Question

To the system
$La{Cl}_3\left(s\right)+H_{2}O\left(g\right)\rightleftharpoons LaClO\left(s\right)+2HCl\left(g\right)$- heat already at equilibrium, more water vapour is added without altering $T$ or $V$ of the system. When equilibrium re-established, the pressure of water vapour is doubled. The pressure of $HCl$ present in the system increases by a factor of:

• A. $2$
• B. $2^{1/2}$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2^{1/2}$

To the system
$La{Cl}_3\left(s\right)+H_{2}O\left(g\right)\rightleftharpoons LaClO\left(s\right)+2HCl\left(g\right)$- heat already at equilibrium, more water vapour is added without altering $T$ or $V$ of the system. When equilibrium re-established, the pressure of water vapour is doubled. The pressure of $HCl$ present in the system increases by a factor of $2^{1/2}$.
The equilibrium constant expression is
$K=\frac{[HCl{]}^2}{\left[H2O\right]}$
Before addition of water vapour,
$K=\frac{[HCl{]}_i^2}{[H2O{]}_i}$......(1)
After addition of water vapour,
$K=\frac{[HCl{]}_f^2}{[H2O{]}_f}$......(2)
But (1) $=$ (2)
$\frac{[HCl{]}_i^2}{[H2O{]}_i}=\frac{[HCl{]}_f^2}{[H2O{]}_f}$......(3)
When equilibrium re-established, the pressure of water vapour is doubled.
$[H2O{]}_f=2[H2O{]}_i$......(4)
Substitute (4) in (3)
$\frac{[HCl{]}_i^2}{[H2O{]}_i}=\frac{[HCl{]}_f^2}{\left(2\right[H2O{]}_i)}$
$[HCl{]}_i^2=[HCl{]}_f^2\times \frac{1}{2}$
$[HCl{]}_i=[HCl{]}_f\times \sqrt{\frac{1}{2}}$
$[HCl{]}_f=\sqrt{2}\times [HCl{]}_i$