Ionic entropies

Conventional Partial Molal Ionic Entropies. Correlation between Ionic Entropy and Viscosity. Conventional Partial Molal Entropy of (H30)+ and (OH)-. The Conventional and the Unitary Entropy of Solution. Solutes in Aaueous Solution. Solutes in Methanol Solution. 

Correlation between Ionic Entropy and Viscosity. In Chapter 9, when we noticed that certain ions in aqueous solution cause a decrease in viscosity, and asked how this should be explained, it seemed natural to interpret the effect in terms of order and disorder. In pure water at room temperature there is a considerable degree of short-range order ... 

When we say that we might expect to find this correlation between viscosity and ionic entropy we are, of course, concerned only with the... 

Solutes in Methanol Solution. In Table 23 we have seen that for four solutes in methanol the viscosity //-coefficients are positive. This is the case even for KC1 and KBr, for which the coefficients are negative in aqueous solution. In Sec. 88 it was pointed out that it would be of interest to see whether this inversion is likewise accompanied by a change in sign for the ionic entropy. Although no accurate values for the entropy of solution of salts in methanol arc available, reliable estimates have been made for KC1, KBr, and NaCl.1 Since the /1-coefficients of KC1 and KBr have been determined both in methanol and in water, all the required data are available for these two solutes. The values of A/S" given in Table 29 have been taken from Table 34 in Chapter 12, where the method of derivation is explained. The cratie term included in each of these values is 14 cal/deg, as already mentioned in Sec. 90. 

As seen from Tables 23 and 21 the ion pair (K+ + Cl") increases the viscosity of methanol but diminishes that of water. We recall that the values for the entropy of solution in Table 29 show a parallel trend in the galvanic cells of Sec. 112 placed back to back, this difference in ionic entropy between aqueous and methanol solutions would alone be sufficient to give rise to an e.m.f. We must ask whether this e.m.f. would be in the same direction, or in the direction opposite to the e.m.f. that would result from a use of (199). 

Although the viscosity B-coefficients for the fluorides are not known, we see. that the value for the ionic entropy of F" listed in Table 45 is — 2.3 + 2, very different from the value +13.5 for Cl". The value for F- is, in fact, very near the value —2.49 for (OH)-. We have then the very interesting question, whether the activities of the fluorides will fall in line with the other halides. In structure the ion F" certainly resembles Cl" and the other halide ions but according to the tentative scheme proposed above, we should perhaps focus attention on the solvent in the co-sphere of each ion. In this case we should expect to obtain for the fluorides a family of curves similar to that of the hydroxides, in contrast to that of the chlorides. The activities are known as a function of concentration for NaF and KF only. It is found that the curve for NaF lies below that of KF—that is to say, the order is the same as that of NaOH and KOII, in contrast to that of NaCl and KC1. 

St complex is the formal ionic entropy of the activated complex St p, =ASt +2rS acianis Some values used for S°reaciani are estimated ones. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

Estimation Procedures. There are basically two ways which have been developed to deal with the fact that heat capacity terms are large in reactions involving ions. One is based on empirical relationships (the entropy correspondence principle) between ionic entropies at different temperatures which Criss and Cobble (62) developed and checked to 200 C. Lewis (63) has checked a number of its predictions against available experimental evidence and has found the method reasonably satisfactory for several... 

For aqueous solutions of electrolytes, a concise method of tabulating such entropy data is in terms of the individual ions, because entropies for the ions can be combined to give information for a wide variety of salts. The initial assembling of the ionic entropies generally is carried out by a reverse application of Equation (7.26) that is, Af6m of a salt is calculated from known values of AfG and AfFT for that salt. After a suitable convention has been adopted, the entropy of formation of the... 

Historically, the usefulness of ionic entropies first was emphasized by Latimer and Buffington (19), who established the convention of setting the standard entropy of hydrogen ion equal to zero that is. 

How Can Temperature Coefficients of Reversible Cells Be Used to Obtain Ionic Entropies ... 

Now, this AS of a cell reaction must be composed of the entropies of at least two different ions in solution (because two electrode reactions are involved, one at each electrode), so that Eq. (2.58) cannot lead directly to an individual ionic entropy. 

Absolute Standard Partial Gram-Ionic Entropies of H and Cf lons ... 

Having obtained the individual value of the gram-ionic entropy of the hydrogen ion in solution, the individual entropy of hydration can be obtained by a straightforward calculation of the value of from statistical mechanical reasoning. 

To use this value of S to obtain the individual ionic entropies of other ions in solution, it is necessary to toow values for the entropy of hydration of a number of electrolytes containing H. Thereafter, the value of the entropy of the counterion can be obtained. It can then be used in conjunction with entropies of hydration of electrolytes containing the counterion to determine the absolute entropies of partner ions in the electrolyte containing the constant anion. Of course, in all cases, the value of the entropy of the ion in the gaseous state must be subtracted from that of the ion in solution to give the entropy ofhydration [i.e., = (S,)so, - (S,)g ]. 

Based on Latimer s scale of conventional ionic entropies. Units are cal K mol... 

Ionic entropy of hydration as AS =5 - Sj when Sf isthe gas-phase ionic entropy. 

The (idealized) radius of a polystyrene styrene sulfonate may be several hundred angstroms. Were you to measure the self-diffusion coefficient, what equation would you use to obtain a measure of the ion s size Explain the principles (showing appropriate equations) of obtaining an individual ionic entropy and an individual ionic entropy of hydration. 

The heat capacity of TiBr2(cr) was estimated by Kelley (2). The value of and the difference between ionic entropy contribution of Cl and Br". 

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