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

Question

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

1/2X2(g)⟶X(g)

Assume that the standard molar Gibbs energy of formation of X(g) is 4.71 kJ·mol−1 at 2000. K and −47.21 kJ·mol−1 3000. K. Determine the value of the thermodynamic equilibrium constant, K at each temperature.

At 2000. K, Δ𝐺f=4.71 kJ·mol−1 What is 𝐾 at that temperature?

𝐾 at 2000.  K=

At 3000. K, Δ𝐺f=−47.21 kJ·mol−1. What is K at that temperature?

𝐾 at 3000.  K=

Answer 1

∆G = -RT ln K

@2000K

4.71 kJ/mol = -(0.008312 kJ/Kmol x 2000K) ln K

ln K = -0.2833

K = 0.753

@3000K

47.21 kJ/mol = -(0.008314 kJ/Kmol x 3000K) ln K

ln K = -1.893

K = 0.151