Partial molar volumes profile

The physical significance of the experimental profile is that it is the probability that a segment of an adsorbed polymer chain is at a distance z from the interface. In order to find the volume fraction (z) at a distance z from the interface we require the mass/unit area T and the partial molar volume of the polymer V (12), where (z) is given by... 

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

Fig. 2.14 The volume profile for reaction (2.173) at 25 °C, Ref. 170. The partial molar volumes of COj, Co(NHj)5H20 + and CofNHjljOH were measured with a digital density apparatus. Reprinted with permission from U. Spitzer, R. van Eldik and H. Kelm, Inorganic Chemistry, 21, 2821 (1982). (1982) American Chemical Society.

FIGURE 7.18 Experimental energy, entropy, and volume profiles for the oxidative addition of H2 to RhI(bpy)2+ in methanol and acetone (a) enthalpy, (b) entropy, and (c) partial molar volume. For details, see reference 345. For clarification, methanol (red), acetone (blue), see original Figure in Ref. 344. Reproduced by permission of the American Chemical Society. 

It is clear that from the integrated form of Equation (4) the volume of reaction can be obtained if the equilibrium constant can be determined over a range of pressure. If the volume of activation is not experimentally accessible for one of the directions of the reaction, A V can be used to calculate its value. Under certain conditions and with suitable properties of reactants and/or products it may be possible to determine their partial molar volumes, hence allowing development of a volume profile on an absolute volume basis, as noted above. Even if A V can be determined either from the pressure dependence of the equilibrium constant and/or from use of Equation (5), it may be possible to confirm its value by determination of the partial molar volumes from density measurements. The conditions for conducting successful determinations of partial molar volumes are rather stringent and will be described in Section 2. The method depends on measuring the density, d, of several solutions of different concentrations of the reactant or product. The following equation is used to obtain... 

A key feature one must consider in proposing volume profiles for a photochemical process is that the ES from which the reaction occurs may have a different partial molar volume than does the analogous GS. Several PAC experiments to determine AV values resulting from excitation were discussed in Section III, but there is relatively little other quantitative information on ES volumes. Although the partial molar volumes of the GS molecules may be determined by standard techniques, the unknown ES volume adds further ambiguity to prospective volume profiles for photochemical reactions, and may have importance to the evaluation of AKS. ... 

A volume profile for the reactions in Eq. (35) was constructed [119] with the aid of partial molar volume measurements on both the isomers, and is presented in Figure 27. The profile clearly demonstrates the dissociative nature of both the photochemical and thermal isomerization reactions, the large difference in the partial molar volume of the transition states being the effect of electrostriction and the difference in partial molar volume between Co11 and Co111. 

The goal of a pressure analysis of a chemical reaction is to construct the volume profile, which specifies at least the relative partial molar volumes of the reactants, products, and transition state. Figure 6.1 shows examples of several profiles. Note that the transition state may lie above, below, or in between the reactant and the product states and note that the difference between the forward and backward value of AV must be equal to AU. ... 

The volume profile indicates an increase in partial molar volume in proceeding to the transition state, which is interpreted in terms of an substitution controlled binding of the methyl radical to the Co(ll) complex. The large volume collapse that occurs subsequent to the formation of the transition state is ascribed to metal-carbon bond formation which is accompanied by oxidation of Co(II) to Co(III) and accompanied by a large volume contraction [86]. 

Indication of an 7d mechanism for substitution reactions of [Co(NH3)5X] + ions and an associative interchange (7a) mechanism for [Cr(NH3)6X] ions comes from studies of these systems at high pressures. These workers prefer to use a volume profile diagram (Figure 2) which involves comparison of the experimentally estimated partial molar volumes of the reactant [M(NH3)sX] + ions and the calculated... 

A variety of transition-metal hydroxo complexes, [M(NH3)50H] [M = Co(III), Rh(III), and Ir(III)], react with CO2 to give the corresponding monodentate carbonato complexes [M(NH3)s0C02]. The formation and decarboxylation kinetics of these complexes have now been studied as a function of pressure up to 1000 bar. The volumes of activation for CO2 uptake are -10.1 0.6 (Co(III)), -4.7 0.8 (Rh(III)), and -4.0 1.0 (Ir(III)) cm mor, whereas the corresponding values for decarboxylation are +6.8 0.3, +5.2 0.3, and +2.5 0.4 cm mol , respectively. Combined with partial molar volume measurements, these values enable the construction of overall reaction volume profiles. Bond formation during CO2 uptake and bond breakage during decarboxylation are approximately 50% completed in the transition state of these processes. 

Kinetic and volume measurements have permitted the establishment of complete volume profiles for formation, and for decarboxylation, of [M(NH3)5(C03)], M = Co and Ir as well as Rh. The volume profiles are compared in Figure 8.2, which shows their similarities volume changes are biggest for the smallest metal center, Co(III). The partial molar volumes of the transition states are intermediate between reactants and products, lying slightly closer to the hydroxo complex plus carbon dioxide side. " Kinetics and mechanisms of formation of carbonatorhodium(III) complexes have been reviewed. " ... 

The mechanistic interpretation of volume of activation and reaction volume data according to a volume profile analysis cannot be treated in this compilation. However, we would like to direct the readers attention to some interesting papers of general interest to this topic in the following references a method to estimate the intrinsic term in activation and reaction volumes/ the ionic-strength dependence of volumes of activation/ the correction for the compressibility of the solvent/ the role of nonlabile ligands in the interpretation of volumes of activation/ and the theoretical prediction of partial molar volumes and volumes of activation. 

The situation is more complex for non-ideal solid solutions because the partial molar volume of each constituent varies as a function of composition. Selective oxidation of one constituent of a solid solution results in concentration gradients for all constituents in the alloy underlying the oxide scale. Therefore, local variations of partial molar volumes result in local volume changes that must be accommodated by an additional displacement field parallel to the growth and diffusion direction to maintain the system in a stress-free state. An accurate evaluation of such a volume change and the related displacement field requires many data, often not available, to determine or calculate concentration profiles and partial molar volumes. However, the assumption of ideal solution behaviour would often provide estimated values of a sufficient accuracy. 

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