Gibb's free energy, ΔG°, is related to the equilibrium constant of the reaction, K, through the equation:
ΔG°= RT(ln K)
By definition, K is the ratio of the equilibrium partial pressure of the products to the reactants, raised to the power of their stoichiometric coefficients, respectively. For this reaction,
N₂ (g) + 3 H₂ (g) → 2 NH₃ (g)
the equilibrium constant is
K = [NH₃]²/[N₂][H₂]³
Assuming that the given partial pressures are the equilibrium pressures, then we can substitute them directly:
K = [0.65 atm]²/[1.9 atm][1.6 atm]³
K = 0.05429 atm⁻²
Then, we can using this value to find ΔG. Note that R is the gas constant equal to 0.08206 L-atm/mol-K.
ΔG°= (0.08206 L-atm/mol-K)(298 K)(ln 0.05429 atm⁻²)
ΔG° = -71.244 L-atm/mol
