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Multiple Choice
Determine the minimum pressure of N₂ required to keep the reaction N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g) spontaneous at 298 K, given ΔG°rxn = -33.3 kJ/mol, P H₂ = 1.00 x 10⁻² atm, and P NH₃ = 1.00 atm.
A
0.10 atm
B
0.05 atm
C
0.50 atm
D
0.20 atm
Verified step by step guidance
1
Understand that the spontaneity of a reaction at constant temperature and pressure is determined by the Gibbs free energy change (ΔG). For a reaction to be spontaneous, ΔG must be negative.
Use the equation ΔG = ΔG° + RT ln(Q) to find the minimum pressure of N₂. Here, ΔG° is the standard Gibbs free energy change, R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and Q is the reaction quotient.
Calculate the reaction quotient Q using the expression Q = (P_NH₃)^2 / (P_N₂ * (P_H₂)^3), where P_NH₃, P_N₂, and P_H₂ are the partial pressures of NH₃, N₂, and H₂, respectively.
Set ΔG to zero for the reaction to be at equilibrium (the threshold of spontaneity), and solve the equation 0 = ΔG° + RT ln(Q) for P_N₂.
Rearrange the equation to find P_N₂: P_N₂ = (P_NH₃)^2 / ((P_H₂)^3 * exp(-ΔG° / (RT))). Substitute the given values (ΔG° = -33.3 kJ/mol, T = 298 K, P_H₂ = 1.00 x 10⁻² atm, P_NH₃ = 1.00 atm) to calculate the minimum pressure of N₂.