Calculating the Crossover Temperature

Calculating a reaction's crossover temperature means setting ΔG to zero in ΔG = ΔH − TΔS and solving T = ΔH/ΔS, using ΔH and ΔS values that are each assumed roughly constant with temperature over the range of interest, an approximation reasonable for modest temperature spans.

For a reaction with ΔH = 178 kJ and ΔS = 160.5 J/K, first converting ΔH to 178,000 J to match ΔS's units, T = 178,000 J / 160.5 J/K ≈ 1109 K, so the reaction becomes spontaneous only above that temperature. Checking Chem 2109's sign categories confirms this reaction has both ΔH and ΔS positive, exactly the combination that produces a genuine crossover rather than uniform spontaneity or its absence.