Answer:
At 2000 K. K: 0.747
At 3000 K. K: 11.79
Explanation:
Let's consider the decomposition of a generic diatomic element in its standard state.
1/2 X₂(g) ⟶ X(g)
The relation between the equilibrium constant (K) and the standard Gibbs energy (ΔG°) is:
[tex]K = e^{-\Delta G \° / R.T}[/tex]
where,
R is the ideal gas constant (8.314 × 10⁻³ kJ/mol.K)
T is the absolute temperature
At 2000 K (ΔG° = 4.84 kJ·mol⁻¹)
[tex]K=e^{-4.84kJ.mol^{-1}/8.314 \times 10^{-3} kJ.mol^{-1}.K^{-1} \times 2000 K } =0.747[/tex]
At 3000 K (ΔG° = −61.53 kJ·mol⁻¹)
[tex]K=e^{61.53kJ.mol^{-1}/8.314 \times 10^{-3} kJ.mol^{-1}.K^{-1} \times 3000 K } =11.79[/tex]
