\mathrm{B},$ rate of reaction $+\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{dt}}$ is equal to

For the following homogeneous reaction, $\mathrm{A}+\mathrm{B}\stackrel{\mathrm{k}}{\to }\mathrm{C}$, the unit of the rate constant is 

A chemical reaction was carried out at $300 \mathrm{K}\left(573 °\mathrm{C}\right)$ and $280 \mathrm{K}\left(553 °\mathrm{C}\right)$. The rate constants were found to be ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$,respectively. Then

A first order reaction is half-completed in $45$ minutes. How long does it need for $99.9\%$ of the reaction to be completed?

A first order reaction is $75\%$ complete after $32$ minutes. When was $50\%$ of the reaction completed?

A reaction which is of the first order with respect to a reactant $\mathrm{A}$, has a rate constant of $6 {\min }^{-1}$. If we start with $\left[\mathrm{A}\right]=0.5 \mathrm{mol} {\mathrm{L}}^{-1}$, when would $\left[\mathrm{A}\right]$ reach the value of $0.05 \mathrm{mol} {\mathrm{L}}^{-1}$?