Solvent pair, solute

Carroll [82] discusses Henry s Law in detail and explains the limitations. This constant is a function of the solute-solvent pair and the temperature, but not the pres-... 

Figure 9.4. Schematic description of the solute-solvent pair potential. The double-arrowed line indicates the hard (repulsive) interaction between a and a water molecule. The dashed lines indicate the interaction between groups on the surface of a and a water molecule, the sum of which is the last term on the rhs of Eq. (9.4.1).

We see that after a rapid initial decay the components evolve slowly in time and that Sbft) falls to a negative value and stays negative over much of the interval depicted. Study of the time evolution of the solvent structure aroimd the solute can help explain the behavior of S f) and of its components. We have examined solute-solvent pair correlations involving the solute C sites that change their partial charges. Fig. 11 shows some of these results, specifically the pair correlations g+jvW and g+c (r) for the solute site that increases its charge by e/2 with an acetonitrile N site and a benzene C site, respectively. 

The ratio (Re/R)3 = (I)3 is thus implicit in the value of in the Flory-Fox equation and has a value of 0.49, corresponding to the Flory-Fox value of 2.1 X 1023. It is clear from Equations 1, 2, and 3 that [77] M cannot be related to the statistical polymer dimensions h and R without a knowledge of , i.e., < , which varies with solvent for a given polymer. It follows, that if all species having the same [77] M elute together from the GPC columns, then only Re can be the universal parameter, since will not be the same for all solute-solvent pairs and h and R will not be equally correct for universal calibration. 

The system studied consists of one solute molecule that is tagged and N solvent molecules, each of mass m. Since we are interested in a spherically symmetrical potential, the pair potential of the solvent-solvent pair and the solute-solvent pair is assumed to be given by the simple Lennard-Jones 12-6 potential... 

Hydrate nucleation and growth may have direct analogies in crystallization processes such as the precipitation of salt from solution. Metastability in salt crystallization was hypothesized to occur through supersaturation by Ostwald (1900). (A supersaturated solution is one in which the liquid [solvent] contains more dissolved solute than can be ordinarily accommodated at that temperature the greater the degree of supersaturation, the greater number of crystal nuclei that will form in solution.) Miers and Isaac (1907) experimentally proved metastability and postulated that for each solute-solvent pair, a concentration-temperature relationship exists that defines the metastable limit, formally called the thermodynamic spinodal. 

The anharmonicity we need to understand our relaxation could actually show up in either of two completely different guises within such a pair framework. The pair dynamics itself certainly could be deeply anhar-monic. That is, the solute-solvent pair distance q(t) could obey fundamentally anharmonic equations of motion. But it is also conceivable that the dynamics is not all that anharmonic (or more precisely, that its anharmonicity is not all that important). It might also be F (t), the force on the solute vibration being driven by the dynamics, that is fundamentally nonlinear. Either one of these kinds of anharmonicities (or both) could affect the instantaneous-pair (IP) vibrational friction (76) ... 

To test our new expression [Equation (25)], all we need to do is to identify the critical solvent for each instantaneous liquid configuration. Consistent with our previous discussion we look for solute-solvent pairs whose intrapair forces are larger than the forces imposed by the rest of the solvent, what we have called mutual-nearest-neighbor pairs (78,79). If the relevant solute-solvent reduced mass and pair potential are /jl and u(q),... 

Thus, perturbation potential of the solution and the distinguished solute in conformation i ". If is not decomposable according to solute-solvent pairs conditional on the solute conformation i ", then this relation introduces an effective pair interaction as the perturbation. 

In Equation (4-1), y is a measure of the effects of interionic or interparticle interactions, and y, a measure of the effect of changing the solvent. As the concentration of solute approaches zero, y approaches unity and y, approaches y a constant for each solute-solvent pair at a given temperature. The value of y, is related to the difference between the free energies of the solute in the usual standard states in the solvent and the reference solvent ... 

Figure 2 Solute-solvent pair correlation function at T = 1.37 and p = 0.40, 0.50, and 0.60. a) Short range structure b) long range structure (note change of axes).

To begin the analysis, the potential energy of solute-solute, solvent-solvent, and solute-solvent pairs is identified as Wga, and Wab- In the first step, an energy equal to 2wbb rnust be absorbed to break the solute-solute interaction between two adjacent solute molecules in the solid. After the solute molecule... 

The solvent is recovered in a second step, typically by distillation. So, the solute-solvent pair should not form an azeotrope and the more volatile component should be the minor component in the mixture. 

For simplicity, we assume that the solute-solvent pair potential is a function of the distance R only, and that this function may be written as... 

For simple solute a, such as argon, one can separate each of the solute-solvent pair potentials into two contributions (see section 7.7)... 

For proteins, the simple split of the solute-solvent pair potential as in (7.246) is not appropriate one needs a more elaborate description of the ingredients of this pair potential. There are several ways of performing such a split into a sum of contributions. One way is to recognize that in addition to the hard and soft parts of the potential, there are also specific functional groups such as charged or polar groups which interact with water in a way different from a simple nonpolar group. 

To account for these specific interactions, we write the solute-solvent pair interaction for protein a, in generalization of (7.246), as... 

The value of the constant of proportionality, called the Henry s law constant, is dependent on the solute-solvent pair,Jemperature, and pressure. At higher concentrations the hnear relationship between f T, P, x) and mole fraction fails a form of Eq. 

If a solute-solvent pair were ideal in the Henry s law sense, Eq. 9.7-4 would be satisfied at all mole fractions in particular, at x-, = 1,... 

Here M is the molality of species i, that is, the number of moles of this species per 1000 g of solvent, and TL is the Henry s law constant based on molality its value depends on the solute-solvent pair, temperature, and pressure. For real soludons the activity coefficient F(7, P, MO is introduced, so that... 

The valu of the partial molar Gibbs energy of species i in the (hypothetical) ideal solution Cf(T, P, M — 1) is obtained by assuming ideal solution behavior and extrapolating th behavior of G T, P, MO in very low-molality solutions to one molal. The value of Gf (and G, as well) obtained in this way depends on temperature, pressure, and the solute-solvent pair. 

Equations 12.1-8 through 12.1-13 can be used in Eq. 12.1-7 to compute the saturation solubility for any regular solution solute-solvent pair. 

While the Stokes-Einstein equation is strictly applicable only in cases where the diffusing particle is large when compared to the surrounding solvent molecules (so that the fluid can be considered a continuum), it has proven to be useful for solute-solvent pairs in which the radius, a, is only two to three times the solvent radius. For a solute with radius comparable to the solvent radius, the 6 in Equations 4-3 and 4-4 should be replaced by a 4, since the assumption of no slip at the solute surface is no longer valid [48]. 

Polar van der Waal s retention forces are a consequence of dipole-dipole interactions and hydrogen bonding between molecules. Only components with dipoles similar to the solvent (stationary phase) will disperse, producing solute-solvent pairs. Dipole induced dipole interactions arise from the charge on one molecule (component or stationary phase) disturbing the electrons in a second associated molecule, producing a shift in charge which then forms the induced dipole. 

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