Isopiestic apparatus

Thiessen and Wilson (1987) presented a modified isopiestic apparatus and obtained osmotic coefficient data for KC1 solutions using NaCl as reference solution. The data are given in Table 15.4. Subsequently, they employed Pitzer s method to correlate the data. They obtained the following values for three Pitzer s... 

For example, even though the main objective of the isopiestic method is to determine the osmotic and activity coefficient of a solvent, the isopiestic technique is a precise measurement of the composition of liquid phase in liquid-gas equilibrium. Some details of isopiestic apparatus used for hydrothermal measurements will be discussed later in Methods of sampling . 

The activity of a volatile solvent in a solution that contains a nonvolatile solute can be obtained from an experimental technique known as the isopiestic method .19 An apparatus is constructed similar to that shown in Figure 6.17. The mixture in container A is a solution of a nonvolatile solute in a solvent in which A], the activity of the solvent, has been accurately determined in other experiments as a function of concentration. Containers B and C hold solutions of other nonvolatile solutes in the same solvent. These are the solutions for which the activity of the solvent is to be determined. 

Fig< 9.9. Signer-type isopiestic molecular weight apparatus. The sample, standard, and solvent are introduced through the upper tubes, which are then sealed off after freezing the solutions and evacuating the apparatus. The apparatus is allowed to stand in the position shown to allow maximum exposure of the solution to the vapor. Volumes of the standard and unknown solutions are found by tipping the apparatus so the calibrated legs are filled. 

The isopiestic (isothermal distillation) method for the determination of molecular weights is closely related to the vapor pressure depression method.10 A weighed amount of standard is introduced into one leg of an apparatus and a weighed portion of the unknown is placed in the other leg. Solvent is introduced into the apparatus, which is then evacuated and thermostated. The solvent will distill from one solution to the other until the vapor pressures (and therefore mole fractions) of the two have equalized. If the solutions are ideal, or if the deviations from ideality are similar, equilibrium will occur when the mole fraction of the known equals that of the unknown. 

Since equilibration sometimes takes days or weeks, the isopiestic method is not suitable for unstable compounds or compounds with appreciable volatilities. Also, long equilibration times require leak-free and grease-free apparatus. Another design for an isothermal distillation apparatus is given in Fig. 9.10. 

In the isopiestic method, the vapor pressure of a solution is determined by equilibrating it with that of a reference solution (aqueous NaCl is often used) whose vapor pressure as a function of salt concentration and temperature is well known. This method can provide osmotic coefficients accurate to better than 1% over a wide range of conditions, but it is accurate only for electrolyte molalities above approximately 0.1 mol kg. The necessary equilibration may take several days, and specialized apparatus is required for measurements significantly above room temperature. 

Fig. 2. Some tantalum seals and apparatus. (A) Crimped and welded (B) capped and welded (C) apparatus for biphasic, isopiestic equilibrations (D) thermal analysis container (E) tantalum tube to be welded under vacuum [tube is brazed to metal-to-glass seal and closed with joint and stopcock at top) not shown)] (F) sublimation container with reservoir or condenser swaged or flared to fit (G) reaction container sealed in silica jacket under vacuum.

If there is no wall between the two systems, then the pressures will be equal in equilibrium. We can try to treat the equilibrium in a distillation apparatus, analogous to isopiestics. Actually, there is no thermal equilibrium as the temperatures are different. However, the pressures must be equal because the system would try to expand through the cooler into the other system otherwise. In order that there is no flow of the distilling matter, the chemical potential in the high-temperature region must be equal to the chemical potential in the low-temperature region, even when the temperatures are artificially kept different. 

An apparatus for isopiestic experiments is easy to construct. Solutions of a volatile solvent with different concentrations of a nonvolatile solute are placed in an apparatus looking like a receiver of a distillation equipment as shown in Fig. 6.16. 

