Isopiestic method, activity

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. 

The isopiestic method is based upon the equality of the solvent chemical potentials and fugacities when solutions of different solutes, but the same solvent, are allowed to come to equilibrium together. A method in which a solute is allowed to establish an equilibrium distribution between two solvents has also been developed to determine activities of the solute, usually based on the Henry s law standard state. In this case, one brings together two immiscible solvents, A and B, adds a solute, and shakes the mixture to obtain two phases that are in equilibrium, a solution of the solute in A with composition. vA, and a solution of the solute in B with composition, a . 

Thiessen, D.B., and Wilson, "An Isopiestic method for Measurement of Electrolyte Activity Coefficients", AIChE J., 33(11), 1926-1929, 1987. 

The activity of the solvent often can be obtained by an experimental technique known as the isopiestic method [5]. With this method we compare solutions of two different nonvolatile solutes for one of which, the reference solution, the activity of the solvent has been determined previously with high precision. If both solutions are placed in an evacuated container, solvent will evaporate from the solution with higher vapor pressure and condense into the solution with lower vapor pressure until equilibrium is attained. The solute concentration for each solution then is determined by analysis. Once the molality of the reference solution is known, the activity of the solvent in the reference solution can be read from records of previous experiments with reference solutions. As the standard state of the solvent is the same for all solutes, the activity of the solvent is the same in both solutions at equUibrium. Once the activity of the solvent is known as a function of m2 for the new solution, the activity of the new solute can be calculated by the methods discussed previously in this section. 

A great deal of information on activities of electrolytes also has been obtained by the isopiestic method, in which a comparison is made of the concentrations of two solutions with equal solvent vapor pressure. The principles of this method were discussed in Section 17.5. 

Activity Coefficients of Electrolytes in Water-Polyethylene Glycol Mixed Solvent by Isopiestic Method... 

With the use of thermodynamic relations and numerical procedure, the activity coefficients of the solutes in a ternary system are expressed as a function of binary data and the water activity of the ternary system. The isopiestic method was used to obtain water activity data. The systems KCl-H20-PEG-200 and KBr-H20-PEG-200 were measured. The activity coefficient of potassium chloride is higher in the mixed solvent than in pure water. The activity coefficient of potassium bromide is smaller and changes very little with the increasing nonelectrolyte concentration. PEG-200 is salted out from the system with KCl, but it is salted in in the system with KBr within a certain concentration range. 

The isopiestic method described elsewhere (8, 9,10) was used to obtain the experimental data of water activity of the aqueous solutions. In our arrangement, eight gold-plated silver crucibles were embedded into hollows of a copper block and placed in the glass vacuum desiccator. The crucibles were provided with covers which can be handled from inside. Three desiccators were placed in a water bath (maintained at 25 0.01 °C) on a brass construction which moved from one side to the other. This movement, aided by a moving glass bead in each crucible, mixed the solutions. The desiccators with the samples were evacuated to the pressure of about 20 torr and the evacuation after a time interval was repeated 2-3 times. The time needed for the establishment of equilibrium was... 

A2.1 Factors to Consider When Estimating Water Vapor Pressure A2.2 Dew-Point Method for the Determination of Water Activity A2.3 Measurement of Water Activity Using Isopiestic Method A2.4 Direct Manometric Determination of Vapor Pressure A2.5 Measurement of Water Activity by Electronic Sensors... 

A2.3 Measurement of Water Activity Using Isopiestic Method A2.3.1... 

Equilibrium constants for the formation of nitrate complexes at hydrogen ion concentrations of 2 and 4 M and metal ion concentrations of 5 X 10 M or less, were determined using ion exchange techniques (353, 465) (Table XVIII). Activity coefficient data for aqueous zirconium and hafnium species are scarce, although there is one report (319) of activity coefficients for metal nitrate solutions as determined by the isopiestic method. 

The vapor pressure of a binary polymer solution is given by the activity of the solvent A, a. Solvent activities in polymer solutions are measured either by the isopiestic method applying a reference system whose solvent activity is precisely known or by determining the solvent partial pressure, Pand calculating the activity of the solvent by equation (1) ... 

