Isoequilibrium temperature

A linear relationship between the standard enthalpies and entropies of a series of structurally related molecular entities undergoing the same reaction thus, AH° -I3AS° = constant or AAH° = (3AS°. When P > 0, this relationship is referred to as an isoequilibrium relationship. When the absolute temperature equals the factor P (often referred to as the isoequilibrium temperature), then all substituent effects on the reaction disappear (i e., AAG° = 0). In other words, a reaction studied at T = p will exhibit no substituent effects. This would suggest that, when one studies substituent effects on a reaction rate, the reaction should be studied at more than one temperature. Note also that the p factor in the Hammett equation changes sign at the isoequilibrium temperature. See Isokinetic Relationship... 

Equation (5) clearly indicates that, at the critical point, or so-called isokinetic or "isoequilibrium temperature fi), the rate or equilibrium constant is totally independent of the change in enthalpy caused by any alterations in substituent, solvent, and so on. It is interesting that such phenomena have been abundantly observed for various reactions and equilibria. 

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. 

The variable factor in reaction series usually was a substituent change, although solvent variation also has been given special attention (39-44). Variations of catalyst (4, 5, 23-25, 45-49), ionic strength (50), or pressure (51, 52) also have been studied. In exceptional cases, temperature can become the variable parameter if the kinetics has been followed over a broad temperature range and the activation parameters are treated as variable (53), or temperature as well as structural parameters can be changed (6). Most of the work done concerns kinetics, but isoequilibrium relationships also have been observed (2, 54-58), particularly with ionization equilibria (59-82). 

Values of AH° and AS° for complex-formation between alpha and beta cyclodextrin and a variety of guest molecules are shown in Tables II and III. If AH° is plotted against AS°, a linear relationship is observed, in which AH° and AS° are compensating (see Figs. 4 and 5). The slope of the graph is called the compensation temperature or isoequilibrium... 

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