Enthalpies of Solution and Dilution

We can also find the effect of temperature on the molar differential reaction enthalpy Af//. From Eq. 11.3.5, we have (9Ar///97 )p j = AfC. Integration from temperature T to temperature T yields the relation 

This relation is analogous to Eq. 11.3.9, using molar differential reaction quantities in place 

The processes of solution (dissolution) and dilution are related. The lUPAC Green Book recommends the abbreviations sol and dil for these processes. 

During a solution process, a solute is transferred from a pure solute phase (soUd, liquid, or gas) to a solvent or solution phase. During a dilution process, solvent is transferred from a pure solvent phase to a solution phase. We may specify the advancement of these two kinds of processes by soi and dii, respectively. Note that both processes take place in closed systems that (at least initially) have two phases. The total amounts of solvent and solute in the systems do not change, but the amounts in pure phases diminish as the processes advance and soi or dii increases (Fig. 11.8). 

The equations in this section are about enthalpies of solution and dilution, but you can replace H by any other extensive state function to obtain relations for its solution and dilution properties. 

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CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES 11.4 Enthalpies of Solution and Dilution... 

There is a simple relation between molar integral enthalpies of solution and dilution, as the following derivation demonstrates. Consider the following two ways of preparing a solution of molality mg from pure solvent and solute phases. Both paths are at constant T and p irn, closed system. 

Molar integral enthalpies of solution and dilution are conveniently expressed in terms of molar enthalpies of formation. The molar enthalpy of formation of a solute in solution is the enthalpy change per amount of solute for a process at constant T and p in which the solute, in a solution of a given molality, is formed from its constituent elements in their reference states. The molar enthalpy of formation of solute B in solution of molality will be denoted by Afi/(B, hib). 

Schick s work includes the study of borides, carbides, nitrides, and oxides of some elements in Groups IIA, IIIB, IVA, IVB, VB, VIIB, and VIII as well as selected rare earths and actinides. As far as possible, the tables have been made compatible with the JANAF tables. Among the subjects treated are phase diagrams, heat capacities, enthalpies, entropies, enthalpies of phase transformation, formation, and reaction, melting temperatures, triple points, free energies of formation, vapour pressures, compositions of vapour species, ionization and appearance potentials, e.m.f. of cells, and enthalpies of solution and dilution. Volume 1 summarizes the techniques used to analyse data and cites the data analysed, and Volume 2 gives tables of values produced by this study. 

Enthalpies of solution in dilute solutions can be expressed as the sum of the lattice enthalpy and the enthalpy of hydration of the compound. 

The lattice enthalpy U at 298.20 K is obtainable by use of the Born—Haber cycle or from theoretical calculations, and q is generally known from experiment. Data used for the derivation of the heat of hydration of pairs of alkali and halide ions using the Born—Haber procedure to obtain lattice enthalpies are shown in Table 3. The various thermochemical values at 298.2° K [standard heat of formation of the crystalline alkali halides AHf°, heat of atomization of halogens D, heat of atomization of alkali metals L, enthalpies of solution (infinite dilution) of the crystalline alkali halides q] were taken from the compilations of Rossini et al. (28) and of Pitzer and Brewer (29), with the exception of values of AHf° for LiF and NaF and q for LiF (31, 32, 33). The ionization potentials of the alkali metal atoms I were taken from Moore (34) and the electron affinities of the halogen atoms E are the results of Berry and Reimann (35)4. 

Duer W. C., Leung W. H., Oglesby G. B., and Millero F. J. (1976) Seawater. A test for multicomponent electrolyte solution theories II. Enthalpy of mixing and dilution of the major sea salts. J. Solut. Chem. 5, 509—528. 

The enthalpy of combustion, a H"(298.15 K), of rhombic sulfur to aqueous sulfuric acid, S(cr, rhombic) + 3/2 0 (g) + HgOCt) HgSO (n HgO), has been determined by many investigators. Based on the reported combusion data, values of a H"(298.15 K) for liquid H SO are derived using tabulated enthalpy of solution and enthalpy of dilution data (1, 2). The value adopted,... 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

Finally, they measured the enthalpy of solution of C HsO in water as a function of concentration and extrapolated to infinite dilution to get a value of -5.84 kJ-mol-1 for the reaction... 

