The Isokinetic or Isoequilibrium Temperature

If we assume a linear relationship between AH and AS for the same reaction but with different substituents we can obtain Eq. 8.64. For most reactions, the AH and AS values are unknown. However, for those cases where these parameters have been measured and an LFER was found to hold, Eq. 8.64 does indeed correlate the AH and AS parameters. The slope is a proportionality constant between AH and AS, telling us how sensitive the compensation effect is between AH and AS. Eq. 8.64 tells us that as the enthalpy of activation becomes larger and less favorable, the entropy of activation becomes larger, too, but is more favorable, leading to a compensating effect. 

Using the Gibbs free energy equation (AG = AH - TAS ) in combination with Eq. 8.64 leads to Eq. 8.65. Now the proportionality constant is seen to have units of temperature, and is referred to as the isokinetic or isoequilibrium temperature for kinetic or thermodynamic LFERs, respectively. 

We have presented the fact that most reactions for which an LFER can correlate rate constants or equilibrium constants have linear relationships between AH and AS as described by Eq. 8.64. Because increases in AH impede a reaction while increases in AS assist a reaction, the two affects are compensating. This compensation is a general phenomenon. 

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