Question

In the system,
$LaC{l}_{3\left(g\right)}+H_{2}O\left(g\right)+Heat\rightleftharpoons LaCl{O}_{\left(s\right)}+2HC{l}_{\left(g\right)},$
is established. More water vapor is added to reestablish the equilibrium. The pressure of water vapor is doubled. The factor by which pressure of HCl is changed is

• A. 2
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. $\sqrt{5}$

Answer 1

The correct option is B $\sqrt{2}$

Before addition of water vapour, here $LaCl{O}_3$ is not taken into account because it's concentration remains constant
$K=\frac{[HCl{]}_i^2}{[H_{2}O{]}_i}$ ...(1)

After addition of water vapour,
$K=\frac{[HCl{]}_f^2}{[H_{2}O{]}_f}$ ...(2)

But (1) = (2)
$\frac{[HCl{]}_i^2}{[H_{2}O{]}_i}=\frac{[HCl{]}_f^2}{[H_{2}O{]}_f}$ ...(3)

When equilibrium re-established, the pressure fo water vapour is doubled. $[H_{2}O{]}_f=2[H_{2}O{]}_i$ ...(4)

Substitute (4) in (3)
$\frac{[HCl{]}_i^2}{[H_{2}O{]}_i}=\frac{[HCl{]}_f^2}{\left(2\right[H_{2}O{]}_i)}$
$[HCl{]}_i^2=[HCl{]}_f^2\times \frac{1}{2}$
$[HCl{]}_i=[HCl{]}_f\times \sqrt{\frac{1}{2}}$
$[HCl{]}_f=\sqrt{2}\times [HCl{]}_i$