Expressing Equilibrium Constants for Gas-Phase Reactions

Q7. Express the equilibrium constant for the following reaction:

2 CH3Cl(g) + Cl2(g) ⇔ 2 CH2Cl2(g) + H2(g)

Background

Topic: Chemical Equilibrium – Equilibrium Constant Expressions

This question tests your ability to write the equilibrium constant expression (KP) for a gas-phase reaction, using partial pressures of the reactants and products.

Key Terms and Formulas

• Equilibrium constant (KP): A ratio of the partial pressures of products to reactants, each raised to the power of their stoichiometric coefficients.

• Partial pressure (P): The pressure exerted by a single gas in a mixture.

• General formula:

  $K_P = \frac{\text{(Partial pressure of products)}^{\text{coefficients}}}{\text{(Partial pressure of reactants)}^{\text{coefficients}}}$

Step-by-Step Guidance

1. Write the balanced chemical equation: $2 \text{CH}_3\text{Cl}(g) + \text{Cl}_2(g) \rightleftharpoons 2 \text{CH}_2\text{Cl}_2(g) + \text{H}_2(g)$

2. Identify the products and reactants, and their stoichiometric coefficients:

   • Products: CH2Cl2 (2), H2 (1)

   • Reactants: CH3Cl (2), Cl2 (1)

3. Set up the equilibrium constant expression using partial pressures:

   $K_P = \frac{[P(\text{CH}_2\text{Cl}_2)]^2 \times P(\text{H}_2)}{[P(\text{CH}_3\text{Cl})]^2 \times P(\text{Cl}_2)}$

4. Check the image options for the correct mathematical form. Look for the expression that matches the formula above.

   

Try solving on your own before revealing the answer!

Final Answer:

$K_P = \frac{P^2(\text{CH}_2\text{Cl}_2) \times P(\text{H}_2)}{P^2(\text{CH}_3\text{Cl}) \times P(\text{Cl}_2)}$

This matches the mathematical form shown in image_2. The equilibrium constant expression is constructed by raising each partial pressure to the power of its coefficient in the balanced equation.