Question

Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction
2NH3(g)+CO2(g)→NH2CONH2(aq)+H2O(l)
Given that ΔG∘ = -13.6 kJ, calculate ΔG at 25 ∘C for the following sets of conditions.

1. 40 atm NH3, 40 atm CO2, 4.0 M NH2CONH2

2. 0.10 atm NH3, 0.10 atm CO2, 1.0 M NH2CONH2

Answer 1

2 NH₃ (g) + CO₂ (g) → NH₂CONH₂ (aq) + H₂O(l)

1. 40 atm NH₃, 40 atm CO₂, 4.0 M NH₂CONH₂

Q = [NH₂CONH₂] / (P NH₃)² (P CO₂)

Q = (4.0) / ((40)² (40)) = 6.25 x 10^-5

ΔG = ΔG^∘ + RT In Q

-13,600 J = ΔG^∘ + (8.314 J / mole K)(298 K) ln (6.25 x 10^-5)
-13,600 J = ΔG^∘ - 23984 J
ΔG^∘ = 10,384 J =10.384 kJ

2. 0.10 atm NH₃, 0.10 atm CO₂, 1.0 M NH₂CONH₂

Q = [NH₂CONH₂] / (P NH₃)² (P CO₂)

Q = (1.0) / ((0.10)² (0.10)) = 1000

ΔG = ΔG^∘ + RT In Q

-13,600 J = ΔG^∘ + (8.314 J / mole K)(298 K) ln (1000)
-13,600 J = ΔG^∘ - 17114 J
ΔG^∘ = 3514 J =3.514 kJ