Question

For the homogeneous equilibrium \(N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}\), the equilibrium constants \(K_P\) and \(K_C\) are related as:

• A. $K_{P}=K_{C}(RT)^{2}$
• B. $K_{P}=K_{C}(RT)^{-2}$
• C. $K_{P}=K_{C}(RT)^{-3}$
• D. $K_{P}=K_{C}(RT)^{3}$
• E. $K_{P}=K_{C}(RT)$

Hint:

Always count gaseous coefficients only to find $\Delta n_g$.

Answer 1

The Correct Option is B

Step 1: Concept
Relationship formula: $K_P = K_C(RT)^{\Delta n_g}$.

Step 2: Meaning
$\Delta n_g$ = (moles of gaseous products) - (moles of gaseous reactants).

Step 3: Analysis
For this reaction: $\Delta n_g = 2 - (1 + 3) = 2 - 4 = -2$.

Step 4: Conclusion
Thus, $K_P = K_C(RT)^{-2}$. Correct answer is (B).
Final Answer: (B)