Stepwise solvation processes

Care must be exercised in taking the limit of ideal gas (p — 0 or P— 0). In general, one cannot take the limiting behavior of Vf and k as  

This would lead to V lg = 0, which in general, is not correct. Further discussion of this point is presented in Appendix O. 

We have defined the solvation process as the process of transfer from a fixed position in an ideal gas phase to a fixed position in a liquid phase. We have seen that if we can neglect the effect of the solvent on the internal partition function of the solvaton s, the Gibbs or the Helmholtz energy of solvation is equal to the coupling work of the solvaton to the solvent (the latter may be a mixture of any number of component, including any concentration of the solute s). In actual calculations, or in some theoretical considerations, it is often convenient to carry out the coupling work in steps. The specific steps chosen to carry out the coupling work depend on the way we choose to write the solute-solvent interaction. 

For simplicity, we discuss here a solute s in a one-component solvent b, in a system atT, V, Ns, Nb We assume that the solute-solvent interaction can be written as a sum of two parts, say 

The coupling work is the same as the work of turning on the interaction Usb(R). If Usb(R) has the form (7.115), we can carry out the coupling work in two steps first we couple U (R), and then we couple the second part Ujb(R). This procedure was found useful in interpreting the solvation quantities of simple solutes in water, the study of hydrophobic hydrophilic interactions and 

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This method is particularly valuable in two respects (1) It allows the direct determination of reaction rates, say kf and k, from which the equilibrium constant, K2 — kf//c, can be derived. (In some instances, direct determination of the equilibrium constant is also possible.) (2) It is very well suited for the study of stepwise (clustering) solvation processes in the gas phase at temperatures near 298 K. 

Another physical effect associated with solvation is cavitation. It is again helpful to visualize the solvation process as a stepwise procedure. Here, we imagine the first step as being creation of a cavity of vacuum within the solvent into which the solute will be inserted as a second step. The energy cost of the cavity creation is the cavitation energy. Note that energy is always required to create the cavity - if it were favorable to create bubbles of vacuum in the liquid, the solvent would not remain in the liquid phase. 

A simplified view of the early processes in electron solvation is given in Figure 7. Initially, electron pulse radiolysis was the main tool for the experimental study of the formation and dynamics of electrons in liquids (Chapter 2), first in the nanosecond time range in viscous alcohols [23], later in the picosecond time range [24,25]. Subsequently, laser techniques have achieved better time resolution than pulse radiolysis and femtosecond pump-probe laser experiments have led to observations of the electron solvation on the sub-picosecond to picosecond time scales. The pioneering studies of Migus et al. [26] in water showed that the solvation process is complete in a few hundreds of femtoseconds and hinted at the existence of short-lived precursors of the solvated electron, absorbing in the infrared spectral domain (Fig. 8). The electron solvation process could thus be depicted by sequential stepwise relaxation cascades, each of the successive considered species or... 

In dlfluorenylstrontlum Itself the solvation Is a stepwise process, l.e., Fl, Sr++,Fl- <— Fl",Sr F1" += Fl 11Sr4 11Fl (31). In the n - 2 bolaform salt the first separation step Is difficult, but once bound THF molecules force Sr to separate from the first Fl Ion, the cyclic structure probably opens up due to the shortness of the (CH2>2 chain. This would leave a free Fl Ion on one end of the chain. Since the conductance of the salt Is known to be very low, this latter species most likely will rapidly dimerize to form a non-conducting cyclic aggregate consisting of loose Ion pairs only,as shown In reaction 14. This aggregation shifts the equilibrium In favor of the loose Ion pairs. 

The process of complexation is believed to occur through the stepwise incorporation of the ligand, i.e. stepwise replacement of the existing solvation, or hydration, sheath. The process is likely to be entropy controlled and entropy increases have been noted in thermodynamic studies on these systems.33... 

The two free hydroxy groups are First protected with acetic anhydride. In a second step the acetyl group is reductively cleaved by a Birch reduction with lithium in liquid ammonia.19 Lithium dissolves in the ammonia with the formation of solvated electrons. Stepwise electron transfer to the aromatic species (a SET process) leads first to a radical anion, which stabilizes itself as benzylic radical 38 with loss of the oxygen substituent. A second SET process generates a benzylic anion, which is neutralized with ammonium chloride acting as a proton source (see Chapter 12). 

Participation of neighbouring groups has been observed in some other nitrous acid deamination reactions. It is not possible to say with certainty whether these reactions proceed through concerted or stepwise processes because they are too fast to be measurable, but in view of the discussion above it seems most reasonable to consider the reactions as leading very rapidly to specifically solvated ion-pairs which then suffer attack from the rear by the neighbouring groups. Some reactions of this type are shown in Fig. 39. 

Few experiments allow one to bridge gas-phase electron transfer mechanism to liquid (or condensed)-phase electron transfer reactions. The major problem is to model the so-called solvent coordinates in the gas phase. Of course, clusters seems to be the ideal medium to build solvent effects in a stepwise manner. However, clusters are much colder than liquids, with the consequence that only a limited number of isomers are explored, as compared with the room temperature configurations involved in liquid processes. Discrepancies are observed in the case of cluster solvation of ionic molecules in clusters Nal remains at the surface of water clusters whereas it dissolves in bulk water [275]. Clusters thus do not allow one to explore in a single step all the aspects of a liquid-phase electron-transfer reaction. Their main advantage arises from this limitation since they allow one to study separate aspects of the solution processes. 

Equation (7.204) corresponds to the following stepwise process. At equilibrium plD = psD. We first freeze in the translational and rotational degrees of freedom of D, then separate the two fragments A and B from their equilibrium distance to two fixed positions but at infinite separation. Next, solvate the two fragments A and B when they are at infinite separation from each other, finally release the two fragments to attain their liberation free energy. 

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