Ion entropy

Entropies can be calculated or estimated, and hence enthalpies can be derived from equilibrium measurements. Gaseous entropies are calculated by statistical mechanics using experimental or estimated molecular dimensions and fundamental frequencies (93). For solids, numerous methods based on additivity rules, or regularities in series of compounds, are available. Khriplovich and Paukov (140), for example, list 20 such relationships and were able to estimate entropies to about 1%. Empirical equations are also available for ion entropies (59). 

The correlation parameters are not well established for the carbamate ion. The determination of entropy of the aqueous salt is uncertain because of its tendency to decompose to ammonia and bicarbonate ions. Entropy of the anion has been estimated by Wagman and Goldberg of NBS at 22 cal/mol K (S° of H = 0.0). (43) This yields a salting-out coefficient for ammonia by ammonium carbamate of 0.036 kg H20/mol. 

As in the case of Gibbs function changes, we also can divide the entropy change for a reaction [such as Equation (20.51)] into two parts and can assign one portion to each ion. As actual values of individual-ion entropies cannot be determined, we must establish some convention for apportioning the entropy among the constituent ions. 

With tables of ion entropies available, it is possible to estimate a Gibbs function change without the necessity of carrying out an experiment or seeking specific experimental data. For example, without seeking data for the potential of calcium electrodes, it is possible to calculate the calcium electrode potential or the Gibbs function change in the reaction... 

Figure 45. Single ion entropies for various ions in methyl alcohol + water mixtures at 298 K full lines represent idealized dependence and dotted lines show observed dependence (Franks and Reid, 1969).

The mathematical description of the edl begins with the definition of a free energy functional which has the minimum contributions of electrolyte ion entropy and total electrostatic energy [10,11]... 

The thermal diffusion potential, td> arises if an electrochemical system is nonisothermal. This phenomenon is due to the heat transport of ionic species and can be taken into account if the individual ion entropy of transport, conductivity, and activity coefficients of the species of interest are known. Therefore, the thermal diffusion potential depends on the temperature, pressure, and composition of the electrolyte liquid junction. Also, td is a function of the temperature gradient and can be a substantial value from tens to hundreds of millivolts [19]. 

Tabulated are single-ion entropies of about 110 diatomic and polyatomic ions in water Gibbs energies, enthalpies, and entropies of hydration of monatomic ions at 25 C partial molar volumes of about 120 common ions at 25 C ionic partial molar heat capacities of ions Gibbs energies of transfer of inorganic electrolytes from HjO to 020 and calorimetrically determined enthalpies of solution of salts in H2O and 020. 

Standard-state entropies of aqueous ions are by convention referenced to S°(H (aq)) = 0. Alternatively, the temperature coefficient of the electromotive force of an equilibrium reaction involving the ion can be used to calculate the entropy of the reaction, and from the reaction entropy as well as necessary auxiliary data the entropy of formation of the ion can be calculated. Four actinide aquo-ion entropies (Th , Pu, UOj, and NpO ) have been determined by the former method. The other aquo-ion entropies of uranium, neptunium, and plutonium have been connected by the latter method. 

The most thorough treatment of uranium and plutonium aquo-ion equilibria over extended temperatures is that of Lemire and Tremaine [71]. This paper uses the systematic relationships developed by Criss and Cobble [72], which relate aquo-ion entropies, heat capacities, and their high-temperature behavior. Although the experimental determination of aquo-ion heat capacities has been dramatically advanced by the development of flow microcalorimeters [73,74], the only measurements of f-block aquo-ion heat capacities were made before this innovation [75,76]. Therefore, Lemire and Tremaine had to rely on estimated heat capacities for almost all of their calculations, and most of their equilibrium constants are uncertain by two or more orders of magnitude. Lemire [77] has also written a report on neptunium aquo-ion equilibria over extended temperatures. 

Among the papers dealing with potential measurements at isothermal half-cells at normal pressure, such of industrial interest are remarkable, e.g. of the chlorine electrode [41]. Very precise studies at thermocells with the hydrogen electrode, the silver-silver chloride electrode and the silver electrode [42] provided single ion entropies and activation entropies. 

Strong PEs show a fundamentally different dilution and complex formation behavior compared to weak PEs. Dilution is mainly driven by the increase in entropy from the release of counterions and not, like in case of weak PEs, by changes of the enthalpy [15, 62]. The structure of the PE itself, as well as its enthalpy, changes only a little during these processes [63, 65]. The change in the counterion and other ion entropy was calculated by Osawa to be ... 

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