Osmotic coefficient, practical

This difficulty can be overcome by writing equivalent expressions whose variables do not go to infinity at the limit of. vi—>0. A function known as the practical osmotic coefficient is one that can be used in a graphical method to obtain In 7 4.2- The practical osmotic coefficient expressed in terms of mole fraction is defined as... 

Equation (7.45) is a limiting law expression for 7 , the activity coefficient of the solute. Debye-Htickel theory can also be used to obtain limiting-law expressions for the activity a of the solvent. This is usually done by expressing a in terms of the practical osmotic coefficient

electrolyte solute, it is defined in a general way as... 

It has been observed by Alexandrowicz139,140) that in salt-free systems the practical osmotic coefficient ipp rather the molecular weight is actually determined. 

Over the last 20-30 years not too much effort has been made concerning the determination of standard potentials. It is mostly due to the funding policy all over the world, which directs the sources to new and fashionable research and practically neglects support for the quest for accurate fundamental data. A notable recent exception is the work described in Ref. 1, in which the standard potential of the cell Zn(Hg)jc (two phase) I ZnS O4 (aq) PbS O4 (s) Pb(Hg)jc (two phase) has been determined. Besides the measurements of electromotive force, determinations of the solubility, solubiKty products, osmotic coefficients, water activities, and mean activity coefficients have been carried out and compared with the previous data. The detailed analysis reveals that the uncertainties in some fundamental data such as the mean activity coefficient of ZnS04, the solubility product of Hg2S04, or even the dissociation constant of HS04 can cause uncertainties in the f " " values as high as 3-4 mV. The author recommends this comprehensive treatise to anybody who wants to go deeply into the correct determination of f " " values. 

In addition, the simple phenomenological relation (6.1.4), with a constant electro-osmotic coefficient lc, was replaced by a more elaborate one, accounting for the w dependence on the flow rate and the concentrations Ci, C2 via a stationary electro-osmotic calculation. This approach was further adopted by Meares and Page [7] [9] who undertook an accurate experimental study of the electro-osmotic oscillations at a Nuclepore filter with a well-defined pore structure. They compared their experimental findings with the numerically found predictions of a theoretical model essentially identical to that of [5], [6]. It was observed that the actual numerical magnitude of the inertial terms practically did not affect the observable features of the system concerned. 

The non-ideality of the solvent in an aqueous 1 1 salt solution can be expressed in terms of a practical osmotic coefficient, 0 (17),... 

Figure 12 Practical osmotic coefficient, of salt-free polyelectrolyte solutions as a function of linear charge density, a/b. The upper and the lower curves correspond to the < )p f, values of polyions of polysaccharide and polyvinyl polymer backbones, respectively.

As a rough estimate, we may assume that G = 1 and that the practical osmotic coefficient of the PP anion is 0.2. The values of (Pi)D(np/Vj,) calculated by use of the values determined under various sodium nitrate concentrations are listed in Table 7. The constancy of the product, (Pi)d( p d) t) assumed attributable to the constancy of both the... 

The polyion domain volume can be computed by use of the acid-dissociation equilibria of weak-acid polyelectrolyte and the multivalent metal ion binding equilibria of strong-acid polyelectrolyte, both in the presence of an excess of Na salt. The volume computed is primarily related to the solvent uptake of tighdy cross-linked polyion gel. In contrast to the polyion gel systems, the boundary between the polyion domain and bulk solution is not directly accessible in the case of water-soluble linear polyelectrolyte systems. Electroneutrality is not achieved in the linear polyion systems. A fraction of the counterions trapped by the electrostatic potential formed in the vicinity of the polymer skeleton escapes at the interface due to thermal motion. The fraction of the counterion release to the bulk solution is equatable to the practical osmotic coefficient, and has been used to account for such loss in the evaluation of the Donnan phase volume in the case of linear polyion systems. 

Carboxylate group fraction of total ionic groups of heparin Sulfete group fraction of total ionic groups of heparin Practical osmotic coefficient Activity coefficient of species i Activity coefficient quotient Concentration of species i Ionic strength... 

On application of the van t Hoff equation to the dmg molecules in solution, consideration must be made of any ionisation of the molecules, since osmotic pressure, being a colligative property, will be dependent on the total number of particles in solution (including the free counterions). To allow for what was at the time considered to be anomalous behaviour of electrolyte solutions, van t Hoff introduced a correction factor, i. The value of this factor approaches a number equal to that of the number of ions, v, into which each molecule dissociates as the solution is progressively diluted. The ratio ijv is termed the practical osmotic coefficient, [Pg.69]

The immediate importance of the practical osmotic coefficient of the solvent lies in its relationship to the mean activity coefficient of an electrolyte. From equation (39.37),... 

