Q

# Help me please, - Physical and Chemical Equilibria - BITSAT

A gaseous phase reaction is allowed to attain equilibrium as , A (g) $\leftrightarrow$ B (g) + C (g)  at constant Pressure 'P' . The partial pressure of A at equilibrium is $\frac{P}{2}$ . The value of equilibrium constant KP is

• Option 1)

$\frac{P}{2}$

• Option 2)

$\frac{P}{4}$

• Option 3)

$\frac{P}{6}$

• Option 4)

$\frac{P}{8}$

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As learnt in

Equilibrium constant in gaseous system -

For equilibrium involving gases, it is usually more convenient to express the equilibrium constant in terms of partial pressure.

- wherein

The ideal gas equation is written as

$PV=nRT$

$A\left ( g \right )\rightleftharpoons B\left ( g \right ) + C \left ( g \right )$

at equilibrium                  $\frac{P}{2}$                    x              x

Total pressure at equilibrium = P

$\Rightarrow \frac{P}{2}+2x = P$

$\Rightarrow x= \frac{P}{4}$

$\therefore K_{p}= \frac{P_{\left ( B \right )}\times P_{\left ( C \right )}}{P\left ( A \right )} = \frac{\frac{P}{4}\times \frac{P}{4}}{\frac{P}{2}} = \frac{P}{8}$

Option 1)

$\frac{P}{2}$

This option is incorrect

Option 2)

$\frac{P}{4}$

This option is incorrect

Option 3)

$\frac{P}{6}$

This option is incorrect

Option 4)

$\frac{P}{8}$

This option is correct

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