Structural changes in the solvent

The spent naphthalene-hs was examined by XH NMR for structural changes in the solvent. No hydrogenation of the naphthalene was detected. The naphthalene-ds was examined to determine the amount of deuterium which was exchanged with protium in the coal. After 10 h, 21.1% of the deuteriun in the a and e positions of naphthalene had exchanged. The a position was the most active position for exchange. 

For a long time the concept of the structure of water and structural changes in the solvent were discussed in the literature in very qualitative terms. There was no molecular definition nor a quantitative measure of the structure of water. No-one has estimated how much structural changes are induced by the solute. A possible definition of the structure of water was discussed in Chapter 1, and an approximate way to obtain a measure of the structure of water was discussed in Sec. 2.7. In Sec. 3.7, I shall present a similar measure of the structural changes induced by a solute based on the isotope effect on the Gibbs energy of solvation. 

Note that in whatever way we define the structure of the solvent, the contribution due to structural changes appearing in (3.4.7) or (3.4.10) also appears in the solvation entropy in either (3.4.5) or (3.4.9). Furthermore, when we form the combination of A — TAS, this term cancels out. We can now draw the general conclusion that structural changes in the solvent induced by the solute might affect A (or AH ) and AS but will have no effect on the solvation Helmholtz energy (or AG ). We shall see the analog of these quantities applied to a two-structure model in Secs. 3.5 and 3.6. 

There are other thermodynamic quantities which, though dependent on the structural changes in the solvent, are not easily explainable in these terms. An important example is the partial molar heat capacity (PMHC) of the solute 5, which can be expressed in either one of the following ways ... 

In this form, Es involves two structural change terms one includes a re-distribution among the v-cules of the solvent, and the second, the redistribution in the solutes. In practical applications of the idea of relaxation, we focus our attention on the structural changes in the solvent. To do this, let us rewrite... 

Thus, the solvation energy of solution of a hard sphere is viewed here as arising only from structural changes in the solvent. This brings us back to Eley s speculation that in water one may assume that is zero because of the existence of natural holes in the water. Clearly, such a conjecture is erroneous if the dissolution of a hard sphere (or creation of a cavity) induces large structural changes in the solvent. 

Note that v>i and v>2 here replace vi and V2 in (3.5.44). Thus, in general, to obtain a large contribution from structural changes in the solvent the distribution x v) does not need to be... 

Thus, the solvation volume of s at infinite dilution consists of the average volume of the VP of the solute plus the structural change in the solvent induced by the solute. The latter is the change in the distribution of the volumes of the VP of the solvent molecules. 

In this particular model, the partial molar volume vf is zero (i.e. inserting a solute in the holes does not contribute to the total volume of the system) hence, all of Vs is made up of structural changes in the solvent. Note also that the exact entropy-enthalpy compensation law is fulfilled in this model. 

In this section, we shall discuss the theoretical aspects of this problem. Starting with the concept of structural temperature which bypasses the need to define the structure, we formulate the problem within the exact framework of the MM approach. This approach naturally leads to the application of the Kirkwood-Buff theory, which provides only the sign of the structural changes. Finally, we present a simple measure of the amount of structural change in the solvent induced by a simple solute. 

We use the experimental results of the solvation Gibbs energies of argon, methane, and ethane to estimate the structural change in the solvent induced by placing such solutes at a fixed position in the liquid. Table 3.7 presents such numerical results. The values shown in this table are all positive. This is consistent with similar conclusions reached by many other authors, i.e. these solutes increase the structure of the solvent and therefore may justifiably be referred to as structure markers or structure promoters. ... 

For the following illustrations, we first examined the region of T,P for which there is maximal structural changes in the solvent. Then, we selected T, P that produce large negative values of A5 and AH. ... 

We now briefly apply a continuous mixture-model approach to demonstrate the general aspect of the contribution of structural changes in the solvent. For simplicity, we refer to the energy change associated with the H(f>0 process. Following Sec. 3.5, we write... 

Let us denote by Nhb)2M - (Nhb)o the structural change in the solvent induced by the process of placing two methane molecules at fixed positions and at infinite separation from each other. Since the structural change occurs in the close vicinity of each of the solutes, the total amount of structural change produced by this process is exactly twice the structural change produced by placing one methane molecule at a fixed position in the liquid. Hence, we have... 

Note that ANi is a result of the addition of the finite quantity of the solute s. The derivative d fXL - Ixh)/BNs is related to the structural changes in the solvent by the identity (see Appendix )... 

The difBculty of interpreting the large value of Cg within the TSM is that the quantity C itself can be split into two terms, the static and relaxation terms (Chapter 6). Therefore, the quantity C already includes contributions due to structural changes in the solvent. The general expression for the PMHC of S is quite involved, and is omitted here (see Ben-Naim, 1970b). Instead, we present a simple example to demonstrate an important result. Suppose that the mixture of L and H is ideal (in any of the senses discussed in Chapter 4). Also, for simplicity, we assume that S is very dilute in water. The total heat capacity of the system can be written as (Section 6.8)... 

We can now go back to Chadwell s explanation of the puzzling observation on the effect of solutes on the compressibility of water. The first term on the rhs of (7.60) can be viewed as the internal contribution of the solute to the compressibility. The second and third terms give the contribution due to structural changes in the solvent. One clearly sees that even if we know for sure that S stabilizes one of the forms L or H, this information is insufficient to draw conclusions as to the effect of S on the compressibility of the system. Of course, the general expression is more complicated than that given in (7.60). However, this example is sufficient to demonstrate the complexity of the expressions for quantities which are second derivatives of the free energy. 

If L represents the component with a relatively low local density, then the second term on the rhs of (7.154) is likely to be positive. Hence, the quantity dNJdNsh, may turn out to be either very small or even negative. As we have seen throughout this chapter, it is the stabilization effect at constant pressure that enters into the various thermodynamic quantities of solution. Therefore, the natural arena for studying the structural changes in the solvent should be the T, P, N ensemble. 

We can extend the above argument to any structural change in the solvent. Let N be any vector that may be used as a quasicomponent distribution function (Chapter 5). For simplicity, we assume that N contains discrete components. Let N and N be the composition of the solvent when the two solutes are at R and at = oo, respectively. Then instead of (8.133) we have... 

Hence, the first-order term drops out of (8.139). We thus conclude that in the limit of macroscopic systems the free energy change per pair of particles for the HI process is the same whether the process is carried out in the frozen-in or equilibrated system. On the other hand, the entropy and the enthalpy changes associated with the HI process may get a large contribution due to structural changes in the solvent. 

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