Solvation numbers compressibility

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

COMPRESSIBILITY AND VIBRATION POTENTIAL APPROACH TO SOLVATION NUMBERS OF ELECTROLYTES... 

In 1938, Passynski made the following argument, which reiates the compressibii-ity of a solution to the sum of the primary solvation numbers of each ion of an electrolyte. Primary here means ions that are so compressed hy the ions field that they themselves have zero compressibility. 

Taking into account a finite compressibility of the hydration waters led Onori to suggest solvation numbers that differed from those of Passynski with his assumption of zero compressibility of the inner region of the solvation shell. For example, for a 1.5 M solution, Onori has the value 19 for the sum of the solvation numbers of Na and cr, whereas the Passynski at 0.05 M solution is 6 However, later on (Section 2.22), when electrostriction is discussed in detail, Onori s estimate will be shown to be unlikely. 

Total solvation numbers arise directly from the discussion following Passynski s Eq. (2.11), which requires measurements only of the compressibility (/S) of the solution (that of the solvent usually being known). Bockris and Salujaused this method in 1972 to obtain the total solvation numbers of both ions in a number of salts (Table 2.5). 

Apart from neutron diffraction, what other method distinguishes between the static or equilibrium coordination number and the dynamic solvation number, the number of solvent molecules that travel with an ion when it moves One method is to obtain the sum of the solvation numbers for both cation and anion by using a compressibility approach, assuming that the compressibility of the primary solvation shell is small or negligible, then using the vibration potential approach of Debye to obtain the difference in mass of the two solvated ions. From these two measurements it is possible to get the individual ionic solvation numbers with some degree of reliability. 

In the text are data on compressibilities as a function of concentration. Use the Passynski equation to calculate the total solvation number of NaBr at infinite dilution. 

Table P.4 lists measured dielectric constants at 25 °C for 1.0 M LiCl, NaCl, and KCl solutions, respectively. Calculate the percentage of water in the primary sheath and the total solvation number. Compare the results with those of the compressibility method (see problem 21) and comment on their reliability. 

Hydration numbers (the number of water molecules in the primary hydration layer) can be determined by various physical techniques (for example, compressibility) and the values obtained tend to differ depending on the method used. The overall total action of the ion on water may be replaced conceptually by a strong binding between the ion and some effective number (solvation number) of solvent molecules this effective number may well be almost zero in the case of large ions... 

Taking into account a finite compressibility of the hydration waters led Onori to suggest solvation numbers that differed from those of Passynski with his assumption... 

Adiabatic Compressibility and Total Solvation Number of Electrolytes as a Function of Concentration at 298 K... 

One method to employ bulk properties of electrolytes to obtain solvation numbers is to consider the electrostriction caused by the electric field of the ion, that is, the compression of the water in its hydration shell. The compression of electrostricted wsiier per mole of water is Ay j=-3.5cm mol" at 25°C, independently of the nature of the ion [83]. This value revised an earlier estimate of -2.9cm mol by Marcus [84] based on less accurately established second pressure derivatives of the density... 

The total solvation number can be calculated from the P value, provided the following two assumptions hold (i) the solvated (or complexed) ion is incompressible, (ii) the compressibility of the free solvent is the same as that of the pure solvent. On the other hand, the ultrasonic absorption of a system undeigoing chemical relaxation is given by... 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

Assuming an incompressible part of the solution, Passynsky derived an equation relating the adiabatic compressibility P, observed for the solution, to the number n of grams of solvating solvent per g of polymer 73) ... 

Supercritical fluid extraction Supercritical fluid extraction (SFE) uses compressed gas as the extraction medium and circumvents some of the problems associated with the use of classical separation techniques involving organic solvents. This technique combines features of distillation (i.e., separation because of differences in component volatiles) and liquid extraction (i.e., separation of components that exhibit little difference in their relative volatilities or that are thermally labile). A number of gases, when compressed isothermally at a temperature greater than their critical temperature and to pressures greater than their critical pressure, exhibit an enhanced solvating power (136), which has been known since the nineteenth century (137, 138), but its actual applications did not come to practice until the late twentieth century. 

Measurement of ultrasonic velocity through an electrolyte solution permits evaluation of the isothermal compressibility, which can be related to ionic solvation phenomena, though only by making a number of necessary assumptions in the treatment. Yeager s review [20] refers to a number of other reviews in this field and also to the absorption of ultrasound by electrolyte solutions, another field widely studied at the time. Again the aim was to elucidate ion solvation and solution... 

Aqueous Solvation.—A review, covering the 1968—1972 publications, deals with physical properties, thermodynamics, and structures of non-aqueous and aqueous-non-aqueous solutions of electrolytes, and complete hydration limits. Thermodynamic aspects of ionic hydration also reviewed include the thermodynamic theory of solvation the molecular interpretation of ionic hydration hydration of gaseous ions (AG s, H s, and AA s) thermodynamic properties of ions at infinite dilution in water, solvent isotope effect in hydration reference solvents and ionic hydration and excess properties. A third review on the hydration of ions emphasizes the structure of water in the gaseous, liquid, and solid states the size of ions and the hydration numbers of ions and the structure of the hydrated shell from measurements of mobility, compressibility, activity, and from n.m.r. spectra. Pure water and aqueous LiCl at concentrations up to saturation have been examined by neutron and X-ray diffraction. For the neutron studies LiCl and D2O are employed. The data are consistent with a simple model involving only... 

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