Question

Given below are the reactions. Identify the reaction for which \(K_p<K_c\):

• A. \(\ce{N2(g)+O2(g)<=>2NO(g)}\)
• B. \(\ce{H2O(g)+CO(g)<=>H2(g)+CO2(g)}\)
• C. \(\ce{H2(g)+I2(g)<=>2HI(g)}\)
• D. \(\ce{N2(g)+3H2(g)<=>2NH3(g)}\)

Hint:

If \(\Delta n_g=0\), then \(K_p=K_c\). If \(\Delta n_g<0\), then \(K_p<K_c\).

Answer 1

The Correct Option is D

To determine the reaction for which \( K_p < K_c \), we use the relation:

\( K_p = K_c(RT)^{\Delta n} \)

where \( \Delta n \) is the difference between the number of moles of gaseous products and gaseous reactants.

For \( K_p < K_c \), the value of \( \Delta n \) should be negative.

Analyzing each option:

1. \( \text{N}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{NO}(g) \)
   • Reactant moles = 2
   • Product moles = 2
   • \( \Delta n = 2 - 2 = 0 \)
2. \( \text{H}_2\text{O}(g) + \text{CO}(g) \rightleftharpoons \text{H}_2(g) + \text{CO}_2(g) \)
   • Reactant moles = 2
   • Product moles = 2
   • \( \Delta n = 2 - 2 = 0 \)
3. \( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \)
   • Reactant moles = 2
   • Product moles = 2
   • \( \Delta n = 2 - 2 = 0 \)
4. \( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \)
   • Reactant moles = 4
   • Product moles = 2
   • \( \Delta n = 2 - 4 = -2 \)

Conclusion:
The reaction for which \( K_p < K_c \) is \( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \).