Solution species

The moles of a solute species adsorbed per gram of adsorbent nl can be expressed in terms of the mole fraction of the solute on the surface N and the moles of adsorption sites per gram as... 

The discussion so far has been confined to systems in which the solute species are dilute, so that adsorption was not accompanied by any significant change in the activity of the solvent. In the case of adsorption from binary liquid mixtures, where the complete range of concentration, from pure liquid A to pure liquid B, is available, a more elaborate analysis is needed. The terms solute and solvent are no longer meaningful, but it is nonetheless convenient to cast the equations around one of the components, arbitrarily designated here as component 2. 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

The entropy of a solution is itself a composite quantity comprising (i) a part depending only on tire amount of solvent and solute species, and independent from what tliey are, and (ii) a part characteristic of tire actual species (A, B,. ..) involved (equal to zero for ideal solutions). These two parts have been denoted respectively cratic and unitary by Gurney [55]. At extreme dilution, (ii) becomes more or less negligible, and only tire cratic tenn remains, whose contribution to tire free energy of mixing is... 

The solute species therefore diffuse independently, rather as in Knudsen diffusion, but with effective diffusion coefficients D, where... 

Hydroxides. The hydrolysis of uranium has been recendy reviewed (154,165,166), yet as noted in these compilations, studies are ongoing to continue identifying all of the numerous solution species and soHd phases. The very hard uranium(IV) ion hydrolyzes even in fairly strong acid (- 0.1 Af) and the hydrolysis is compHcated by the precipitation of insoluble hydroxides or oxides. There is reasonably good experimental evidence for the formation of the initial hydrolysis product, U(OH) " however, there is no direct evidence for other hydrolysis products such as U(OH) " 2> U(OH)" 2> U(OH)4 (or UO2 2H20). There are substantial amounts of data, particulady from solubiUty experiments, which are consistent with the neutral species U(OH)4 (154,167). It is unknown whether this species is monomeric or polymeric. A new study under reducing conditions in NaCl solution confirms its importance and reports that it is monomeric (168). 8olubihty studies indicate that the anionic species U(OH) , if it exists, is only of minor importance (169). There is limited evidence for polymeric species such as Ug(OH) " 25 (1 4). 

For a binaiy system, r = Otg = L/Ot g. The symbol r applies primarily to the process, while Ot is oriented toward interactions between pairs of solute species. For each binaiy pair, fij = C( ji = l/Otiy. ... 

When there is a large difference between ys(A) and ys(B) in the equation above, there must be signihcant deparmres from dre assumption of random mixing of the solvent atoms around tire solute. In this case tire quasi-chemical approach may be used as a next level of approximation. This assumes that the co-ordination shell of the solute atoms is hlled following a weighting factor for each of tire solute species, such that... 

The interaction between a solute species and solvent molecules is called solvation, or hydration in aqueous solution. This phenomenon stabilizes separated charges and makes possible heterolytic reactions in solution. Solvation is, therefore, an important subject in solution chemistry. The solvation of ions has been most thoroughly studied. 

The interpretation of these remarkable properties has excited considerable interest whilst there is still some uncertainty as to detail, it is now generally agreed that in dilute solution the alkali metals ionize to give a cation M+ and a quasi-free electron which is distributed over a cavity in the solvent of radius 300-340 pm formed by displacement of 2-3 NH3 molecules. This species has a broad absorption band extending into the infrared with a maximum at 1500nm and it is the short wavelength tail of this band which gives rise to the deep-blue colour of the solutions. The cavity model also interprets the fact that dissolution occurs with considerable expansion of volume so that the solutions have densities that are appreciably lower than that of liquid ammonia itself. The variation of properties with concentration can best be explained in terms of three equilibria between five solute species M, M2, M+, M and e ... 

The n values were high for all of the ionic liquids investigated (0.97-1.28) when compared to molecular solvents. The n values result from measuring the ability of the solvent to induce a dipole in a variety of solute species, and they will incorporate the Coulombic interactions from the ions as well as dipole-dipole and polarizability effects. This explains the consistently high values for all of the salts in the studies. The values for quaternary ammonium salts are lower than those for the monoalkylammonium salts. This probably arises from the ability of the charge center on the cation to approach the solute more closely for the monoalkylammonium salts. The values for the imidazolium salts are lower still, probably reflecting the delocalization of the charge in the cation. 

