Extrathermodynamic functions

In /c (or In values and the hydrocarbonaceous surface areas of the solutes. For example, the dependence of the activity coefficient, for the phosphorylation of ten myosin-related analogues on the extrathermodynamic functional group effect, t, was assessed [10] according to the linearised expression... 

Now, it can be postulated that solvolysis rate should be a function of two properties of the solvent one is its ionizing power, and the other is its nucleo-philicity. An SnI process should be promoted by high ionizing power, and an Sn2 process by high solvent nucleophilicity. At this point, we are ready to bring the extrathermodynamic approach to bear on this problem. This was initiated by Grun-wald and Winstein, who defined a solvent ionizing power parameter Y by... 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

It is well known that such quantities as the standard free energy, enthalpy and entropy display a remarkable tendency to be additive functions of independent contributions of part-structures of the molecule. This property, on which the mathematical simplicity of many extrathermodynamic relationships is largely based, is well illustrated, for example, by the enthalpies of formation at 298°K of several homologous series of gaseous hydrocarbons Y(CH2)mH, which are expressed by the relation (28) (Stull et al., 1969). In... 

It is not possible to evaluate k directly, for it appears with the entropy of activation in the temperature-independent part of the rate constant. An estimate of k requires an extrathermodynamic assumption. In two cases of iron(II) spin equilibria examined by ultrasonic relaxation the temperature dependence of the rates was precisely determined. If the assumption is made that all of the entropy of activation is due to a small value of k, minimum values of 10-3 and 10-4 are obtained. Because there is an increase in entropy in the transition from the low-spin to the high-spin states, this assumption is equivalent to assuming that the transition state resembles the high-spin state. There is now evidence that this is not the case. Volumes of activation indicate that the transition state lies about midway between the two spin states. This is a more chemically reasonable and likely situation than the limiting assumption used to evaluate k. In this case the observed entropy of activation includes some chemical contributions which arise from increased solvation and decreased vibrational partition functions as the high-spin state is compressed to the transition state. Consequently, the minimum value of k is increased and is unlikely to be less than about 10 2. 

The thermodynamic functions of transfer of individual ions cannot, of course, be studied experimentally, since only complete electrolytes are thermodynamic components, so that an extrathermodynamic assumption is needed in order to split the measurable quantity into the contributions from the individual ions. A commonly employed assumption is that for a reference electrolyte with large, univalent, nearly spherical cation and anion of nearly equal sizes the measured... 

The attempt to correlate biological activity with chemical structure in quantitative terms assumes that a functional dependence exists between the observed biological response and certain physicochemical properties of molecules. Without a mechanistic model one obtains it by an empirical correlation. A rational way to define such empirical relationships is within the extrathermo-dynamic approach (1). Although extrathermodynamic relationships... 

The discussed calculation procedure is not based on any extrathermodynamic assumptions and therefore the inaccuracy of the result obtained is determined only by the experimental errors of measuring a work function and the Volta potential difference. Furthermore, from the solvent surface potential x determined by any estimation method we can find the ideal solvent-electron interaction energy Vq = U — ex . Unlike U , V, is not a strictly thermodynamic quantity and the inaccuracy in determining it, besides experimental errors, is caused by the inaccuracy of model assumptions made for estimating x -... 

QS AR) represents an attempt to correlate structural or property descriptors of compounds with reactivities (Topliss, 1983 Hansch and Hoekman, 1995). An explanation of the struc-tnral effect on the eqnilibria or rates of chemical reactions often involve some kind of comparison with a snitable model or set of models. The quantities compared are thermodynamic, nsnally free energies, enthalpies or entropies, but the simple relationships found among snch qnantities are often not part of the formal structure of thermodynamics, hence they are referred to extrathermodynamic relationships. Useful extrathermodynamic relationships are nsnally simple in form. The mathematical simplicity of many extrathermo-dynamic relationships resnlts from the tendency of such quantities to be additive functions of molecular structure. The molar values of the property under comparison are assumed to be approximately additive functions of independent contributions assignable to substructures of the molecules. 

We close this section with a reminder of a fnndamental issue in electrochemistry Not all the quantities in Equations 13.8 throngh 13.13 are accessible to measurement by electrochemical or thermodynamic methods. Only the electrochemical potential ( i ), the work function (W ) or equivalently the real potential (a ) and the Volta potential ( / ) are. Equations 13.9, 13.11, and 13.13 are therefore formal resolutions. It is not possible to assign actual values to the separate terms, the chemical potential ( t ), the Galvani potential (cp ), nor the surface potential (x ), without making extrathermodynamic assumptions. These quantities must therefore be considered unphysical, at least from the point of view of thermodynamics. This statement, which is called the Gibbs-Guggenheim Principle in [42], is often met with disbelief from theoretical and computational chemists, particularly in the case of the chemical potential (Equation 13.10). The standard chemical potential is essentially the (absolute) solvation free energy AjG of species i. One would hope that a molecular simulation contains all information needed to compute AjG . Indeed, there seems to be a way around this thermodynamic verdict for computation and also mass spectroscopic. This continues to be, however, hazardous territory, particularly for DFT calculations in periodic systems. ... 

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