Thermodynamics of hydrates

If melting points and melting enthalpies can be measured accurately, the transition temperature can be estimated by Equation 5.6, which can be derived from Equation 5.5  

Hydrates are of large practical importance because water is ubiquitous in the atmosphere and, as mentioned in Section 5.2, the probability that a certain compound can crystallize as a hydrate is large. Both stoichiometric and non-stoichiometric hydrates are known. In the first case, the ratio between the number of water molecules and the number of compound molecules in the crystal is well 

While the thermodynamic properties of nonsolvated forms depend only on temperature and pressure, the free energy of hydrates (and solvates) is influenced by the activity of the water (or solvent) in the environment Formation ofa stoichiometric hydrate with n molecules of water per compound molecule can be described by Equation 5.7  

From the mass law of action, the equflibrium constant Kh can be expressed by Equation 5.8, where a[A (solid)jeq, a[H20]eq, and a[A-nH20]eq are the activities of A, water, and the hydrate A nH20, respectively, at the equilibrium  

Since the activities of solids are 1, Equation 5.8 simplifies to Equation 5.9 with the 

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The substituent effects calculated for A show that aromatic and vinylic jT-donors in the para-position have a stabilizing effect on the nitrenium ions that is much larger than is seen in Op. For example, Op for Me, MeO, and Ph are —0.31, —0.78, and —0.18, respectively, while A for 75y (Ar = 4-tolyl), 75cc (Ar = 4-MeOphenyl) and 75n (Ar = 4-biphenylyl) are 8,1 kcal/mol, 22.7 kcal/mol, and 19.3 kcal/mol, respectively. The calculations and experimental data show that a para-phenyl substituent is about as stabilizing for a nitrenium ion as is a para-methoxy substituent. This unusual stabilization is the major reason that correlations of logS vs. cr are so scattered for nitrenium ions. Substituent effects at N are relatively small. Replacement of NH by NAc destabilizes the ion toward hydration by 4.5 l.Okcal/mol. Based on the correlation line, at 20°C this amounts to a predicted increase in by a factor of 4 to 11 when NH is replaced by NAc. The experimentally observed range of 1.5 to 9.0 (Table 1) is very close to this prediction. These calculated substituent effects on the thermodynamics of hydration and the calculated geometries of nitrenium ions (discussed in another section) indicate that for most nitrenium ions the canonical structure II of Scheme 38 is dominant. ... 

In dilute solutions of purified microsomal epoxide hydrolase, the kinetics and thermodynamics of hydration of arene oxides216 like 1 are similar. The epoxide hydrolase is sensitive to the stereochemistry of the substrate, as shown by the 40-fold differences in the rates of hydration of the ( + ) and ( —) enantiomers of 28. 

Marcus, Y. (1994). A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shapes. Biophys. Chem. 51, 111—127. 

Michael E. Paulaitis is Professor of Chemical and Biomolecular Engineering and Ohio Eminent Scholar at Ohio State University. He is also Director of the Institute of Multiscale Modeling of Biological Interactions at Johns Hopkins University. His research focuses on molecular thermodynamics of hydration, protein solution thermodynamics, and molecular simulations of biological macromolecules. 

Atomic and group additivity schemes, derived from solvent accessibility calculations and measurements on model systems, have been used to estimate the thermodynamics of hydration of proteins and peptides (Eisenberg and McLachlan, 1986 Ooi and Oobatake, 1988a Ooi et al., 1987). 

Contributions specifically from the protein to the thermodynamics of hydration are included in the values given above for transfer of solvent into the interface. 

We will restrict our discussion to stoichiometric hydrate. The thermodynamics of hydrate formation has been discussed by Lohani and Grant (45). Assuming that a drug D, forms a hydrate with m moles of water of crystallization, the equilibrium can be... 

Hydration of Ionomers The knowledge of Gc is of course fundamental for the understanding of the thermodynamics of hydration of ionomers. We can calculate from it the chemical potential p of water by deriving dGc we do that from an approximation of G... 

