Write the expression for the equilibrium constant K c for the synthesis of ammonia reaction: N 2(g) + 3H 2(g) ⇌ 2NH 3(g)

The given reaction is the synthesis of ammonia:

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

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.

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

• Products: $\text{NH}_3$ with a coefficient of 2.
• Reactants: $\text{N}_2$ with a coefficient of 1, and $\text{H}_2$ with a coefficient of 3.

Therefore, the $K_c$ expression is:

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