Determination of hydration numbers

Uchida, T. Hirano, T. Ebinuma, T. Narita, H. Gohara, K. Mae, S. Matsumoto, S. (1999a). Raman spectroscopic determination of hydration number of methane hydrates AIChEJ., 45 (12), 2641-2645. 

The concentrations of O17 used in the work of Jackson, Lemons, and Taube proved too low for very accurate determination of hydration numbers. Water samples more highly enriched in O17 should provide the basis for important studies of solvation phenomena in solution. This approach could be extended to other solvent systems such as liquid ammonia, amines, and acetonitrile (N14 or N16 resonances), ethers, sulfur dioxide, and di-methylsulfoxide (O17), and BrF3 (F19). 

A number of hydration of 21 for sucrose, and of 10 for D-glucose, were found213 from the i.r. spectra of these sugars at 25°, compared to the i.r. spectrum of water at higher temperatures. The same method of determination of hydration numbers was applied221 to eight different sugars at 25°. The influence of temperature and concentration on the hydration number... 

After 1900 the direct determination of hydrate number was abandoned in favor of the second, indirect method. The indirect method is still in use today and is based on calculation of the enthalpies of formation of hydrate from gas and water, and from gas and ice. This method was originally proposed by de Forcrand (1902) who used the Clapeyron equation to obtain the heat of dissociation from three-phase, pressure-temperature data, as in the below paragraph. With this more accurate method many exceptions were found to Villard s Rule. The historical summary provided in Chapter 1 indicates that while the number of hydrated water molecules was commonly thought to be an integer, frequently that integer... 

After de Forcrand s Clapeyron, and Handa s methods, a third method for the determination of hydrate number, proposed by Miller and Strong (1946), was determined to be applicable when simple hydrates were formed from a solution with an inhibitor, such as a salt. They proposed that a thermodynamic equilibrium constant K be written for the physical reaction of Equation 4.14 to produce 1 mol of guest M, and n mol of water from 1 mol of hydrate. Writing the equilibrium constant K as multiple of the activity of each product over the activity of the reactant, each raised to its stoichiometric coefficient, one obtains ... 

Fluorescence kinetic measurements were applied to the determination of hydration numbers in lanthanide-polyaminocarboxylate complexes the results are given in table 5 (Brittain et al. 1991, Brittain and Jasinski 1988). Measurements of hydration numbers as a function of the solution pH for Eu " and Tb " complexes showed the presence of three buffer regions the first one at low pH in which the hydration number of the cations is equivalent to that of the free ions the second one in the pH range of 4-8 in which complexation decreases the hydration numbers and the third one at high pH (ca. 9-12) being associated with the formation of ternary hydroxo complexes. 

Table 4 Equations used for the determination of hydration numbers of the helicate complexes using phenomenological equations. Afcobs represents the difference HjO — itoiO and the number of amide N-H oscillators present in the first coordination sphere...

In this chapter some problems connected with the utilization of subzero temperature differential scanning calorimetry (SZT-DSC) are discussed. Among them are the determination of hydration numbers of surfactants and organic compounds, the determination of the hydration shell thickness, the effect of alcohol on the distribution of water between free and bound states in nonionic surfactant-based systems, and some considerations regarding the problem of phase separation of such systems in subzero temperatures. The signihcance of SZT-DSC for some novel applications is also discussed. 

The solvation numbers of ions such as Mg2+, Al3+, and Be2+ may be determined by low temperature PMR techniques as mentioned earlier. The solvation number for small spherical ions may be determined in certain circumstances using a titration technique suggested by Van Geet (15). It is based on the competition by water for the solvation sphere of sodium ions in tetrahydrofuran (THF) measured by Na shifts. The salt must contain a large anion, which is assumed to be unhydrated during the titration otherwise a sum of hydration numbers would be determined. The assumptions made by Van Geet are basically those of the present treatment. His apparent constant is for the reverse of the equilibrium of Equation 21 and can be identified as l/K[P]p, where [P]f is the free THF concentration, effectively constant in the early stages of the titration. 