The solution experiments may be made in aqueous media at around ambient temperatures, or in metallic or inorganic melts at high temperatures. Two main types of ambient temperature solution calorimeter are used adiabatic and isoperibol. While the adiabatic ones tend to be more accurate, they are quite complex instruments. Thus most solution calorimeters are of the isoperibol type [33]. The choice of solvent is obviously crucial and aqueous hydrofluoric acid or mixtures of HF and HC1 are often-used solvents in materials applications. Very precise enthalpies of solution, with uncertainties approaching 0.1% are obtained. The effect of dilution and of changes in solvent composition must be considered. Whereas low temperature solution calorimetry is well suited for hydrous phases, its ability to handle refractory oxides like A1203 and MgO is limited. 

Fig. 1. Enthalpies of solution of lanthanide trihalides in aqueous media ( ) anhydrous trichlorides (183) and trichloride hexahydrates (189) in water (A) trichloride hex-ahydrates in dilute hydrochloric acid (190) ( ) trichloride hexahydrates in aqueous magnesium chloride solution (191) ( ) anhydrous triiodides in water (192). Values for the trichlorides refer to 25°C, for the triiodides to 20°C. Filled symbols represent experimental determinations, open symbols represent estimates.

Enthalpies of Solution of Trichloride Hydrates in Water (25°C and Infinite Dilution) ... 

Enthalpies of transfer of trihalides from water into nonaqueous and mixed solvents can be obtained by simple arithmetic for all the cases where enthalpies of solution in nonaqueous and mixed aqueous media are known. As long as the enthalpies concerned have been measured in reasonably dilute conditions, or have been estimated for infinite dilu-... 

Reactive ionic compounds are therefore useless to derive hydration enthalpies (or more generally, solvation enthalpies). Fortunately, there are many alternatives. Take lithium chloride, for example, and data from the NBS Tables [ 17]. The enthalpy of solution of this solid in water, at infinite dilution, is given by... 

With most properties (enthalpies, volumes, heat capacities, etc.) the standard state is infinite dilution. It is sometimes possible to obtain directly the function near infinite dilution. For example, enthalpies of solution can be measured in solution where the final concentration is of the order of 10-3 molar. With properties such as volumes and heat capacities this is more difficult, and, to get standard values, it is usually necessary to measure apparent molal quantities 0y at various concentrations and extrapolate to infinite dilution (y° = Y°). Fortunately, it turns out that, at least with volumes and heat capacities, the transfer functions AYe (W — W + N) do not vary significantly with the electrolyte concentration as long as this concentration is relatively low (3). With most of the systems investigated, the transfer functions were calculated from apparent molal quantities at 0.1m and assumed to be equivalent to the standard values. 

The enthalpy of solution measurements of n-Bu4NBr in DMF-water were made in very dilute solutions (0.02-0.001 mole kg-1) so that, in view of the experimental error, any concentration dependence of the enthalpies of solution in these solutions was neglected. Consequently, the enthalpy of solution at infinite dilution, AH°(sol.), was taken to be the average of three or more independent measurements agreeing within 150 J mol-1. Final results of AH°(sol.) of n-Bu4NBr with their mean deviations at 5°, 25°, and 55°C are given in Table I. The results for the other tetraalkylammonium bromides, for RbCl, and for urea in DMF-water at 25 °C are summarized in Table II. 

At this point we should note that it is not a trivial task to measure accurately A aw//, values. This is particularly true for very hydrophobic compounds. Therefore, it is also not too surprising that experimentally determined Aawtf, values reported by different authors may differ substantially (see examples given in Table 6.3). Furthermore, particularly for many very hydrophobic compounds, there seems to be a discrepancy between Aaw//, values derived from measurements of Kixw at different temperatures (Eq. 6-10) under dilute conditions, and Aawf/, values calculated from the enthalpy of vaporization and the enthalpy of solution (AwL//, = H, see Fig. 5.1 note that Awa/7, = -Aaw//(). Note that this latter approach reflects saturated conditions. Nevertheless, before using an experimentally determined Aaw//, value, it is advisable to check this value for consistency with that calculated from Aaw//i and HI. 

In most common chemical reactions, one or more of the reactants is in solution. Thus, an easy method to determine thermodynamic quantities of solution is desirable. Enthalpy of solution (heat of solution) is defined as the change in the quantity of heat which occurs due to a combination of a particular solute (gas, liquid, or solid) with a specified amount of solvent to form a solution. If the solution consists of two liquids, the enthalpy change upon mixing the separate liquids is called the heat of mixing. When additional solvent is added to the solution to form a solution of lower solute concentration, the heat effect is called the heat of dilution. The definitions of free energy of solution, entropy of solution, and so on follow the pattern of definitions above. 

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