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Thermodynamic Information from the Temperature Dependence of Keq

We can calculate the value of the standard state enthalpy change, DeltaHo, and the standard state entropy change, DeltaSo, for a chemical change from measurements of the equilibrium constant for the change at several different temperatures.

Calculating Enthalpy Changes and Entropy Changes from the Change in Keq with Temperature

To determine DeltaHo and DeltaSo, plot ln Keq vs 1/T. The resulting straight line will have a slope equal to -DeltaHo/R and an intercept equal to DeltaSo/R.

Graph of ln K vs inverse of temperature

The derivation for this relationship follows:

We have seen that Delta G 0 equals minus R T ln K
and Calculating delta G from delta H and delta S
Thus we can write The relation of K, delta H, and Delta S
or Linear equation with ln K, delta H, and delta S

This last equation is the equation of a straight line with a a slope of -DeltaHo/R and an intercept equal to DeltaSo/R.

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