Question

For the equilibrium, \[ 2NOCl (g) \rightleftharpoons 2NO (g) + Cl_2 (g) \] The value of the equilibrium constant, \( K_c \), is \( 3.75 \times 10^{-6} \) at 1069 K. The value of \( K_p \) for the reaction at this temperature will be:

• A. 0.133
• B. 1.242
• C. 0.033
• D. 0.00033

Hint:

When converting \( K_c \) to \( K_p \), use the formula \( K_p = K_c (RT)^{\Delta n} \) and carefully consider the number of gas molecules in the products and reactants.

Answer 1

The Correct Option is C

The relationship between the equilibrium constants \( K_c \) and \( K_p \) is given by the equation: \[ K_p = K_c \left( RT \right)^{\Delta n} \] Where: - \( R \) is the universal gas constant (0.0821 L·atm/mol·K),
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in moles of gas, calculated as \( (moles \, of \, products) - (moles \, of \, reactants) \). For the reaction \( 2NOCl \rightleftharpoons 2NO + Cl_2 \), \[ \Delta n = (2 + 1) - 2 = 1 \] Given: - \( K_c = 3.75 \times 10^{-6} \),
- \( T = 1069 \, K \),
- \( R = 0.0821 \, L·atm/mol·K \), Substitute into the equation: \[ K_p = (3.75 \times 10^{-6}) \times (0.0821 \times 1069) = 0.033 \] Thus, the correct answer is option (C).