Question

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 4.25 kJ·mol−1 at 2000. K and −63.12 kJ·mol−1 at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature.

Answer 1

Answer:

$K^{2000K}=0.774\\\\K^{3000K}=12.56$

Explanation:

Hello,

In this case, considering the reaction, we can compute the Gibbs free energy of reaction at each temperature, taking into account that the Gibbs free energy for the diatomic element is 0 kJ/mol:

$\Delta _rG=\Delta _fG_{X}-\frac{1}{2} \Delta _fG_{X_2}=\Delta _fG_{X}$

Thus, at 2000 K:

$\Delta _rG=\Delta _fG_{X}^{2000K}=4.25kJ/mol$

And at 3000 K:

$\Delta _rG=\Delta _fG_{X}^{3000K}=-63.12kJ/mol$

Next, since the relationship between the equilibrium constant and the Gibbs free energy of reaction is:

$K=exp(-\frac{\Delta _rG}{RT} )$

Thus, at each temperature we obtain:

$K^{2000K}=exp(-\frac{4250J/mol}{8.314\frac{J}{mol\times K}*2000K} )=0.774\\\\K^{3000K}=exp(-\frac{-63120J/mol}{8.314\frac{J}{mol\times K}*3000K} )=12.56$

In such a way, we can also conclude that at 2000 K reaction is unfavorable (K<1) and at 3000 K reaction is favorable (K>1).

Best regards.