If no catalyst $\left({\mathrm{H}}^{+}\right)$ is present in acid hydrolysis of ester then rate constant $\mathrm{k}$ is: (Where ${\mathrm{V}}_0,{ \mathrm{V}}_{\mathrm{t}}$ and ${\mathrm{V}}_{\infty }$ are volumes of $\mathrm{NaOH}$ used to titrate reaction mixture at $\mathrm{t}=0,\mathrm{t}=\mathrm{t}$ and $\mathrm{t}=\infty$)

The following data were obtained in an experiment on inversion of cane sugar; (a first order kinetics)

The rate constant (in ${\mathrm{second}}^{-1}$) is $[\ln 2=0.693]$

The decomposition of $N_2{O}_5$in chloroform was followed by measuring the volume of O₂ gas evolved : $2N_2{O}_5$($CC{1}_{4 }$)$\to$$2N_2{O}_4$($CC{1}_{4 }$) + $O_2 \left(g\right)$. The maximum volume of $O_{2 }$gasobtained was$100c{m}^3$. In 500 minutes, $90c{m}^3$of $O_{2 }$were evolved. The first order rate constant $\left(in mi{n}^{-1}\right)$ for the disappearance of $N_2{O}_5$is :

The substance undergoes first-order decomposition. The decomposition follows two parallel first-order reactions:

${\mathrm{K}}_1=1.26\times {10}^{-4}{\sec }^{-1}$ and ${\mathrm{K}}_2=3.8\times {10}^{-5}{\sec }^{-1}$

The percentage distribution of $\mathrm{B}$ and $\mathrm{C}$.

For a hypothetical elementary reaction.

where $\frac{{\mathrm{k}}_1}{{\mathrm{k}}_2}=\frac{1}{2}$

Initially, only $2$ moles of $\mathrm{A}$ are present. The total number of moles of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ at the end of $75\%$ of reaction are: