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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}

 
Answers (1)
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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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