`T = (DeltaH_"rxn") / (DeltaS_"rxn") ("at equilibrium")`

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The Temperature at Equilibrium^[1] equation, T = ΔH_rxn/ΔS_rxn, estimates the temperature at which a process has reached equilibrium. This equation is derived from the Gibbs Free Energy and disorder laws (ΔG and ΔS). The inputs are as follows:

 

·      T is temperature in Kelvin (K)

·      ΔH_rxn is the change in enthalpy over time with units of kilojoules per mole (kJ/mol)

·      ΔS_rxn is the change in entropy over time with units of kilojoules per mole*K (kJ/mol*K)

 

When entered into the calculator, ΔH_rxn and ΔS_rxn must have units of kJ/mol (or kJ/mol*K for ΔS_rxn) in order to cancel out correctly. Due to the division, the kJ and moles will cancel, leaving only Kelvin (K) left as units for temperature. 

Derivation

We know the Gibbs Free Energy equation: 

ΔG_rxn = ΔH_rxn - TΔS_rxn

When ΔG_rxn equals zero, we know the reaction has reached equilibrium. So, if we're trying to find the temperature at equilibrium, we can substitute zero for ΔG_rxn:

0 =  ΔH_rxn - TΔS_rxn

And after rearranging the substituted equation above, we get the Temperature at Equilibrium equation:

T = ΔH_rxn/ΔS_rxn

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 594

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