We can use the following equation to calculate the Gibbs free energy change at non-standard conditions:
ΔG = Δ°G + RT ln(Q)
where Δ°G is the standard Gibbs free energy change, R is the gas constant (8.314 J/mol-K), T is the temperature in Kelvin, and Q is the reaction quotient.
First, we need to calculate Q for the given partial pressures:
Q = (P(NH3))^2 / (P(N2) * P(H2)^3)
= (0.750 atm)^2 / (0.350 atm * 0.300 atm^3)
= 4.08
Next, we can substitute the values into the equation:
ΔG = -32.8 kJ/mol + (8.314 J/mol-K * 298 K) * ln(4.08)
= -32.8 kJ/mol + (2471 J/mol) * 1.407
= -32.8 kJ/mol + 3476 J/mol
= -29.3 kJ/mol
Therefore, the Gibbs free energy change for the reaction at 298 K and the given partial pressures is -29.3 kJ/mol.