What is Kc for N2(g) +3H2(g) <=> 2NH3(g)?

The given reversible reaction is:

$$\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$$

For a general reversible reaction $a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$, the equilibrium constant $K_c$ is given by:

$$K_c = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b}$$

where $[\text{X}]$ represents the molar concentration of species X at equilibrium, and $a, b, c, d$ are the stoichiometric coefficients. Only species in the gaseous or aqueous phases are included in the $K_c$ expression.

In the given reaction, all reactants and products are in the gaseous phase, so they are all included in the $K_c$ expression.
The products are $\text{NH}_3$ with a stoichiometric coefficient of 2.
The reactants are $\text{N}_2$ with a stoichiometric coefficient of 1, and $\text{H}_2$ with a stoichiometric coefficient of 3.

Therefore, the expression for $K_c$ is:

$$K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2]^1 [\text{H}_2]^3}$$ $$K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2] [\text{H}_2]^3}$$