Thermodynamic measurements solutions

On the experimental side, one may expect most progress from thermodynamic measurements designed to elucidate the non-configurational aspects of solution. The determination of the change in heat capacity and the change in thermal expansion coefficient, both as a function of temperature, will aid in the distinction between changes in the harmonic and the anharmonic characteristics of the vibrations. Measurement of the variation of heat capacity and of compressibility with pressure of both pure metals and their solutions should give some information on the... 

Thermodynamic measurements such as heat of solution from solution calorimetry [11,12], heat of fusion from differential scanning calorimetry (DSC) [12], and entropy of processing, ASp [12]... 

Equations (2) and (3) relate intermolecular interactions to measurable solution thermodynamic properties. Several features of these two relations are worth noting. The first is the test-particle method, an implementation of the potential distribution theorem now widely used in molecular simulations (Frenkel and Smit, 1996). In the test-particle method, the excess chemical potential of a solute is evaluated by generating an ensemble of microscopic configurations for the solvent molecules alone. The solute is then superposed onto each configuration and the solute-solvent interaction potential energy calculated to give the probability distribution, Po(AU/kT), illustrated in Figure 3. The excess... 

This permits provisional calculation of the compositional dependence of the equilibrium constant and determination of provisional values of the solid phase activity coefficients (discussed below). The equilibrium constant and activity coefficients are termed provisional because it is not possible to determine if stoichiometric saturation has been established without independent knowledge of the compositional dependence of the equilibrium constant, such as would be provided from independent thermodynamic measurements. Using the provisional activity coefficient data we may compare the observed solid solution-aqueous solution compositions with those calculated at equilibrium. Agreement between the calculated and observed values confirms, within the experimental data uncertainties, the establishment of equilibrium. The true solid solution thermodynamic properties are then defined to be equal to the provisional values. 

As seen from Eq. (130) an activity coefficient may deviate significantly from unity at higher salt concentrations. The activity coefficient can therefore also be used as a measure of the deviation of the salt solution from a thermodynamically ideal solution. If the chemical potential of a solute in a (pressure-dependent) standard state of infinite dilution is /x°, we find the standard partial molar volume from... 

The first type applies in solutions of hydrogen halide in benzene and methylbenzenes, where thermodynamic measurements force one to the conclusion of an intermolecular interaction between the solvent molecules and the dissolved hydrogen halide molecules (Brown and Brady, 1952). 

The chloride concentration thus corresponds to the sulphite concentration in the test solution. The chloride ISE can be used for various thermodynamic measurements, such as determination of the activity of NaCl [361], also in the pressure range 0.1-60MPa and temperature of 0-25 [217]. This ISE is also... 

It follows that retention measurements on silica based stationary phases for the purpose of obtaining thermodynamic data is fraught with difficulties. Data from solutes of different molecular size cannot be compared or related to other Interacting variables ideally, thermodynamic measurements should be made on columns that contain stationary phases that exhibit no exclusion properties. However, the only column system that might meet this requirement is the capillary column which, unfortunately introduces other complications wmcn will be discussed later. 

The enthalpy change associated with formation of a thermodynamically ideal solution is equal to zero. Therefore any heat change measured in a mixing calorimetry experiment is a direct indicator of the interactions in the system (Prigogine and Defay, 1954). For a simple biopolymer solution, calorimetric measurements can be conveniently made using titra-tion/flow calorimeter equipment. For example, from isothermal titration calorimetry of solutions of bovine P-casein, Portnaya et al. (2006) have determined the association behaviour, the critical micelle concentration (CMC), and the enthalpy of (de)micellization. 

Both modifications affect the analysis of dilute solution behavior, and it is difficult to judge how much the e/e0 term is actually needed. In any case, as the authors themselves point out (41), the e/e0 term makes an entirely negligible contribution to solvent activity in concentrated solutions. For example, simple calculations yield a contribution of approximately l%ina 10% solution of natural rubber in benzene at 30° C (M = 500000, [t/]g = 250, y=0.4). It is therefore clear that thermodynamic measurements can furnish no evidence for or against continued collapse in concentrated solutions. 

The value of log K for the copper complex of 6.24 is 4.3, whilst for that of 6.23 it is 1.97. The macrocyclic complex is thus about 100 times more stable than the open-chain complex, and this is presumably due to the macrocyclic effect. In this case, thermodynamic measurements have shown that Afor the macrocyclic and open-chain complexes are almost identical, and so the macrocyclic effect is due almost entirely to the entropy term. However, even with these ligands the involvement of solvation may not be neglected entirely. The stability values given above are for the complexes in aqueous solution if the measurements are repeated in 80 % aqueous methanol, the value of log K for the formation of the macrocyclic complex is only 3.5. A hole-size effect (section 6.6) is also apparent if we move to the larger thioether macrocycle 6.26. For the formation of the copper complex of 6.26 (again in 80 % aqueous methanol) log K is found to be 0.95. 

Thermodynamic measurements in dilute hydrocarbon surfactant solutions give negative values for the enthalpy change on micellization (AH0mic), and the entropy change (AS°mic) in the negative range (see Chapter 1, Table 1.1 for comparison). 

No doubt structural differences are also responsible for the 0-36% increase in molecular volume of liquid water on going from H20 to D20. The molecular volumes of mixtures obey an ideal mixture law very closely (Kirshenbaum, 1951). However, in the main, the density difference between H20 and its mixtures with D20 is due to the change in average molecular weight. Because of this density difference, the quantitative results for thermodynamic measurements on solutions in H20-D20 mixtures are different according to the concentration scale adopted. For dilute solutions in ordinary water the difference between... 

Equations (3.2) and (3.3) relate intermolecular interactions to measurable solution thermodynamic properties. The excess chemical potential is obtained from... 

---