Question

For the reaction ${PCl}_5\rightleftharpoons {PCl}_3+{CI}_2$ the degree of dissociation varies inversely as the square root of the pressure of the system. Supposing at constant temperature If the volume is increased $16$ times the initial volume, the degree of dissociation for its reaction will become:

• A. $4$ times
• B. $\frac{1}{4}$ times
• C. $2$ times
• D. $\frac{1}{2}$ times

Answer 1

The correct option is A $4$ times

As degree of dissociation varies inversely as the square root of pressure of the System.

$\alpha \propto \frac{1}{\sqrt{P}}.....\left(1\right)$

From the ideal gas equation-

$PV=nRT$

At constant temperature,

$P\propto \frac{1}{V}$

$\therefore P\propto \frac{1}{V}.....\left(2\right)$

From ${eq}^n\left(1\right)\&\left(2\right)$, we have

$\alpha \propto \sqrt{V}$

$\therefore \frac{{\alpha }_1}{{\alpha }_2}=\sqrt{\frac{V_1}{V_2}}.....\left(3\right)$

Given that at constant temperature, the volume is increased 16 times the initial volume, i.e.,

Let V be the initial volume.

$\therefore V_2=16V_1$

From ${eq}^n\left(3\right)$, we get

$\frac{{\alpha }_1}{{\alpha }_2}=\sqrt{\frac{V}{16V}}$

$\Rightarrow \frac{{\alpha }_1}{{\alpha }_2}=\sqrt{\frac{1}{16}}$

$\Rightarrow {\alpha }_2=4{\alpha }_1$

Hence at constant temperature if the volume is increased $16$ times the initial volume, the degree of dissociation for its reaction will becomes $4$ times.