In an ideal solution the components A, B, and C. . . are on an equal footing, and there is no distinction between solvent and solute. In this book we are mainly interested in very dilute ionic solutions, where the mole fraction of one component, known as the solvent, is very near unity, and where (at least) two solute species are present, the positive and the negative ions we shall use nA and xA to refer to the solvent particles and shall denote the solute species by B and C. Let us write... 

Equilibrium in Any Process. We have discussed a reaction involving either four solute species or three solute and one solvent species. The method can be used to describe the equilibrium in any type of reaction or process, involving any number of solute species in extremely dilute solution. The method could be applied, for example, to the ionic dissociation of a molecule, or to the dissociation of a molecular ion. In general, when the expression for the reaction has been written down, we suppose that the reaction takes place from left to right then each particle (of species i) on the right-hand side makes to the cratic term the contribution - -kT In x, while each particle on the left-hand side makes the contribution —kT In x,. The sum of these quantities, which may be denoted by kT 2 In x, will contain as many terms as there are particles in the reaction as written down. 

It was mentioned in Sec. 46 that 1000 grams of HjO contains 55.5 moles. For any solute species in aqueous solution... 

In general, when the equation for any reaction or process has been written down, let there be q solute particles on the left-hand side, and let there be (q + Aq) solute particles on the right-hand side. In any solvent let M denote the number of moles of solvent that are contained in the mass that has been adopted as the b.q.s. then for each solute species m = My. At extreme dilution the ratio of K to Kx takes the value1... 

Suppose now that we build a series of cells, alike in all respects save that the (very dilute and completely dissociated) solute has a different concentration in each cell. If the cells are alike in all other respects, the unitary terms must be the same in each coll the values of the e.m.f. for the various cells will differ owing to the difference in the communal terms. In very dilute solutions the contribution made to each communal term by the interionic forces will be small, and the dependence of the e.m.f. on the concentration will arise almost entirely from the cratic term which, for each solute species, may be written — kT In y or — IcT In x. Since we are considering a uni-univalent solute, the numerical values of y+ and t/ for the positive and negative ions will both be the same as the mole ratio of the solute. 

We notice that, although there is only one solute species on the left-hand side, there are two on the right-hand side. The process is therefore accompanied by an increase in entropy, and the AF of the process will contain a term — T AScrat,c Let us first discuss the values of the unitary terms to do this we may carry out the process in a different manner. Choosing two distant water molecules, we transfer a proton from one to the other. According to Table 12, at 25°C the work required amounts... 

When interpreting proton transfers in Chapter 7, we found that the experimental data showed that for most solute species in aqueous solution the values of J lay between 0.25 and 1.0 electron-volts. We shall now be interested in the values of L that are necessary to account for the observed solubilities of solids in water. We may expect the range of values of L to be rather similar the main difference is that in the solution of a crystal the value of Aq in (8G) is never less than 2, whereas in most of the proton transfers discussed in Chapter 7 the value of Aq was either unity or zero. 

Consider now the non-ideal solution of a completely dissociated uni-divalent salt, and its comparison with the corresponding ideal solution. In choosing the ideal solution, if we denote the two solute species by B and C, we must obviously take a solution that contains twice as many... 

Consider now two solute species Bi and B3, between which no direct experimental comparison by the colorimetric method is possible, because their useful concentration ranges just fail to overlap. We can find an intermediate indicator solute B2, whose useful range partly overlaps that of B, and partly overlaps that of B3. Using B2, a relation between Bi and B3 may thus be established indirectly. In dilute solution this relation will be a simple one. We do not know enough about concentrated solutions to be in a position to say whether a similar relation should be expected. In the experiments to be described, the first aim was to obtain an answer to this question. 

By a statistical model of a solution we mean a model which does not attempt to describe explicitly the nature of the interaction between solvent and solute species, but simply assumes some general characteristic for the interaction, and presents expressions for the thermodynamic functions of the solution in terms of an assumed interaction parameter. The quasi-chemical theory is of this type, and we have noted that a serious deficiency is its failure to consider the vibrational effects in the solution. It is of interest, therefore, to consider briefly the average-potential model which does include the effect of vibrations. 

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