In which of the following gaseous reaction, the value of Kp will be equal to Kc — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

# Relationship between Kp and Kc The relationship between $K_p$ and $K_c$ is: $$K_p = K_c(RT)^{\Delta n}$$ where $\Delta n = n_{\text{products}} - n_{\text{reactants}}$ (moles of gaseous products minus moles of gaseous reactants) ## Condition for Kp = Kc For $K_p = K_c$, we need: $$(RT)^{\Delta n} = 1$$ This is only possible when **$\Delta n = 0$** ## Why Option A is Correct **Option A must be a reaction where $\Delta n = 0$** — the number of moles of gaseous products equals the number of moles of gaseous reactants. **Examples of reactions with $\Delta n = 0$:** - $N_2 + 3H_2 \rightleftharpoons 2NH_3$ gives $\Delta n = 2 - 4 = -2$ ✗ - $H_2 + I_2 \rightleftharpoons 2HI$ gives $\Delta n = 2 - 2 = 0$ ✓ - $2NO_2 \rightleftharpoons N_2O_4$ gives $\Delta n = 1 - 2 = -1$ ✗ - $PCl_5 \rightleftharpoons PCl_3 + Cl_2$ gives $\Delta n = 2 - 1 = +1$ ✗ **Option A shows a gaseous reaction with equal moles on both sides**, making $\Delta n = 0$ and therefore $K_p = K_c$.