The apparatus is put in a thermostat. The solvent will be transferred via the gaseous phase until all the chemical potentials are equal. A more sophisticated experimental technique of the isopiestic method is the following [20, 21]. Sample cups with solutions are placed in a closed chamber where all solutions share the same vapor phase. The vapor space of the chamber is evacuated to contain only water vapor. Solvent is transferred through the vapor phase. The chamber containing the solutions is kept at isothermal conditions at specific temperature until no more change in the concentration of the solution is observed thus, thermodynamic equilibrium is reached. When the solutions are in thermodynamic equilibrium, then... 

Isopiestic Method.— The isopiestic method can be used to determine provided only one of the components is volatile. The unknown solution and reference solution containing the same volatile component but different involatile components are placed in dishes on a metal block in an airtight enclosure. The volatile component distils between the two solutions until their compositions are such that they have the same chemical potential of volatile component. After equilibration the two solutions are analysed. As the isopiestic method is a comparative method it is necessary to know the variation of vapour pressure with composition for the reference solution. The technique has the advantage that no pressure measurements are required. The method has been frequently used in the study of electrolytes and involatile non-electrolytes in aqueous solutions. Corneliussen et a/. have used the method to study polymer solutions. An apparatus suitable for measurements with organic mixtures has been described by Harris and Dunlop. The method is suitable only when there is no possibility of distillation between the involatile component in the reference solution and the involatile component in the unknown solution. 

Figure 4.4.7a. Isopiestic vapor-sorption apparatus using a quartz spring 1 - connection to the vacuum line, 2 - connection to the thermostating unit which realizes the constant measuring temperature T2 (the correct value of T2 is obtained by a Pt-100 resistance thermometer within the cell that is not shown), 3 - closing plug, 4 - quartz spring (reading of its extension is made by a cathetometer), 5 - sample pan with the polymer solution, 6 -pure solvent reservoir at temperature T[. [Reprinted with permission from Ref 82, Copyright 1982, Wiley-VCH].

Figure 4.4.8. Isopiestic vapor-sorption apparatus with built-in manometer using a quartz spring 1 - connection to the vacuum, 2-9 -stop corks, 10, 11, 12 - connections to nitrogen, 13 - degassing flask for the pure solvent, 14, 18 - buffers, 15 - cold trap, 16,19 - Hg-ma-nometers, 17,20 - mercury float valves, 21 -pure solvent reservoir at temperature Ti provided by 22 - thermostat, 23 - temperature controlled air box, 24 - measuring cell, 25 - quartz spring (four quartz springs can be inserted into the equilibrium cell, only one is shown), 26 - pan with the polymer solution, 27 - closing plug sealed with epoxy resin, 28 - heating to avoid solvent condensation.

Figure 4.4.9. Schematic diagram of an isopiestic vapor sorption apparatus using an electronic microbalance PC - personal computer, MB - microbalance, WBl-3 - water bath thermostats with T3>T2>Ti, Vl-3 - valves, WM - W-tube mercury manometer, S - polymer sample/solution, SV - solvent reservoir, MS -magnetic stirrer, CT - cold trap, VP - vacuum pump. [Reprinted with permissitm from Ref. 92, Copyright 1998, American Chemical Society].

Figure 4.4.10. Schematic diagram of an isopiestic vapor sorption apparatus using a piezoelectric crystal detector. [Reprinted with permission from Ref 101, Copyright 1995, American Chemical Society].

Figure 4.4.7b. Dynamic isopiestic vapor-sorption apparatus using a quartz spring (drawing provided by G. Sadowski) a) evaporator, b) superheater, c) measuring cell, d) condenser, e) quartz spring, f) polymer sam-ple/solution, g) Pt-100 resistance thermometer. [Reprinted with permission from Ref. 87, Copyright 1995, Wiley-VCH].

The design of a much simpler isopiestic vessel that can operate at temperatures up to 150 °C is described in (Groitheim et al., 1978). This apparatus is really a sampling... 

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