The equation represents the decomposition of a generic diatomic element in its standard state. 12X2 (g) ⟶X (g) Assume that the standard molar Gibbs energy of formation of X (g) is 5.61 kJ·mol-1 at 2000. K and - 52.80 kJ·mol-1 at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature. K at 2000. K = K at 3000. K = Assuming that ΔH∘rxn is independent of temperature, determine the value of ΔH∘rxn from this data. ΔH∘rxn=

The equilibrium constant at 2000 K is 0.7139

The equilibrium constant at 3000 K is 8.306

ΔH = 122.2 kJ/mol

Explanation:

Step 1: Data given

the standard molar Gibbs energy of formation of X (g) is 5.61 kJ/mol at 2000 K

the standard molar Gibbs energy of formation of X (g) is - 52.80 kJ/mol at 3000 K

Step 2: The equation

1/2X2 (g) ⟶X (g)

Step 3: Determine K at 2000 K

ΔG = - RT ln K

⇒R = 8.314 J/mol * K

⇒T = 2000 K

⇒K is the equilibrium constant

5610 J/mol = - 8.314 J/molK * 2000 * ln K

ln K = - 0.337

K = e^-0.337

K = 0.7139

The equilibrium constant at 2000 K is 0.7139

Step 4: Determine K at 3000 K

ΔG = - RT ln K

⇒R = 8.314 J/mol * K

⇒T = 3000 K

⇒K is the equilibrium constant

-52800 J/mol = - 8.314 J/molK * 3000 * ln K

ln K = 2.117

K = e^2.117

K = 8.306

The equilibrium constant at 3000 K is 8.306

Step 5: Determine the value of ΔH∘rxn

ln K2/K1 = - ΔH/r * (1/T2 - 1/T1)

ln 8.306 / 0.713 = - ΔH/8.314 * (1/3000 - 1/2000)

2.455 = - ΔH/8.314 * (3.33*10^-4 - 0.0005)

2.455 = - ΔH/8.314 * (-1.67*10^-4)

-14700 = - ΔH/8.314

-ΔH = - 122200 J/mol

ΔH = 122.2 kJ/mol