Question

Benzene diazonium chloride in aqueous solution decomposes as :
${\text{C}}_6{\text{H}}_5-\text{N}={\text{N}}^{+}{\text{Cl}}_{\left(\text{aq}\right)}^{-}+{\text{H}}_2{\text{O}}_{\left(\text{aq}\right)}⟶{\text{C}}_6{\text{H}}_5{\text{OH}}_{\left(\text{aq}\right)}+{\text{N}}_{2\left(\text{g}\right)}+{\mathrm{HCl}}_{\mathrm{(aq)}}$
The reaction follows first order kinetics. If ${\mathrm{p}}_{\mathrm{t}}$ is the pressure of${\mathrm{N}}_2$ at constant volume and temperature corresponding to time $\mathrm{t}$ and ${\mathrm{p}}_{\mathrm{f}}$ that after completion of the reaction, then which of the following graphs conforms to the kinetics of the reaction?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

$\begin{array}{cc}{\text{p}}_{\text{f}}\propto & \text{Initial moles of}{\text{C}}_6{\text{H}}_5{\text{N}}_2^{+}{\text{Cl}}^{-}\left(\text{a}\right)\\ {\text{p}}_{\text{t}}\propto & \text{Moles of}{\text{N}}_2\text{evolved at time t}\\ \propto & \text{Moles of}{\text{C}}_6{\text{H}}_5{\text{N}}_2^{+}{\text{Cl}}^{-}\text{reacted}\end{array}$
$\left({\text{p}}_{\text{f}}-{\text{p}}_{\text{t}}\right)\propto \text{mole of}{\text{C}}_6{\text{H}}_5{\text{N}}_2^{+}{\text{Cl}}^{-}$ left at time t (a - x)
${\text{kt}}_{}=2\text{.}303\text{log}\frac{\text{a}}{\text{a - x}}$
${\text{k}}_{}t=2\text{.}303\text{log}\frac{{\text{p}}_{\text{f}}}{\left({\text{p}}_{\text{f}}-{\text{p}}_{\text{t}}\right)}$
$\frac{\text{k}\text{t}}{2.303}=\text{log}{\text{P}}_{\text{f}}-\text{log}\left({\text{P}}_{\text{f}}-{\text{P}}_{\text{t}}\right)$
$\text{log}\left({\text{p}}_{\text{f}}-{\text{p}}_{\text{t}}\right)=\text{log}{\text{p}}_{\text{f}}-\frac{\text{k}}{2\text{.}303}\text{t}$
Interception y axis = log p_f
$\text{Slope}=-\frac{\text{k}}{2\text{.}303}$