What is the temperature at which this reaction would be at equilibrium assuming that enthalpy and entropy are independent of temperature?

Question

Consider the following reaction at 25 °C: 5 SO₃(g) + 2 NH₃(g) → 2 NO(g) + 5 SO₂(g) + 3 H₂O(g) If ∆H° = 42.4 kJ./mol and ∆S° = 562.3 J/mol•K, estimate the temperature at which this reaction would be at equilibrium assuming that enthalpy and entropy are independent of temperature.

Answer 1

For a reaction to be at equilibrium, ∆G should be zero

∆G = ∆H - T∆S

∆G = 0

∆H = 42.4 kJ/mol

T = ?

∆S = 562.3 J/molK = 0.562 kJ / Kmol (change units to agree with those for ∆H, i.e. kJ instead of J)

0 = 42.4 kJ/mol - T(0.562 kJ/molK)

T = 42.4 kJ/mol / 0.562 kJ/molK

T = 75K or greater