Ionic entropy, aqueous

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 ... 

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). 

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... 

Ionic entropies in all the non-aqueous solvents examined up to the present time can be expressed as a linear function of the entropies of the ions in water as ... 

Since results for ionic entropies in organic solvent systems are more plentiful than for ionic mobilities, it would appear that one could use the correspondence plot method, in the reverse manner from which Gurney employed it to evaluate i ion in aqueous solutions. Plots of this type, for the very few data that do exist for electrolytes of simple ions... 

In an extension of these ideas, Franks and Reid have examined the ionic entropies in mixed water-methanol solutions (see Appendix 2.4.42) and in 20 % aqueous dioxan, and have observed that the entropies of the ions for each of these systems can be expressed by an equation having the same form as eqn. 2.11.36. Similar to the pure solvent systems, the entropy of a given ion has no correlation with the solvent dielectric constant, nor is there a linear correlation of the entropy with solvent composition. Instead, the entropies reach a maximum in the vicinity of 40 mol per cent methanol. The authors explain this in terms of the solvent having the highest degree of structure near this composition. As in the pure non-aqueous solvents, the relative magnitude of the effect of ions on the solvent structure is the same for all ions, both negative and positive. This observation led the authors to conclude that there is no evidence for preferential solvation in these mixed solvent systems. 

Solutes in Aqueous Solution. As mentioned in See. 88, when we say that we expect to find a correlation between the /1-coefficients of viscosity of various species of ions, and their entropy of solution, this refers only to the unitary part of the entropy, the part associated with the ionic co-sphere. We are inclined to adopt the view that a negative //-coefficient for a pair of ions should be accompanied by a positive increment in entropy, while a positive //-coefficient should be accompanied by a decrease in entropy. The values of AS0, the conventional entropy of solution, to be found in the literature, do not, give a direct answer to this question, since they contain the cratic term, which in water at room temperature amounts to 16 e.u. This must be subtracted. 

The conclusions are evidently relevant to the amount of entropy lost by ions in methanol solution—see Table 29. If, however, the expression (170) is used for an atomic ion, we know that it is applicable only for values of R that are large compared with the ionic radius—that is to say, it will give quantitative results only when applied to the solvent dipoles in the outer parts of the co-sphere. The extent to which it applies also to the dipoles in the inner parts of the co-sphere must depend on the degree to which the behavior of these molecules simulates that of the more distant molecules. This can be determined only by experiment. In Table 29 we have seen that for the ion pair (K+ + Br ) and for the ion pair (K+ + Cl-) in methanol the unitary part of ASa amounts to a loss of 26.8 e.u. and 30.5 e.u., respectively, in contrast to the values for the same ions in aqueous solution, where the loss of entropy in the outer parts of the co-sphere is more than counterbalanced by a gain in entropy that has been attributed to the disorder produced by the ionic field. 

Turning next to the unitary part of AS0, this is given in Table 36 under the heading — N(dL/dT). It was pointed out in Secs. 90 and 106 that, to obtain the unitary part of AS0 in aqueous solution, one must subtract 16.0 e.u. for a uni-univalent solute, and 24.0 e.u. for a uni-divalent solute. In methanol solution the corresponding quantities are 14.0 and 21.0 e.u. In Table 36 it will be seen that, except for the first two solutes KBr and KC1, the values are all negative, in both solvents. It will be recalled that for KBr and KC1 the B-coefficients in viscosity are negative, and we associate the positive values for the unitary part of the entropy, shown in Table 29, with the creation of disorder in the ionic co-spheres. In every solvent the dielectric constant decreases with rise of temperature and this leads us to expect that L will increase. For KBr and KC1 in methanol solution, we see from Table 36 that dL/dT has indeed a large positive value. On the other hand, when these crystals dissolve in water, these electrostatic considerations appear to be completely overbalanced by other factors. 

The increase in ionic radius from Be2+ to Mg2+, which is accompanied by an increase in coordination number from 4 to 6, is responsible for a substantial increase in lability (Table III, (37-43)). The two activation volumes measured are positive as well as all the activation entropies. The rate laws determined for non-aqueous solvents in inert diluent are first order, showing a limiting D mechanism for all solvent exchange reactions on [MgS6]2+. 

Criss, C. M. Cobble, J. W. "The Thermodynamic Properties of High Temperature Aqueous Solutions. V. The Calculation of Ionic Heat Capacities up to 200OC. Entropies and Heat Capacities above 200 C" J. An. Chan. Soc., 1964, 86, 5390. 

FORMATION. Aqueous solutions of highly surface-active substances spontaneously tend to reduce interfacial energy of solute-solvent interactions by forming micelles. The critical micelle concentration (or, c.m.c.) is the threshold surfactant concentration, above which micelle formation (also known as micellization) is highly favorable. For sodium dodecyl sulfate, the c.m.c. is 5.6 mM at 0.01 M NaCl or about 3.1 mM at 0.03 M NaCl. The lower c.m.c. observed at higher salt concentration results from a reduction in repulsive forces among the ionic head groups on the surface of micelles made up of ionic surfactants. As would be expected for any entropy-driven process, micelle formation is less favorable as the temperature is lowered. 

This book offers no solutions to such severe problems. It consists of a review of the inorganic chemistry of the elements in all their oxidation states in an aqueous environment. Chapters 1 and 2 deal with the properties of liquid water and the hydration of ions. Acids and bases, hydrolysis and solubility are the main topics of Chapter 3. Chapters 4 and 5 deal with aspects of ionic form and stability in aqueous conditions. Chapters 6 (s- and p-block). 7 (d-block) and 8 (f-block) represent a survey of the aqueous chemistry of the elements of the Periodic Table. The chapters from 4 to 8 could form a separate course in the study of the periodicity of the chemistry of the elements in aqueous solution, chapters 4 and 5 giving the necessary thermodynamic background. A more extensive course, or possibly a second course, would include the very detailed treatment of enthalpies and entropies of hydration of ions, acids and bases, hydrolysis and solubility. 

Fig. 7. Schematic diagram of the contributions of various types of interactions to the free energy of the native conformations of a hypothetical protein or a DNA molecule in aqueous solution. Fs, Fb, Fi/b, and Fm represent the free energy contributions of conformational entropy, electrostatic interactions, hydrogen bonding, and hydrophobic interactions, respectively. The magnitude oi Fg may vary considerably with the pH and ionic strength of the aqueous solution.

The standard molar entropy of acetic acid at 298.15 K can be calculated using the program calcentropy298. To calculate S ° for the acetate ion in dilute aqueous solution at 298.15 K and zero ionic strength, the formation reaction is balanced by adding H (aq) on the right side. 

---