We’re being asked to determine the **equilibrium constant (K)** at **25 ˚C** for the given reaction:

**N _{2} (g) + 3H_{2} (g) → 2NH_{3} (g)**

Recall that ** ΔG˚_{rxn} and K** are related to each other:

$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$

We can use the following equation to solve for ** ΔG˚_{rxn}**:

$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{\Delta H}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{-}}{\mathbf{T\Delta S}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}}$

We can get the value of the **ΔH˚ _{rxn} and ΔS˚_{rxn}** of the reaction from the textbook or the internet.

We have:

ΔH˚** _{rxn}** =

ΔS˚** _{rxn}** =

**For this problem, we need to do the following steps:**

*Step 1:* Use ΔH˚_{rxn} and ΔS˚_{rxn} to calculate for ΔG˚_{rxn}.

*Step 2:* Calculate for K.

The Haber process is the principal industrial route for converting nitrogen into ammonia:

N_{2} (g) + 3H_{2} (g) → 2NH_{3} (g).

Using the thermodynamic data in Appendix C in the textbook, calculate the equilibrium constant for the process at room temperature.