Force interionic

The degree of polarity has considerable influence on the physical properties of covalent compounds and it can also affect chemical reactivity. The melting point (mp) and boiling point (bp) are higher in ionic substances due to the strong nature of the interionic forces, whereas the covalent compounds have lower values due to the weak nature of intermolecular forces. 

We may say then that in each of those processes the change AF in the free energy consists of two parts, a unitary part and a communal part. When an ionic solution is not extremely dilute, the free energy of the solution receives a contribution from the interionic forces this quantity depends on the concentration of the solute and is a communal quantity. When, however, the solution is extremely dilute, the interionic contribu-... 

In Sec. 41 it was pointed out that, when we are dealing with a solution that is not formed by a process of one-for-one substitution, this is, by itself, sufficient to make the solution a non-ideal solution—that is to say, is sufficient, by itself, to introduce a communal term that is different from the simple cratic term. Nevertheless, in an ionic solution at any concentration this deviation is small compared with the deviation caused by the electrostatic forces between the ions. In this book it will therefore be sufficient to mention only the interionic forces when speaking of the difference between a communal term and a eratic term. 

If we go on to consider the reaction (66) in a solution so dilute that the interionic forces make a negligible contribution to the communal term in AF, we may refer to the cratic term, instead of the communal term we may describe the equilibrium by saying that the concentrations of the four species adopt values which give to the cratic term iu (60) a value equal and opposite to that of the unitary term ... 

The Disparity of a Solution. We may begin to use the word disparity in a technical sense, for the quantity defined above, and to speak of d as the disparity of the solution when the mole fraction of the solute is x. In dilute ionic solutions the sign of d is always negative. The effect of the interionic forces is that ions added to a dilute solution always lose more free energy than they would when added to the corresponding ideal solution hence the total communal term is less than the cratic term. 

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. 

Accordingly, the conventional partial molal entropies of ions in solution are often said to refer to the ions in a one-molal solution (m = 1) hot in a real one-molal solution, but in a hypothetical ideal one-molal solution, where the contribution from the interionic forces is taken to be zero, and the cratic term replaces the communal term. 

In both processes the ions are supposed to be introduced into solutions where the interionic forces are negligible. When in (191) the COJ ion is formed, the solvent in the co-sphere of this ion loses a certain amount of entropy. Likewise, in (192) when the CO, ion is formed, the solvent in the co-sphere of the ion loses precisely the same amount of entropy. At the same time, the amount of entropy associated with the thermal energy of the COJ" ion in aqueous solution is, of course, the same in (192) as in (191). In the process (192) we shall be concerned with the unitary term for the two Li+ ions in contrast to (191) where two protons are added to two II20 molecules. 

There are, in fact, two reasons why we should prefer to discuss proton transfers of class I. In concentrated solutions the average electrostatic forces between the ions will be intense. Only in proton transfers of class I does the number of positive and negative charges in the solution remain unaltered when the proton is transferred only here do we find the possibility that the contribution from the interionic forces will remain almost unchanged in a proton transfer. At the same time, although the number... 

It was pointed out in Sec. 126 that in any proton transfer of class I the number of negative ions remains unchanged and the number of positive ions remains unchanged and consequently there is the possibility that the contribution from the interionic forces shall remain unchanged. Whether this is so or not can be decided only by experiment. Consider what result should be obtained if (218) and (219) are applicable. In this case, if experimental values of the left-hand side of (218) are plotted... 

The ions in solution are subject to two types of forces those of interaction with the solvent (solvation) and those of electrostatic interaction with other ions. The interionic forces decrease as the solution is made more dilute and the mean distance between the ions increases in highly dilute solutions their contribution is small. However, solvation occurs even in highly dilute solutions, since each ion is always surrounded by solvent molecules. This implies that the solvation energy, which to a first approximation is independent of concentration, is included in the standard chemical potential and has no influence on the activity. 

Because of the interionic forces, the conductivity is directly proportional to the concentration only at low concentrations. At higher concentrations, the conductivity is lower than expected from direct proportionality. This decelerated growth of the conductivity corresponds to a decrease of the molar conductivity. Figure 2.4 gives some examples of the dependence of... 

Interionic forces are relatively less important for weak electrolytes because the concentrations of ions are relatively rather low as a result of incomplete dissociation. Thus, in agreement with the classical (Arrhenius) theory of weak electrolytes, the concentration dependence of the molar conductivity can be attributed approximately to the dependence of the degree of dissociation a on the concentration. If the degree of dissociation... 

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

Note For concentrated solutions, the calculated values of mOsm/L may not be accurate because of factors such as solvation and interionic forces which influence the osmotic pressure. Thus, results from the above calculations should be referred to as theoretical or approximate osmolarities. However, since most intravenous infusions are dilute solutions, results obtained from the above calculations are accurate enough to be clinically meaningful. 

From the thermodynamic viewpoint, the basic statistical theory is still too complex to provide useful working equations, but it does suggest forms of equations with some purely theoretical terms, and other terms including parameters to be evaluated empirically. In general, the theoretical terms arise from the electrostatic interactions which are simple and well-known while the empirical, terms relate to short-range interionic forces whose characteristics are qualitatively but not quantitatively known from independent sources. But, as we shall see, this division is not complete - there are interactions between the two categories. 

However, for more precise calculations, it is necessary to consider that the mobility (hence, the conductance) of ions changes with concentration, even when dissociation is complete, because of interionic forces. Thus, Equation (20.20) is oversimplified in its use of Aq to evaluate a, because at any finite concentration, the equivalent conductances of the and Ac ions, even when dissociation is complete, do not equal Aq. 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

A Detailed Discussion of the Effect of Relative Ionic Sizes on the Properties of the Alkali Halogenides.—A simple detailed representation of interionic forces in terms of ionic radii has been formulated that leads to complete agreement with the observed values of interionic distances for alkali halogenide crystals and provides a quantitative theory of the anion-contact and double-repulsion effects. 0... 

It should be noted that in ionic compounds the interionic forces are much stronger than the intermolecular forces in simple covalent substances and so the melting and boiling points are generally higher. 

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