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Multiple Choice
Calculate the Gibbs free energy change (ΔG_rxn) at 298 K for the reaction N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g) given the standard Gibbs free energy change (ΔG° = -33.3 kJ) and the partial pressures: P(N2) = 1.5 atm, P(H2) = 4.5 atm, P(NH3) = 6.0 atm.
A
-29.7 kJ
B
-40.5 kJ
C
-25.0 kJ
D
-33.3 kJ
Verified step by step guidance
1
Identify the reaction and the given data: N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g), ΔG° = -33.3 kJ, P(N2) = 1.5 atm, P(H2) = 4.5 atm, P(NH3) = 6.0 atm.
Use the equation for Gibbs free energy change under non-standard conditions: ΔG_rxn = ΔG° + RT ln(Q), where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K).
Calculate the reaction quotient Q using the formula Q = (P(NH3)^2) / (P(N2) * (P(H2)^3)). Substitute the given partial pressures into this expression.
Convert the gas constant R from J/mol·K to kJ/mol·K by dividing by 1000, since ΔG° is given in kJ.
Substitute ΔG°, R, T, and Q into the Gibbs free energy equation to find ΔG_rxn. Ensure all units are consistent, particularly converting R to kJ/mol·K.