Question

\( a \) moles of \( \text{PCl}_5 \) is heated in a closed container to equilibrate \[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \] at a pressure of \( P \) atm. If \( x \) moles of \( \text{PCl}_5 \) dissociate at equilibrium, then the correct expression for the equilibrium constant is

• A. \( \frac{x}{a} = \frac{K_p}{K_p + P} \)
• B. \( \frac{x}{a} = \frac{K_p + P}{K_p} \)
• C. \( \frac{x}{a} = \left( \frac{K_p + P}{K_p + P} \right)^{1/2} \)
• D. \( \frac{x}{a} = \frac{K_p}{P + K_p + P} \)

Hint:

For reactions involving gases, the equilibrium constant is related to the partial pressures of the reactants and products.

Answer 1

The Correct Option is A

Step 1: Equilibrium Expression.
The equilibrium expression for this reaction is given by: \[ K_p = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]} \] Using the mole fractions and pressures at equilibrium, we can derive the expression for \( \frac{x}{a} \).
Step 2: Conclusion.
The correct answer is (A), \( \frac{x}{a} = \frac{K_p}{K_p + P} \).