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Question

Nitrogen fixation is the process of converting diatomic nitrogen, which is difficult for organisms to utilize, into ammonia which is much more convenient.

N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g)

Assume that a nitration fixation reaction is carried out at 25 C starting with 1.75 M N2 and 2.15 M H2. At equilibrium the concentration of NH3 (g) is 1.34 M, determine the Delta G^o for the reaction, identify whether the reaction is spontaneous or not, and explain how you determined spontaneity.

Answer 1

N₂(g) + 3 H₂(g) <==> 2 NH₃(g)

1.75.........2.15..............0...........Initial

-x............-3x................+2x........Change

1.75-x....2.15-3x...........2x........Equilibrium

2x = 1.34 M

x = 0.67 M

Equilibrium concentrations are as follows:

[N₂] = 1.75 - 0.67 = 1.08 M

[H₂] = 2.15 - 2.01 = 0.14 M

[NH₃] = 1.34 M

K_c = [NH₃]² / [N₂][H₂]³ = (1.34)² / (1.08)(0.14)³ = 606

∆Gº = -RT ln K

∆Gº = -(8.314 J/Kmol)(298K) ln 606

∆Gº = -2478 x 6.41

∆Gº = -15,884 J/mole

∆Gº = -15.9 kJ/mol

The reaction is SPONTANEOUS. This is true because ∆Gº is negative indicating spontaneity. This is also in agreement with the large value of K_c indicating the reaction lies far to the right (product side).