The decomposition of a generic diatomic element in its standard state is represented by the equation

Question

1/2X2(g)⟶X(g)

Assume that the standard molar Gibbs energy of formation of X(g) is 5.46 kJ·mol−1 at 2000. K and −47.29 kJ·mol−1 at 3000. K. Determine the value of the thermodynamic equilibrium constant, 𝐾, at each temperature.

At 2000. K, Δ𝐺f=5.46 kJ·mol−1. What is 𝐾 at that temperature?

At 3000. K, Δ𝐺f=−47.29 kJ·mol−1. What is K at that temperature?

Answer 1

1/2 X₂(g) ==> X(g) .. ∆Gºf = 5.46 kJ/mol @ 2000K

1/2 X₂(g) ==> X(g) .. ∆Gºf = -47.29 kJ/mol @ 3000K

NOTE: at 3000K, ∆Gº is negative meaning the reaction is spontaneous. At 2000, it is not spontaneous.

∆Gº = -RT ln K

@2000K:

5.46 kJ/mol = - (0.008314 kJ/molK)(2000K) ln K

K = 0.720

@3000K:

-47.29 kJ/mol = -(0.008314 kJ/molK)(3000K) ln K

K = 6.66

NOTE: At 3000K, K is >1 and at 2000K, K is <1 which is in agreement with spontaneity predicted above.