Molar entropies hydration

The derivation of values of conventional and absolute molar enthalpies and molar entropies of hydration of ions... 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

The calculation of the values for the standard molar entropies of hydration of ions requires some groundwork using the data presented in the following sub-section. 

In this section the standard molar entropies of a small selection of cations and anions are tabulated and the manner of their derivation discussed. The values themselves are required in the calculation of entropies of hydration of ions, discussed in Section 2.7.2. 

Absolute Standard Molar Entropies of Hydration of Ions... 

The Absolute Standard Molar Entropy of Hydration of the Proton... 

Table 2.17 Absolute standard molar entropies of hydration for some ions (in J K-1 mol-1)...

The behavior of hA in real micellar systems is more complex as seen in Fig. 2.12. Similar data have been obtained for several other amphiphiles148,149). The deviations in hA from the standard value at infinite dilution appear clearly below the CMC, but at these concentrations one has a compensating change in the partial molar entropy. This effect might be due to a repulsive interaction between the hydrophobically hydrated alkyl chains leading to a breakdown of the water structure with a concomitant increase in entropy. 

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.

Tetranitromethane is frequently used in inorganic systems, for example, as a scavenger of superoxide. Upon one-electron reduction the immediate products are C(N02)3" and N02 (248). An estimate of E° for this couple can be made by using published values of A(H° for C(N02)4 and HC(NOz)3 in the gas phase 82.0 and —0.2 kj/mol, respectively (241). The calculation also uses AfG° from this review for aqueous N02, entropies from the NBS tables, and pKa = 0.06 for HC(N02)3 (284). It is assumed that HC(NOz)3 and C(N02)4 have identical heats of hydration and identical partial molar entropies. The outcome is E° = 0.93 V for the C(N02)4/(C(N02)3", NOz) couple. Berdnikov et al. performed a similar calculation and obtained E° = 0.9 V (47). These workers used different sources of data and made more refined estimates of the entropies and hydration energies the agreement is gratifying. 

The second indicator of kosmotropicity is the standard molar entropy of hydration. For all ions it is highly negative the higher its absolute value, the more water is ordered upon ionic hydration, and the higher the electrolyte kosmotropicity [2,21]. 

Frank HS, Evans MW. Eree volume and entropy in condensed systems. 3. entropy in binary liquid mixtures - partial molar entropy in dilute solutions - structure and thermodynamics in aqueous electrolytes. J. Chem. Phys. 1945 13 507-532. Gallicchio E, Kubo MM, Levy RM. Enthalpy-entropy and cavity decomposition of alkane hydration free energies numerical results and implications for theories of hydrophobic solvation. J. Phys. Chem. B 2000 104 6271-6285. 

The entropy of hydration is the difference between the partial molar entropy of the ion in its standard state in solution and that of the gaseous ion in its standard state. There will be several contributions to this change in entropy, the most significant being ... 

AG4 = 0, AH = 0 and therefore A5 = 0. This is a different convention to that used in Section 13.16.6 where AS yj a o values have been calculated from standard partial molar entropies for the individual hydrated ions which were based on the convention that +(aq) = 0- Th two sets of values for wiU not be the same. 

These standard molar entropies of hydration of ions are related to the effect that ions have on the structure of water (Abraham et al. 1982 Marcus 1994), see Sect. 3.3.3. 

Frank and Robinson (1940) suggested that the partial molar entropy of the water in aqueous electrolyte solutions is affected by the structure-making or -breaking properties of their ions. Frank and Evans (1945) suggested that rather the entropies of hydration of the ions shed light on these properties. Gurney (1953) showed that a linear relationship exists between the partial molar entropy of monatomic ions, and their viscosity coefficients (see Sect. 3.1.1). Nightingale (1959) reverted to the Frank and Evans emphasize of partial molar entropies of hydration of the... 

The standard molar entropy of hydration of an ion, Ahydr5° , should contain contributions from the formation of the ionic hydration shell and also from the limitation of the ionic rotation of a multiatomic ion in the solution compared with the gas. Hence, such contributions should be deducted, according to Krestov (1962, 1962a), from Ahydr5° in order to obtain the water structural effects of the ion beyond the hydration shell, Astmc (AS ii in the notation of Krestov) ... 

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