Chemistry / Unit 11 Chem 2115 worked example, 60 to 90 seconds
Calculating the Crossover Temperature
The idea
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.
In practice
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.
Where people slip
Mixing units — kilojoules for ΔH against joules for ΔS — before dividing gives a crossover temperature off by a factor of a thousand, an error the final answer's implausible magnitude should catch.
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