This review is concerned with the hydration and hydrolysis of the lanthanide cations. The reported structures in solids and in solution are compared and the thermodynamics of hydration and the kinetics of exchange reviewed. 

Cappa CD, 8mith JD, Messer BM, Cohen RC, Saykally RJ (2007) Nature of aqueous hydroxide ion probed by x-ray absorption spectroscopy. J Phys Chem Bill 4776-4785 Cavalleri M, Naslund L-A, Edwards DC, Wernet P, Ogasawara H, Myneni 8, Ojamae L, Odelius M, Nilsson A, Pettersson LGM (2006) The local structure of protonated water from x-ray absorptionh and density functional theory. J Chem Phys 124 1945081-1945088 Chalikian TV (2001) 8tructural thermodynamics of hydration. J Phys Chem B 105 12566-12578 Chen T, Hefter G, Buchner R (2003) Dielectric spectroscopy of aqueous solutions of KCl and CsCl. J Phys Chem A 107 4025-4031... 

Another key feature is the availability of a nearly perfect acceptor dopant (i.e. a dopant which does not change the electronic structure of the oxygen). While in all other reported cases, the increase of the acceptor dopant concentration leads to a reduction of the proton mobility and an entropic destabilization of protonic defects [222], both the proton mobility and the thermodynamics of hydration are practically unchanged for dopant levels up to 20% Y in BaZr03 (Fig. 3.2.13). High proton mobility and entropically stabilized protonic defects even at high dopant concentrations and the high-solubility limit lead to the enormous proton... 

Alternatively, Bratsch and Lagowski (1985a, b, 1986) proposed an ionic model to calculate the thermodynamics of hydration AGj, A/fJ and ASj using standard thermochemical cycles. This model is based on the knowledge of the values of quantities such as the enthalpy of formation of the monoatomic gas [A/f (M )], the ionization potential sum for the oxidation state under consideration and the crystal ionic radius of the metal ion. This approach, however, is difficult to apply for the actinides since the ionization potentials are, for the most part, unavailable. To overcome this problem, the authors back-calculated an internally consistent set of thermochemical ionization potentials from selected thermodynamic data (Bratsch and Lagowski 1986). The general set of equations developed are ... 

Extensive data for thermodynamics of hydration of the actinyl ions are limited to UOj. Comparison of AH and A5 with typical di- and tripositive ions indicated that... 

Understanding of the processes and thermodynamics of hydration and hydrolysis is a necessary background to understanding complexation of f-block elements. As such, this chapter has a relationship to the topics covered in the chapter by Choppin and Rizkalla (Ch. 128) in this volume. 

HI also affect organic reactivity in water. This topic has been reviewed recently.The thermodynamics of hydration and of HI are of immediate relevance for the interpretation of aqueous kinetic rate effects using transition state theory. 

The Maddox et al. procedure is based on equations describing the thermodynamics of hydrate formation and applies to either methanol or ethylene glycol. A hand calculation version of the technique includes several simplifying assumptions, but appears to give results that are comparable to the computer version and much closer to experimental data than the previously proposed calculation methods. The hand calculation model for hydrate formation is... 

Figure 11.2 shows the partial proton conductivity for a number of acceptor-doped perovskites, calculated from data for proton mobility and thermodynamics of hydration. 

In this chapter, I have treated the defect chemistry and thermodynamics of hydration. I have, moreover, put special emphasis on inherently not acceptor-doped—oxygen-deficient systems and their hydration in the ordered or disordered states. Finally, I have discussed the new oxyhydroxide compounds that arise from such hydration and advocated that radically new and better proton conductors may rely on understanding how to stabilize, disorder, dope, and in general control the defect chemistry of such oxyhydroxides. 

The thermodynamics of hydration of C-4 to C-6 polyhydric alcohols and some thermodynamic functions of activation for viscous flow and a volumetric study " of D-mannitol and D-glucitol in aqueous solution have been reported. 

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