In the haber process, ammonia is synthesized from nitrogen and hydrogen: n2 (g) + 3h2 (g) → 2nh3 (g) δg° at 298 k for this reaction is -33.3 kj/mol. the value of δg at 298 k for a reaction mixture that consists of 1.9 atm n2, 1.6 atm h2, and 0.65 atm nh3 is a -40.5 b -1.8 c -3.86 ´ 103 d -104.5 e -7.25 ´ 103

The change in free energy of the system under the given conditions is -40.5 KJ/mol.

N2 (g) + 3H2 (g) → 2NH3 (g)  

We have to use the relation; ΔG = ΔG⁰ + RT ln Q

ΔG = Free energy change under the given conditions

ΔG⁰ = standard free energy change

R = gas constant

Q = reaction quotient

We can obtain the reaction quotient from;

Q = [NH3]^2/[N2] [H2]^3

Q = [0.65]^2/[1.9] [1.6]^3

Q = 0.4225/7.7824

Q= 0.0543

Substituting the values;

ΔG⁰ = -33.3 KJ/mol

R = 8.314 JK-1mol-1

T = 298 K

Q = 0.0543

ΔG = -33.3 KJ/mol + (8.314 JK-1mol-1 × 298 K) ln (0.0543)

ΔG =   -33.3 KJ/mol + (-7.2  KJ/mol)

ΔG = -40.5 KJ/mol

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e- 7.25 x 10³.

Explanation:

∵ ΔG = -RTlnK,

where, ΔG is the free energy change.

R is the general gas constant (R = 8.324 J/mol.K).

K is the equilibrium constant of the reaction.

K = (PNH₃)²/(PN₂)(PH₂)³ = (0.65)²/(1.9)(1.6)³ = 5.43 x 10⁻².

∵ ΔG = -RTlnK.

∴ ΔG = -(8.314 J/mol.K)(298 K) ln(5.43 x 10⁻²) = 7.218 x 10³ J/mol.