Much deeper insights into the water sorption properties of polyelectrolytes can be provided by evaluating the (nNa)p term directly. By the use of the activity coefficient of Na+ ions in the PA A polyelectrolyte phase, (yNa)p, (aNa)p can be expressed as (aNa)p = (yNa)P [Na]p. Two concentration terms, i.e., (1) Na+ ions present in the polyelectrolyte phase to neutralize free car-boxylate groups and (2) Na+ ions imbibed in the polyelectrolyte phase in the form of NaCl, contribute the [Na]p term. Escape of Na+ ions from the polyelectrolyte phase due to their thermal motion, which produces a site vacancy of the polyion, should also be taken into consideration. The fraction of site vacancy of polyelectrolytes is available as a practical osmotic coefficient, c/>p-Na, which can simply be related to the linear charge separation of the PAA polyion. It has been revealed that PiNa is not affected by the change in the polyion concentration nor Cs, which is known as an additivity rule [16,17]. Thus the (aNa)p term can finally be expressed as... 

M free metal ion fraction of total metal ions (f>p practical osmotic coefficient G activity coefficient quotient [i] free concentration of species i... 

It is convenient to express the relation of the vapour pressure j> of the solution and the vapour pressure of the pure solvent at the same temperature by an osmotic coefficient. There are two such coefficients in use called the "practical osmotic coefficient

osmotic coefficient g defined by (Robinson and Stokes, loc. cit.)... 

The practical osmotic coefficient obtained directly from cryoscopic measurements gives a measure of the deviation from ideality for the solvent species. The corresponding measure of deviation from ideality for the solute species is the activity coefficient, y. y and (f> are related as a consequence of the Gibbs-Duhem equation. The following expression was first derived by Bjerrum ... 

In principle the activity coefficients yb of solute substances B in a solution can be directly determined from the results of measurements at ven temperature of the pressure and the compositions of the liquid (or solid) solution and of the coexisting gas phase. In practice, this method fails unless the solutes have volatilities comparable with that of the solvent. The method therefore usually fails for electrolyte solutions, for which measurements of ye in practice, much more important than for nonelectrolyte solutions. Three practical methods are available. If the osmotic coefficient of the solvent has been measured over a sufficient range of molalities, the activity coefficients /b can be calculated the method is outlined below under the sub-heading Solvent. The ratio yj/ys of the activity coefficients of a solute B in two solutions, each saturated with respect to solid B in the same solvent but with different molalities of other solutes, is equal to the ratio m lm of the molalities (solubilities expressed as molalities) of B in the saturated solutions. If a justifiable extrapolation to Ssms 0 can be made, then the separate ys s can be found. The method is especially useful when B is a sparingly soluble salt and the solubility is measured in the presence of varying molalities of other more soluble salts. Finally, the activity coefficient of an electrolyte can sometimes be obtained from e.m.f. measurements on galvanic cells. The measurement of activity coefficients and analysis of the results both for solutions of a single electrolyte and for solutions of two or more electrolytes will be dealt with in a subsequent volume. Unfortunately, few activity coefficients have been measured in the usually multi-solute solutions relevant to chemical reactions in solution. 

Oq is called the practical osmotic coefficient relative to the solvent. It is a function of different variables, pressure, temperature and composition. So, we obtain go if 0 -... 

Boiling point elevation and freezing point depression can be tied to the osmotic coefficient, (p, and are practical means for its measurement. We start with the Gibbs-Duhem equation at constant pressure and temperature ... 

The radial distribution functions appearing in Eq. (13) correspond to the anion-anion, the cation-cation, and the anion-cation distribution functions which are implicitly dependent on the salt density. In practice, the compressibility is obtained for a few concentrations, augmented by the exactly known low density behaviour, and then numerically integrated according to Eq. (11) to obtain the osmotic coefficient. 

Now if we adhere strictly to the conception (sec 3d, p 125) that a potential difference between different phases cannot be determined cq (121) has no practical signifi-cance Eq (119) can be used to determine /+ in the colloidal system when the anal3rtical data are available and/+ in the colloid-free solution has been determined. Likewise the osmotic coefficient g can be determined from eq. (122) if all other quantities (notably the molar fraction of the colloid) are known. But as there is no simple relation between /+ and g in this case, that would mean nearly the end of all practical application of the Donnan equilibrium. 

In practice, from a knowledge of measured values of the osmotic second virial coefficients it is rather easy to calculate the spinodal curve. It is worthy of note here to observe that reciprocal values of m, for biopolymers of rather high molecular weight (> 104 g/mol) are often comparable with the magnitude of A 24. This requires that, as well as values of the osmotic second virial coefficients, the molecular weight should also be taken into account in the prediction of the boundary conditions relating to phase separation. 

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