Question

For the reaction of oxygen and nitrogen to form nitric oxide, consider the following thermodynamic data: ΔH∘rxn 180.5 kJ/mol ΔS∘rxn 24.8 J/(mol⋅K) Calculate the temperature above which this reaction is spontaneous. Express your answer numerically in kelvins.

Answer 1

7.28 × 10³ K

Step-by-step explanation:

Let's consider the following reaction.

N₂(g) + O₂(g) → 2 NO(g)

The reaction is spontaneous when the standard Gibbs free energy (ΔG°) is negative. ΔG° is related to the standard enthalpy of the reaction (ΔH°) and the standard entropy of the reaction (ΔS°) through the following expression.

ΔG° = ΔH° - T . ΔS°

If ΔG° < 0,

ΔH° - T . ΔS° < 0

ΔH° < T . ΔS°

T > ΔH°/ΔS° = (180.5 × 10³ J/mol)/(24.8 J/mol.K) = 7.28 × 10³ K

The reaction is spontaneous above 7.28 × 10³ K.