Isoequilibrium relationship

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). 

Figure 1. Example of the isokinetic relationship in the coordinates AH versus AS isoequilibrium relationship in the ionization of anilinium ions (69, 71).

Linert W, Grunert MC, Koudriavtsev AB (2004) Isokenetic and Isoequilibrium Relationships in Spin Crossover Systems. 235 105-136 Liu S, Edwards DS (2002) Fundamentals of Receptor-Based Diagnostic Metalloradio-pharmaceuticals. 222 259-278 Liu Y, see Arico F (2005) 249 in press Liz-Marzan L, see Mulvaney P (2003) 226 225-246 Llamas-Lorente P,see Alajan n M (2005) 250 77-106... 

Isokinetic and Isoequilibrium Relationships in Spin Crossover Systems... 

Linert and Kudryavtsev (1999) Isokinetic and isoequilibrium relationships in spin crossover systems [244]. 

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... 

ISOEQUILIBRIUM RELATIONSHIP ISOKINETIC RELATIONSHIP ISOERGONIC OOOPERATIVITY ISOKINETIC RELATIONSHIP... 

ISOEQUILIBRIUM RELATIONSHIP ISOLATED SYSTEM CLOSED SYSTEM OPEN SYSTEM... 

L. Liu and Q-X. Guo, Isokinetic Relationship, Isoequilibrium Relationship, and Enthalpy-Entropy Compensation, Chem. Rev., 2001,101, 673. R.A. Marcus, Skiing the Reaction Rate Slopes, Science, 1992, 256, 1523. 

As an exception to the above-noted trend, the reduction enthalpies and entropies for Cys-77Ser differ markedly from native (Table VII), although the AG values are similar. Such an isoequilibrium relationship implies that the mutant differs from the native only with regard to the electronic properties of the cluster, with no significant structural perturbation of the surrounding peptide. 

A similar relationship involving AG , AH°, and AS° is known as an isoequilibrium relationship. 

Liu, L., Guo, Q.-X. (2001). Isokinetic relationship, isoequilibrium relationship, and enthalpy-entropy compensation. Chemical Reviews, 101, 673-695. 

Liu L, Guo OX (2001) Isokinetic relationship isoequilibrium relationship, and enthalpy - entropy compensation. Chem Rev 101 673-695... 

A calorimetric study revealed the thermodynamic characteristics for the formation of complex 9 in the various solvents [9,23]. The formation of 9 is enthalpically driven in all solvents, and complexation entropies are mostly unfavorable. Complexation in protic solvents exhibits die largest exothermicity and, in general, die enthalpic driving force decreases fiom polar protic, to dipolar aprotic, and to apolar solvents. Correspondingly, the complexation entropy becomes increasingly less favorable as the exothermicity increases, resulting in a strong isoequilibrium relationship. 

The mathematics of the Lewis acid/base concept is that of a data matrix of m rows and n columns. Data are complexation constants, as logA" or AG. Each row corresponds to a Lewis acidity scale towards a reference base B° (/ = 1 to m) and each column corresponds to a Lewis basicity scale towards a reference acid A°j (J = I to n). For a rigorous treatment, the data measured in different media cannot be mixed in the same data matrix. In the matrix measuring Lewis affinity, the data are complexation enthalpies. There are extrathermodynamic relationships (isoequilibrium relationships or enthalpy-entropy compensation law) which allow transformations between blocks of the affinity and basicity matrices. In the principal component analysis of Lewis basicity, this justifies, somewhat, the mixing of affinity columns and basicity columns in a unified basicity-affinity matrix. 

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