For the reaction Fe2N(s) + 32H2(g) 2Fe(s) + NH3(g)

Formula: $K_P = K_C (RT)^{\Delta n_g} \Rightarrow K_C = K_P (RT)^{-\Delta n_g}$

Step 1 — Identify gaseous species only (solids excluded from K expression):

• Gaseous reactants: $\frac{3}{2}\mathrm{H_2}$ $\rightarrow$ $\frac{3}{2}$ moles
• Gaseous products: $\mathrm{NH_3}$ $\rightarrow$ 1 mole

Step 2 — Calculate $\Delta n_g$: $\Delta n_g = 1 - \frac{3}{2} = -\frac{1}{2}$

Step 3 — Relationship: $K_C = K_P \cdot (RT)^{-\Delta n_g} = K_P \cdot (RT)^{+1/2} = K_P(RT)^{1/2}$

Answer: Option (3)