The initial predictive method by Wilcox et al. (1941) was based on distribution coefficients (sometimes called Kvsi values) for hydrates on a water-free basis. With a substantial degree of intuition, Katz determined that hydrates were solid solutions that might be treated similar to an ideal liquid solution. Establishment of the Kvsj value (defined as the component mole fraction ratio in the gas to the hydrate phase) for each of a number of components enabled the user to determine the pressure and temperature of hydrate formation from mixtures. These Kysi value charts were generated in advance of the determination of hydrate crystal structure. The method is discussed in detail in Section 4.2.2. 

Historically, two periods occurred for the determination of the number of hydrate water molecules per guest molecule. In the first century (1778-1900) after the discovery of hydrates, the hydration number was determined directly. That is, the amounts of hydrated water and guest molecules were each measured via various methods. The encountered experimental difficulties stemmed from two facts (1) the water phase could not be completely converted to hydrate without some occlusion and (2) the reproducible measurement of the inclusion of guest molecules was hindered by hydrate metastability. As a result, the hydrate numbers differed widely for each substance, with a general reduction in the ratio of water molecules per guest molecule as the methods became refined with time. After an extensive review of experiments of the period, Villard (1895) proposed Villard s Rule to summarize the work of that first century of hydrate research ... 

Patil (1987) determined the hydrate number of simple propane hydrates to be 18.95 by the de Forcrand method using the Miller and Strong method he obtained hydrate numbers of 19.20,19.95, and 19.89 for NaCl solutions of 3,5, and... 

Cady (1983a,b) provided the below illustration of how Equations 5.22a and 5.23 may be used to determine the hydration number for seven simple hydrates of structure I. 

Cady suggested that a value of n may be estimated at a pressure corresponding to 273.15 K for a hydrated guest using de Forcrand s method with the Clapeyron equation (Section 4.6.2.1). Equations E5.1.1 and E5.1.3 may then be solved simultaneously for 0l and 6s. In turn, 0l and 6s may be substituted into Equation E5.1.2a and b to calculate Cl and Cs. Since the values of Cl and Cs are constant at constant temperature, they may be used to determine the hydrate numbers at pressures higher than the equilibrium value, using Equations E5.1.1 and E5.1.2. 

Table 12.2. Comparison of hydration numbers as determined by various techniques...

Often the solvates (hydrates) are not detected since, according the corresponding phase diagram, at ambient temperature, they can be partly or completely dissociated. Suspensions of hydrates in water should shift the equilibrium toward the formation of the stable hydrated form. The ability of DSC measurements at subambient temperatures allow to determine phase transitions. Giron et al. proposed to use the melting peak of freezable water for the analysis of suspensions of drug substances in water in combination with TG for the determination of the number of molecules of water bounded as hydrates. 

It is best if hydration can be studied using the two peaks corresponding to coordinated water and the rest of the water which comprises secondary solvation of the cation and primary and secondary solvation of the anion and the bulk water. When two signals are observed it is possible to determine individual hydration numbers. 

Typical values of hydration numbers are given alongside values determined by other methods in Table 13.3. 

The determination of the number and position of unsaturated bonds in components of a sample mixture is one of the most important tasks in identifying unknown compounds. This is essential, first, for the correct choice of the conditions under which the samples must be chemically treated in order to avoid side-reactions that often occur with unsaturated bonds. At present the GC determination of unsaturated bonds is almost exclusively based on the hydration method, which simplifies chromatograms of complex mixtures [223]. The position of double bonds in a molecule is detected by oxidation methods. In principle the hydration method has much in common with that for determining a carbon skeleton as far as the catalysts, equipment and analytical techniques are concerned. The main differences are lower temperatures and shorter catalyst beds. Thus, the catalyst bed length can be 5—10 cm [224—226] and even several millimetres, which allows the hydration to be run directly at the point of sample injection into the... 

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