Partial molar interpretation

For the mechanistic interpretation of activation volume data for nonsymmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species, when these are available, or can be determined from density measurements. Efforts have in recent years focused on the electrochemical determination of reaction volume data from the pressure dependence of the redox potential. Tregloan and coworkers (139, 140) have demonstrated how such techniques can reveal information on the magnitude of intrinsic and solvational volume changes associated with electron-transfer reactions of transition... 

The volume profile indicates an increase in partial molar volume in going to the transition state, which is interpreted in terms of an 7d... 

At temperatures well below UCST, solubilities of hydrocarbons in water or water in hydrocarbons drop to very low values. The solutions are very nearly ideal in the Henry s law sense, and the isotope effects on solubility can be directly interpreted as the isotope effect on the standard state partial molar free energy of transfer from the Raoult s law standard state to the Henry s law standard state. Good examples include the aqueous solutions of benzene, cyclohexane, toluene,... 

Any physical interpretation of a partial molar quantity must be consistent with its definition. It is simply the change of the property of the phase with a change of the number of moles of one component keeping the mole numbers of all the other components constant, in addition to the temperature and pressure. It is a property of the phase and not of the particular component. One physical concept of a partial molar quantities may be obtained by considering an infinite quantity of the phase. Then, the finite change of the property on the addition of 1 mole of the particular component of this infinite quantity of solution at constant temperature and pressure is numerically equal to the partial molar value of the property with respect to the component. 

As a preliminary to a discussion of kinetics of reactions in aqueous mixtures, it is interesting to review briefly the behaviour of equilibrium quantities as a function of co-solvent mole fraction. Interpretation of the data is necessarily complex because, for example, in the case of acid dissociation constants, the quantity 5mAXie represents the result of the individual variations of the partial molar quantities for acid, conjugate base and hydrogen ion. Nevertheless patterns of behaviour are observed which demonstrate the impact of co-solvent on water structure and on solute properties along the lines discussed in the previous section. 

Equation (11.5) implies that a molar solution property is given as a sum its parts and that Mi is the molar property of species i as it exists in solutio This is a proper interpretation provided one understands that the defining equati for Mit Eq. (11.2), is an apportioning formula which arbitrarily assigns to eac species i a share of the mixture property, subject to the constraint of Eq. (11.5), The constituents of a solution are in fact intimately intermixed, and ov to molecular interactions cannot have private properties of their own. Neverthel they can have assigned property values, and partial molar properties, as defin by Eq. (11.2), have all the characteristics of properties of the individual speci as they exist in solution. 

Example 11.1 What physical interpretation can be given to the defining expression [Eq. (11.1)] for the partial molar volume ... 

In this section, we investigate the relations between the macroscopic susceptibilities and the molecular polarizabilities. Consistent microscopic interpretations of many of the non-linear susceptibilities introduced in Section 2 will be given. Molar polarizabilities will be defined in analogy to the partial molar quantities (PMQ) known from chemical thermodynamics of multicomponent systems. The molar polarizabilities can be used as a consistent and general concept to describe virtually all linear and non-linear optical experiments on molecular media. First, these quantities will be explicitly derived for a number of NLO susceptibilities. Physical effects arising from will then be discussed very briefly, followed by a survey of experimental methods to determine second-order polarizabilities. 

From an interpretive and structurai point of view, it is not much use to know the partial molar volumes of electrolytes unless one can separate them into vaiues for each ion. One way of doing this might he to find electrolytes having ions with the same... 

The temperature variation of the solvation free energy is the partial molar entropy and, because of its interpretation as an indicator of disorder, is of wide interest. As above, we focus here on the conditions of infinite dilution of a solute M in a W solution. Show that the interaction contribution to the partial molar entropy is... 

The Kirkwood—Buff (KB) theory of solution (often called fluctuation theory) employs the grand canonical ensemble to relate macroscopic properties, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volnmes, to microscopic properties in the form of spatial integrals involving the radial distribution function. This theory allows one to obtain information regarding some microscopic characteristics of mnlti-component mixtures from measurable macroscopic thermodynamic quantities. However, despite its attractiveness, the KB theory was rarely used in the first three decades after its publication for two main reasons (1) the lack of precise data (in particular regarding the composition dependence of the chemical potentials) and (2) the difficulty to interpret the results obtained. Only after Ben-Naim indicated how to calculate numerically the Kirkwood—Buff integrals (KBIs) for binary systems was this theory used more frequently. 

Eckert et al. (1) interpreted partial molar volume data for supercritical solutions as indicating the collapse of 100 solvent molecules about a solute molecule. Kim and Johnston (2) interpreted the solvent shift in the UV absorption of phenol blue dissolved in supercritical ethylene to suggest a local solvent density surrounding a solute molecule more than 50% greater... 

Another interesting way of interpreting (G.22) is to use the relation for the partial molar volume of a particle placed at a fixed position in a system characterized by T, P, N. The relevant relation is (see section 7.5 and appendix O)... 

However, the partial differentiations here are not at constant T and p consequently, pn is not partial molar U, nor partial molar H, nor partial molar A. The conditions of the partial differentiation for U and H cannot be physically interpreted, making the partial derivatives of U and H of little interest for the description of real systems. But the partial differentiation of A is at a physically meaningful condition that makes the partial derivative useful for the calculation of chemical potential. 

In this expression Vatom and Vcavities are the volumes of the atoms and the cavities respectively and AVhydrat.on is the volume change of the solution resulting from the interactions of the protein molecule with the solvent. More defined models for the partial molar volumes of proteins are discussed by Chalikian [27,28]. Care should be taken if quantities derived Ifom the volume (such as compressibility and thermal expansion) are interpreted on the molecular level. The experimental results may depend on the sensitivity range of the method used. Global measurements such as ultrasonics detect the whole molar volume, while some local probes may feel only the change of the protein interior volume. 

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