Osmotic coefficient from vapour pressure

From isopiestic measurements to determine the osmotic coefficient in 0.1 and 0.2 molal potassium nitrate and to estimate its activity coefficient at 0.1 molality. 

KNO3 at molality have been shown to be isopiestic (Robinson, J. Amer. Chem. Soc. 1935, 57,1165) by direct equilibration at 25 C. 

Values of the activity coefficient y of KCl in dilute solutions at 25 °C have been determined by measurements of e.m.f. and of transport numbers (Shedlovsky and Macinnes, J. Amer. Chem. Soc. 1937, 59, 503, compare problem 86). From these the osmotic coefficient 95 has been calculated by use of the Gibbs-Duhem relation (Robinson, Trans. Roy. Soc. New Zealand, 1945, 75, 203). Examples of such values are given in table 2. 

Hence knowing ti, and we can calculate For purposes of smoothing it is convenient to plot — 1 against 

To estimate having obtained we shall assume that at least up to 0.1 mole kg- the difference is proportional to m (compare problem 83), that is to say 

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To compare values of osmotic coefficients in aqueous sucrose solutions obtained from vapour pressure measurements and from osmotic pressure measurements. 

Osmotic coefficients in saturated solutions of citric add at different temperatures are known from vapour pressure measuremeuts, but not their changes with concentration near the saturation points. At 25 °C, Levien [89] using her and A / Am values aud the Dahnan solubilities [10] obtained from Eq. (2.33) the molar enthalpy of solution AH j=29.8 kJmol. Similar calculations performed by Apel-blat [83] ted to lower vdue AH j=26.0 kJmol and this result is veiy close to that which was determined from calorimetric measurements, AH, =26.3 kJ mol, by using the molar enthalpy of solution at infinite dilution of citric acid monohydrate [90] and the molar enthalpy of dilution of citric acid [91]. The apparent... 

It is known from physical chemistry that the equilibrium vapour pressure is smaller over solutions than over pure water. In the case of ideal solutions this vapour pressure decrease is proportional to x0, the mole fraction of the solvent (Raoult s law). If the solution is real, the interaction of solvent and solute molecules cannot be neglected. For this reason a correction factor has to be applied to calculate the vapour pressure lowering. This correction factor is the so-called osmotic coefficient of water (g ). We also have to take into account that the soluble substance dissociates into ions, forming an electrolyte. 

In the absence of vapour pressure or osmotic coefficient data, the solvent activity can be obtained from the Gibbs-Duhem relation... 

This involves the determination of Ago (i- e., vapour pressure or osmotic pressure) at various temperatures. Finally the entropy of dilution may be obtained from and Aho (since Ago == Aho — TAso) or also from the temperature coefficient of go ... 

The determination of single molar mass averages from simple solution properties, such as colligative and viscosity methods, has not been a popular held of research in the past few years. The state of the art has been reviewed by Slade and by Billingham. Since the publication of ref. 2, two major manufacturers (Perkin-Elmer and Hewlett-Packard) have withdrawn from the market so that there is now a much reduced choice in equipment for membrane osmometry and for vapour pressure osmometry. Membrane osmometry as a technique has received virtually no attention during the review period, although its use has been reported in a number of papers. Oman has described studies of the osmotic coefficients of aqueous polyelectrolytes, and Oman and Batho describe theoretical models for... 

The osmotic coefficient of the solvent substance A in a solution containing molality ms of an involatile solute substance B can be determined from measurements of the vapour pressures p of the solution and p of the pure solvent according to the relation ... 

Using vapour pressures over saturated solutions from Eq. (2.39) and solubilities of citric acid from Eqs. (2.31), the water activities aJ T) and osmotic coefficients in two forms (7) and (w), can be represented by... 

Available from the literature values of relative humidity RH and vapotu pres-siues of water over aqueous citric acid solutions as a function of mass fraction of citric acid w are presented in Table 2. 13. There is a reasonable agreement between reported vapour pressures or water activities coming from different investigations as can be observed in Figs. 2.29 and 2.30 where the vapom-pressure lowerings are plotted as a function of molality or molar fraction of citric acid in aqueous solutions. However, in the case of more sensitive quantity, the apparent osmotic coefficients... 

An approach that is conceptually simpler and does not require the prescription of transport to hydraulic or diffusion mechanisms was proposed by Janssen [47], and Thampan et al. [22] (hereafter TMT) based on the use of chemical potential gradients in the membrane. More recently, Weber and Newman [27] developed a novel model where the driving force for vapour-equilibrated membranes is the chemical potential gradient, and for liquid-equilibrated membranes it is the hydraulic pressure gradient. A continuous transition is assumed between vapour- and liquid-equilibrated regimes with corresponding transition from 1 to 2.5 for the electro-osmotic drag coefficient. 

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