Question

In the haber process, ammonia is synthesized from nitrogen and hydrogen: n2 (g) + 3 h2 (g) ? 2 nh3 (g) ?g° at 298 k for this reaction is -33.3 kj/mol. the value of ?g at 298 k for a reaction mixture that consists of 1.9 atm n2, 1.6 atm h2, and 0.65 atm nh3 is __________.

Answer 1

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