Standard Partial Molar Enthalpies

Thus, the partial molar enthalpy along the Henry s-law line is constant and equal to the standard partial molar enthalpy. The only real solution along the Henry s-law line is the inhnitely dilute solution, so that... 

Note that thermodynamic tabulations do not normally report the standard partial molar properties of solutes and G p, but rather the enthalpy of formation... 

The standard partial molar Gibbs free energy of solution is related to the enthalpy and entropy functions at the column temperature T by the expression... 

In electrochemistry we make it a rule that the standard chemical potential ju. of hydrogen ions is set zero as the level of reference for the chemical potentials of all other hydrated ions. The standard chemical potentials of various hydrated ions tabulated in electrochemical handbooks are thus relative to the standard chemical potential of hydrogen ions at unit activity in aqueous solutions. Table 9.3 shows the numerical values of the standard chemical potential, the standard partial molar enthalpy h°, and the standard partial molar entropy. 5 ,° for a few of hydrated ions. 

Table 9.3. Standard chemical potential jj°, standard partial molar enthalpy h°, and standard partial molar entropy s,° for a few hydrated ions Standard state 101.3 kPa, 298 K, unit activity in molality scale.

Calculation of A//e -quantities from the dependence of AG on temperature is less reliable than direct calorimetric measurements (Franks and Reid, 1973 Frank, 1973 Reid et al., 1969). However, disagreement between published A//-functions for apolar solutes in aqueous solutions may also stem from practical problems associated with low solubilities (Gill et al., 1975). Calorimetric data have the advantage that, as theory shows, the standard partial molar enthalpy H3 for a solute in solution is equal to the partial molar enthalpy in the infinitely dilute solution, i.e. x3 - 0. A similar identity between X3 and X3 (x3 - 0) occurs for the volumes and heat capacities but not for the chemical potentials and entropies. The design of a flow system for the measurement of the heat capacity of solutions (Picker et al., 1971) has provided valuable information on aqueous solutions. 

Standard partial molar free enthalpies, enthalpies, and entropies of vaporization from infinitely dilute solutions in Apiezon M were calculated from retention volumes determined over a range of temperatures data are listed for many organic and a few MR4 compounds (M = Si, Ge, and Sn), including Ge(C2H5)4 [29]. Apiezon L and two polar stationary phases were used in similar studies on a variety of MRr,R4 n compounds, yielding relative molar enthalpies and entropies of solution at 100°C referred to Si(CH3)4 as the standard [43]. Retention volumes and heats of solutions on two stationary phases have also been compared for M(C2H5)4 and M(C2H5)3H compounds with M = Si, Ge, and Sn [38]. 

TABLE 4.3 Ionic Standard Partial Molar Enthalpies of Transfer from Water into Nonaqneons Solvents, W->S)/kJ-mol at 25°C ... 

The properties of ions in solution depend, of course, on the solvent in which they are dissolved. Many properties of ions in water are described in Chapters 2 and 4, including thermodynamic, transport, and some other properties. The thermodynamic properties are mainly for 25°C and include the standard partial molar heat capacities and entropies (Table 2.8) and standard molar volumes, electrostriction volumes, expansibilities, and compressibilities (Table 2.9), the standard molar enthalpies and Gibbs energies of formation (Table 2.8) and of hydration (Table 4.1), the standard molar entropies of hydration (Table 4.1), and the molar surface tension inaements (Table 2.11). The transport properties of aqueous ions include the limiting molar conductivities and diffusion coefficients (Table 2.10) as well as the B-coefficients obtained from viscosities and NMR data (Table 2.10). Some other properties of... 

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. 

The quantity //, - H° is called the relative partial molar enthalpy and given the symbol L,. It is the difference between the partial molar enthalpy in the solution and the partial molar enthalpy in the standard state. That is,... 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

Solute. The standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4). In both cases, the standard state is obtained by extrapolation from the Henry s-Iaw line that describes behavior at infinite dilution. Thus, the partial molar enthalpy of the standard state is not that of the actual pure solute or the actual 1 -molal solution. 

We have pointed out that a concentration m2(o of the solute in the real solution may have an activity of 1, which is equal to the activity of the hypothetical 1-molal standard state. Also, Hm2, the partial molar enthalpy of the solute in the standard state, equals the partial molar enthalpy of the solute at infinite dilution. We might inquire whether the partial molar entropy of the solute in the standard state corresponds to the partial molar entropy in either of these two solutions. 

Hg is the partial molar enthalpy under standard-state conditions. 

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