Thermodynamic properties of ions

We have seen in Chapters 4 and 5 that in thermodynamic work it is customary to obtain values of standard enthalpies and Gibbs energies of species. It will be remembered that these quantities relate to the formation of 1 mol of substance from elements in their standard states, usually at 25.0 C. In the case of entropies it is common to obtain absolute values, based on the third law of thermodynamics. 

It is a comparatively straightforward matter to determine, for pairs of ions in solution, standard enthalpies of formation, Gibbs energies of formation, and absolute entropies. However, one cannot carry out experiments on ions of only one kind. The conventional procedure, as explained in Chapters 4 and 5, is to set the value for H as zero. This allows complete sets of values to be built up, and one then speaks of 

Whereas absolute thermodynamic values for individual ions cannot be measured directly, they can be estimated on the basis of theory. Unfortunately, owing to the large number of interactions involved, the theoretical treatment of an ion in aqueous solution is very difficult. The following absolute values are generally agreed to be not far from the actual values, for the proton  

Once these values are accepted, absolute values for the other ions can be calculated from their conventional values. 

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Desnoyers, J. B. Hydration Effects and Thermodynamic Properties of Ions 5... 

The standard thermodynamic properties of ions are given in tables of standard thermodynamic properties at I = 0. The effect of ionic strength on ArG° for a chemical reaction is obtained by substituting equation 3.6-3 in equation 3.1-12 ... 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

However, studies of the thermodynamic properties of ion exchange have revealed an unexpected result ... 

Thus far we have been concerned with isolated ions and with their interaction with surrounding solvent molecules. In Chapter 6 we saw that for strong electrolytes the interactions between ions have an important effect on the conductances of solutions at all except exceedingly low concentrations. These interactions also have a significant effect on the thermodynamic properties of ions. A very convenient way of dealing with this matter is in terms of activity coefficients. 

The same rules apply for all other thermodynamic properties of ions. For instance. 

Measuring Thermodynamic Properties of Ions from Half-Cell Potentials... 

This table contains standard state thermodynamic properties of ions and neutral species in aqueous solution. It includes enthalpy and Gibbs energy of formation, entropy, and heat capacity, and thus serves as a companion to the preceding table, Standard Thermodynamic Properties of Chemical Substances . The standard state is the hypothetical ideal solution with molality m = 1 mol/kg (mean ionic molality in the case of a species which is assumed to dissociate at infinite dilution). Further details on conventions may be found in Reference 1. 

Aqueous Solvation.—A review, covering the 1968—1972 publications, deals with physical properties, thermodynamics, and structures of non-aqueous and aqueous-non-aqueous solutions of electrolytes, and complete hydration limits. Thermodynamic aspects of ionic hydration also reviewed include the thermodynamic theory of solvation the molecular interpretation of ionic hydration hydration of gaseous ions (AG s, H s, and AA s) thermodynamic properties of ions at infinite dilution in water, solvent isotope effect in hydration reference solvents and ionic hydration and excess properties. A third review on the hydration of ions emphasizes the structure of water in the gaseous, liquid, and solid states the size of ions and the hydration numbers of ions and the structure of the hydrated shell from measurements of mobility, compressibility, activity, and from n.m.r. spectra. Pure water and aqueous LiCl at concentrations up to saturation have been examined by neutron and X-ray diffraction. For the neutron studies LiCl and D2O are employed. The data are consistent with a simple model involving only... 

Cl27 C. M. Criss, Thermodynamic Properties of Ions, U.S. Atomic Energy Comm. Rept., TID-22366... 

FIGURE 1 Irving-Williams double-humped plot (representing the change in properties of the doubly charged ions M +) for thermodynamic properties of ions of the first transition series. The dashed plot show the related changes for the triply charged M +. 

In addition to the thermodynamic properties of ions, Latimer gives extensive tables for the properties of elements in the crystalline and gaseous states and for inorganic compounds in the form of crystals and in aqueous solution. 

Thermodynamic properties of ions in nonaqueous solvents are described in terms of the transfer from water as the source solvent to nonaqueous solvents as the targets of this transfer. These properties include the standard molar Gibbs energies of transfer (Table 4.2), enthalpies of transfer (Table 4.3), entropies of transfer (Table 4.4) and heat capacities of transfer (Table 4.5) as well as the standard partial molar volumes (Table 4.6) and the solvation numbers of the ions in non-aqueous solvents (Table 4.10). The transfer properties together with the properties of the aqueous ions yield the corresponding properties of ions in the nonaqueous solvents. 

J. Padova, J. Chem. Phys., 56, 1606 (1972). Thermodynamic properties of ions in methanol solution. 

We have now acquired all the tools with which to perform one of the most practical calculations of chemical thermodynamics determining the equilibrium constant for a reaction from tabulated data. Example 13-10, which demonstrates this application, uses thermodynamic properties of ions in aqueous solution as well as of compounds. An important idea to note about the thermodynamic properties of ions is that they are relative to H" (aq), which, by convention, is assigned values of zero for AfH°, AfG°, and S°. This means that entropies listed for ions are not absolute entropies, as they are for compounds. Negative values of S° simply denote an entropy less than that of H (aq). 

In Chapter 7, we learned how to combine thermodynamic properties of different substances to calculate the heat absorbed or released by a reaction. In Chapter 13, we learned how to combine thermodynamic properties of different substances to calculate equilibrium constants for reactions. Many chemical reactions occur in aqueous solution and involve ions. To be able to calculate heats of reaction or equilibrium constants for such reactions, we need values for the thermodynamic properties of the aqueous ions involved. In this section, we discuss the standard thermodynamic properties of ions in solution, particularly with respect to how their values are established and interpreted. 

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