The following equation represents the decomposition of a generic diatomic elemen

Question

The following equation represents the decomposition of a generic diatomic element in its standard state. 1/2X2(g) ---> X(g)

Assume that the standard molar Gibbs energy of formation of X(g) is 5.52 kJ·mol–1 at 2000. K and –55.12 kJ·mol–1 at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature.

1. K at 2000. K=___________

2. K at 3000. K=___________

Assuming that ?H°rxn is independent of temperature, determine the value of ?H°rxn from these data.

3. delta H rxn=____________

Explanation / Answer

1)

T = 2000 K
?G = 5.52 KJ/mol
?G = 5520 J/mol

use:
?G = -R*T*ln Kc
5520 = - 8.314*2000.0* ln(K)
ln K = -0.332
K = 0.7175

2)

T = 3000 K
?G = -55.12 KJ/mol
?G = -55120 J/mol

use:
?G = -R*T*ln K
-55120 = - 8.314*3000.0* ln(K)
ln K = 2.2099
K = 9.115

3)
Given:
T1 = 2000 K
T2 = 3000 K
K1 = 0.7175
K2 = 9.115

use:
ln(K2/K1) = (Hrxn/R)*(1/T1 - 1/T2)
ln(9.115/0.7175) = ( Hrxn/8.314)*(1/2000.0 - 1/3000.0)
2.5419 = (Hrxn/8.314)*(1.667*10^-4)
Hrxn = 126800 J/mol
Hrxn = 126.8 KJ/mol
Answer: 126.8 KJ/mol

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