Determination of the Hydration Number

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  

The dissociable (hydrate) compounds, that form through the unification of water with different gases and that are only stable in the solid form, all crystallize regularly and have the same constitution that can be expressed by the formula M + 6H2O, where M designates a molecule of the respective gas 

While the above estimate may seem antiquated, Villard s Rule is a good rule of thumb in many cases. Note that if a guest fills all of both cavities in si and sll, the hydration number would be 5.75 and 5.67, respectively, so a value of 6 allows for the possibility of empty cages, and is frequently taken as a good approximation to the hydration number for methane hydrates. However, Villard s Rule is not a good approximation for components that only fill the large cavity of either si (e.g., ethane) or sll (e.g., propane). 

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Kimura, T. Choppin, G. R. 1994. Luminescence study on determination of the hydration number of Cm(III). Journal of Alloys and Compounds, 213/214,313-317. 

Identical results are obtained in the determination of the hydration number of the anion associated either to the cation complexed by a crown ether or to a quaternary salt. In both cases, the hydration sphere of the anion in the organic phase is the cause of the anomalous nucleophilicity scale found under PTC conditions... 

All these considerations allow quantitative determination of the hydration number. An example is shown in Figure 15, where the O ENDOR spectrum of... 

Raitsimring AM, Astashkin AV, Baute D, Goldfarb D, Poluektov OG, Lowe MP, Zech SG, Caravan P. 2006. Determination of the hydration number of gadolinium(III) complexes by high-field pulsed O ENDOR spectroscopy. ChemPhys Chem 7 1590-1597. 

Determination of the Hydration Number of Ions by Gusztav Buchbock... 

He was a well-known scientist (see e.g., the invitation from the Nobel Prize Committee for nomination). He elaborated a method for the determination of the hydration number of ions by measuring the transference numbers of the ions in the presence of indifferent (organic) compounds of different concentrations (Fig. 12.5). At that time, it was the most accurate measurement of the hydration number as pointed out by Nemst in his book [5],... 

A systematic determination of both hydration number (Cady, 1983) and relative cage occupancies (Davidson and Ripmeester, 1984) shows that molecules such as CH3CI and SO2 are the most nonstoichiometric. Although theoretical calculations using the van der Waals and Platteeuw model provides some rationale for the nonstoichiometry, experimental quantification of nonstoichiometry as a function of guest/cavity size ratio has yet to be determined. 

It has been found that, in the case of several electrolytes, the values of the hydration numbers obtained by fitting the theory [Bq. (3.130)] to experiment are in reasonable agreement with hydration numbers determined by independent methods (Table 3.14). Alternatively, one can say that, when independently obtained hydration numbers are substituted in Eq. (3.130), the resulting values of log show fair agreement with experiment. 

Properties and reactivity of a calcium sulfate 3-hemihydrate are widely dependant on the preparation procedure. Although kinetical studies on the hydration reaction are done by a number of researchers, there is no standard procedure to elaborate a stable, reproducible calcium -hemihydrate specimen. This paper presents a very simple apparatus and an experimental procedure setup to elaborate a specimen that is stable and allows kinetical studies even after a long time of conservation. This apparatus also allows the simultaneous determination of the hydration rate for six different species of incompletely hydrated plasters and demonstrates experimentally that the amount of heat involved in the hydration... 

The value of the primary hydration number is in dispute. Different methods of measurement yield quite different values because they respond to different strengths and times of ion-water interaction. Careful measurements of the hydration number of Na+, for example, yielded values of 1, 2, 2.5, 4.5, 6 to 7, 16.9, 44.5, and 71, depending on the method used. Table 3.1 shows hydration numbers for common ions determined by several methods that tend to agree. The last column shows Bockris and Reddy s estimates of primary hydration numbers for the univalent ions. 

Error for the definitions averaged in the measuring of the hydrate number of the density vO.1%, in the determination of the parameters v1%. 

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. 

There has been considerable discussion about the extent of hydration of the proton and the hydroxide ion in aqueous solution. There is little doubt that this is variable (as for many other ions) and the hydration number derived depends both on the precise definition adopted for this quantity and on the experimental method used to determine it. H30" has definitely been detected by vibration spectroscopy, and by O nmr spectroscopy on a solution of HF/SbFs/Ha O in SO2 a quartet was observed at —15° which collapsed to a singlet on proton decoupling, 7( 0- H) 106 Hz. In crystalline hydrates there are a growing number of well-characterized hydrates of the series H3O+, H5O2+, H7O3+, H9O4+ and H13O6+, i.e. [H(0H2) ]+ n = 1-4, Thus... 

The hydration numbers N of the quaternary ammonium alkanesulfonates (217) and alkylidene- ,oj-disulfonates (218) were determined from the melting points of their saturated aqueous solutions. Both the N values and the melting poins were fairly high (217 N tv 37, mp 13-19°C 218a N tv 52, mp 1-10°C 218b N tv 76, mp 13-18°C). The water molecules probably assume a clathrate structure438. 

In preparing sodium monohydrated carbonate, the wet crystals may combine with the adherent mother liquor, forming the decahydrated salt, and this accounts for the high results usually obtained in determinations of the amouut of water in the crystals and it possibly explains how a number of other hydrated salts have been reported at different times. The evidence of the individuality of the crystals of sodium carbonate with 2, 2 , 3, 5, or 6H20 is quite inadequate. 

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