Which of the following is the correct expression for K_p for the reaction: N_2(g) + 3 H_2(g) ⇌ 2 NH_3(g)?

• A. K_p = (P_{N_2}) (P_{H_2})^3 / (P_{NH_3})^2
• B. K_p = (P_{NH_3}) / [ (P_{N_2}) (P_{H_2}) ]
• C. K_p = (P_{NH_3})^2 / [ (P_{N_2}) (P_{H_2})^3 ]
• D. K_p = (P_{N_2})^2 (P_{H_2})^6 / (P_{NH_3})^4

Answer: (C)

Verified step by step guidance

1. Identify the balanced chemical equation: \(\mathrm{N_2(g) + 3 H_2(g) \rightleftharpoons 2 NH_3(g)}\).
2. Recall that the equilibrium constant in terms of partial pressures, \(K_p\), is expressed as the ratio of the product of the partial pressures of the products raised to their stoichiometric coefficients to the product of the partial pressures of the reactants raised to their stoichiometric coefficients.
3. Write the general expression for \(K_p\) for this reaction: \(K_p = \frac{(P_{\mathrm{NH_3}})^2}{(P_{\mathrm{N_2}})^1 (P_{\mathrm{H_2}})^3}\)
4. Note that the exponents correspond to the coefficients in the balanced equation: 2 for \(\mathrm{NH_3}\), 1 for \(\mathrm{N_2}\), and 3 for \(\mathrm{H_2}\).
5. Compare this expression to the options given to identify the correct one.