In the system,
$L a C l_{3 (g)} + H_{2} O (g) + H e a t ⇌ L a C l O_{(s)} + 2 H C l_{(g)},$
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

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\sqrt{2}

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\sqrt{3}

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\sqrt{5}

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Solution

The correct option is B $\sqrt{2}$
Before addition of water vapour, here $L a C l O_{3}$ is not taken into account because it's concentration remains constant
$K = \frac{[H C l]_{i}^{2}}{[H_{2} O]_{i}}$ ...(1)

After addition of water vapour,
$K = \frac{[H C l]_{f}^{2}}{[H_{2} O]_{f}}$ ...(2)

But (1) = (2)
$\frac{[H C l]_{i}^{2}}{[H_{2} O]_{i}} = \frac{[H C l]_{f}^{2}}{[H_{2} O]_{f}}$ ...(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)
$\frac{[H C l]_{i}^{2}}{[H_{2} O]_{i}} = \frac{[H C l]_{f}^{2}}{(2 [H_{2} O]_{i})}$
$[H C l]_{i}^{2} = [H C l]_{f}^{2} \times \frac{1}{2}$
$[H C l]_{i} = [H C l]_{f} \times \sqrt{\frac{1}{2}}$
$[H C l]_{f} = \sqrt{2} \times [H C l]_{i}$

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$L a C l_{3 (g)} + H_{2} O (g) + H e a t ⇌ L a C l O_{(s)} + 2 H C l_{(g)},$
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