Hydration number, definition

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... 

Remarkable data on primary hydration shells are obtained in non-aqueous solvents containing a definite amount of water. Thus, nitrobenzene saturated with water contains about 0.2 m H20. Because of much higher dipole moment of water than of nitrobenzene, the ions will be preferentially solvated by water. Under these conditions the following values of hydration numbers were obtained Li+ 6.5, H+ 5.5, Ag+ 4.4, Na+ 3.9, K+ 1.5, Tl+ 1.0, Rb+ 0.8, Cs+0.5, tetraethylammonium ion 0.0, CIO4 0.4, NO3 1.4 and tetraphenylborate anion 0.0 (assumption). 

In recent years, X-ray diffraction studies of aqueous solutions have established primary hydration numbers for several fast-exchange cations 45,187-190 the timescale of X-ray diffraction is very much shorter than that of NMR spectroscopy. Octahedral hydration shells have been indicated for Tl3+,191 Cd2+, Ca2+, Na and K+, for example. For the lanthanides, [Ln(OH2)9]3+ is indicated for La, Pr and Nd, but [Ln(OH2)8]3 for the smaller Tb to Lu.192,193 Sometimes there are difficulties and uncertainties in extracting primary hydration numbers from X-ray data. Thus hydration numbers of eight and of six have been suggested for Na+ and for K+,194 and for Ca2+,195 and 8 and 9 for La3+, 196 In some cases rates of water exchange between primary and secondary hydration shells are so fast as to raise philosophical questions in relation to specific definitions of hydration numbers.197... 

Mishchenko and Dymarchuk (111) have studied the integral heats of reaction of cellulose with both water and aqueous solutions of electrolytes. A notable maximum in the integral heat of reaction occurs at approximately 2.5m. The authors visualize this sharp maximum as caused by the different behavior above and below the concentration where all the water is intimately tied up as water of hydration. Thus, assuming for calcium chloride that the hydration number is 8 for both the calcium ion and for the chloride ion, a concentration of 2.52m corresponds to complete hydration of the ions. Hence, they suggest that definite hydration numbers exist. It may well be argued, however, that heat of reaction with standard cotton cellulose is a poor probe to choose for studying the aqueous environment. The idea of fixed total hydration of the ions appears a somewhat unlikely interpretation if for no other reason than... 

For the specific case of a standard for fluoride ion activity KF rather than NaF has been suggested. KF is a better choice because ion pairing is much less. Further, the average hydration number of the fluoride ion is almost the same as that for potassium ion, so that activity coefficients of the two ions are similar. Suggested reference activity values (pM or pAJ for use in the operational definitions for ion-activity measurements [Equations (13-26) or (13-27)] are shown in Table 13-2. For the case of fluoride ion, measurements of its activity in NaF-NaCl mixtures up to 1 m and KF-KX mixtures up to 4 m yielded the same values as pure NaF or KF at the same ionic strength. 

Here, we adopt a definition of dynamic hydration numbers based on the average number of water molecules that are bounded to the ion with enough strength to participate in its diffusive motion. - To quantify the concept, the following expression is used ... 

Ultrasonic velocity measurements are convenient for measuring hydration numbers from ion compressibilities (Padova 1964). For the di- and trivalent cations of the first transition series, the aqua ions are octahedral [M(H20)6] or [M(H20)6] , although in Cr(II), Mn(II) and Cu(II) definite distortions of the octahedra are present (Cotton and Wilkinson 1980). 

Information accumulated thus far on the hydration of mineral ions has been critically analyzed in the recent review by Marcus [163] entitled Effect of ions on the structure of water Structure making and breaking. It is important that definite changes have been noted in the water structure and in the structure of diffuse hydration shells with electrolyte concentrations. Neutron diffraction of CaCl2 and Ca(N03)2 solutions in D2O has shown [164] a decrease of Ca hydration number from 10 to 6 when the salt concentration increased from 1 to 4.5 M. 

Finally, definite bends can be noticed on the abnormally stretched front of the peaks. These bends can reflect the stepwise change in the hydration number of the ions with their concentration increasing on the leading edge of the peak. 

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

FIG. 13 Average number of hydrogen bonds (for definition see text) as a function of p in five simulations at different levels of hydration in a Vycor pore. Full hues show the number of water-water bonds, long-dashed hnes show the number of bonds between water molecules and Vycor, and short-dashed lines denote the sum of the two. From top to bottom, the frames correspond to a water content of about 96, 74, 55, 37, and 19% of the maximum possible (corresponding to 2600, 2000,1500, 1000, and 500 water molecules in a cylindrical cavity of about 4nm diameter and 7.13 nm length). (From Ref. 24.)... 

Most solvents have unshared pairs of electrons, and they are polar. Therefore, they have the ability to attach to metal ions or interact with anions. As a result, when many solids crystallize from solutions, they have included a definite number of solvent molecules. When this occurs in water, we say that the crystal is a hydrate. An example of this is the well-known copper sulfate pentahydrate,... 

The terminal numbers with potassium, rubidium, and csesium nitrates represent the b.p. of sat. soln. at nearly normal press. for sodium nitrate the corresponding value is 67 6 (119°). Determinations of the solubility of sodium nitrate have been made by G. J. Mulder, Earl of Berkeley, A. Ditte, L. Maumene, A. fitard, etc.30 The solubility curve of sodium nitrate has been carried upwards 781 (180°), 83 5 (220°), 915 (225°), and 100 (313°), the last-named temp, represents the m.p. of the salt. According to L. C. de Coppet, the eutectic or cryohydric temp, of sodium nitrate is —18"5°, and the eutectic mixture is not a definite hydrate, NaN03.7H20, as A. Ditte once supposed. A. fitard represents the solubility S... 

In crystallizing salts from solution, it frequently happens that it is possible to obtain more than one hydrate. In all such cases, a perfectly definite temperature can be found above which the one hydrate will deposit, and below which the other one with a larger number of molecules of water of hydration appears. Thus, above 38°, zinc sulfate deposits crystals of the composition ZnS04 6H20, while crystals deposited below that temperature have the formula ZnS04-7H20. This is also called a transition point. 

It now seems reasonably definite that an entity such as the hydrated electron exists. Further, the rate constants of reaction of e aq with a large number of species have now been measured using the technique of pulse radiolysis. This paper describes some of the properties of e aq and discusses the rate constants of reaction of e aq with the other species produced in the pulse radiolysis of water. These rate constants are significant for any diffusion theory model of the radiolysis of water. 

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