Answer:
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