The isopiestic method has proved invaluable at molalities down to 0.1 but below this it becomes too inaccurate. Consequently activity coefficients at 0.1 moledity have to be estimated by some such method as used in this problem. Activity coefficients at higher molalities can then be obtained by integrating the Gibbs-Duhem relation. A comprehensive survey of results thus obtained is given by Robinson and Stokes (Trans. Faraday Soc. 1949, 45, 612). 

Tse] Activities measurements / isopiestic method 1600°C / all compositions in the ternary... 

The isopiestic method is a highly accurate but time-consuming relative method. In a constant-temperature enclosure the solvent distills isothermally from a reference solution of known activity to a solution of unknown activity or vice versa, which entails a change in concentration. At equilibrium the solvent activities of both samples are equal and (R denotes reference solution)... 

The fugacity was introduced by G.N. Lewis in 1901, and became widely used after the appearance of Thermodynamics, a very influential textbook by Lewis and Randall in 1923. Lewis describes the need for such a function in terms of an analogy with temperature in the attainment of equilibrium between phases. Just as equilibrium requires that heat must flow such thaf temperature is the same in all parts of the system, so matter must flow such thaf chemical potentials are also equalized. He referred to the flow of matter from one phase to another as an escaping tendency, such as a liquid escaping to the gas form to achieve an equilibrium vapor pressure. He pointed out that in fact vapor pressure is equilibrated between phases under many conditions (and in fact is the basis for the isopiestic method of activity determinations, 5.8.4), and could serve as a good measure of escaping tendency if it behaved always as an ideal gas. 

We must be aware of one very important relationship between solution components, which is that they are not all independent of one another. This seems reasonable enough qualitatively. You can well imagine that changing the concentration, say, of one component of a binary system would have some effect on the activities and activity coefficients of both components, not just one. These changes can be quantified, and this is a highly useful device, because it is very common to measure the activity of only one component in a binary system as a function of concentration, and then calculate the activity of the other component, instead of measuring it too. We mentioned one way of doing this in 5.8.4, the isopiestic method. 

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 . 

Isopiestic measurements. High-temperature isopiestic method could be considered as an instrumental method among other methods of sampling without temperature and pressure drops to study hquid-gas equilibrium (Tsopiesf in Table 1.1). One of the electrolyte solutions present in the isopiestic vessel is a reference since its vapor pressure is known imder the conditions of the experiment. The compositions of the solutions placed in the same vessel change during equilibration due to a redistribution of water between liquid solutions to reach the common vapor pressure at the constant temperature. The equilibrium composition of the isopiestic solutions could be measured at the experimental or at the room temperature if the samples of isopiestic solutions carefidly preserved and analyzed in order to determine the concentration (isopiestic molality) at the equilibrium, isopiestic vapor pressures and activity coefficients for the electrolytes. 

A measurement of m then permits 0 to be established. The process is repeated for many different mr and m values, so that the corresponding activity of the dissolved unknown species may be found via Eq. (3.6.14). This procedure is known as the isopiestic method. 

For a two-component solution with a volatile solvent such as water and a nonvolatile solute, values of the activity of the solvent can be determined for several values of the solvent mole fraction between unity and the composition of interest. Integration of the Gibbs-Duhem relation can then give the value of the activity coefficient of the solute. The activity of the solvent is usually determined using the isopiestic method. The solution of interest and a solution of a well-studied nonvolatile reference solute in the same solvent are placed in a closed container at a fixed temperature. A solution of KCl is usually used as the reference solute for aqueous solutions, since accurate water activity coefficient data are available for KCl solutions. The solutions are left undisturbed at constant temperature until enough solvent has evaporated from one solution and condensed into the other solution to equilibrate the solvent in the two solutions. 

The activities and activity coefficients of nonvolatile electrolytes can be determined by the isopiestic method, as described in Chapter 6. They can also be determined by electrochemical measurements. As an example consider the cell of Figure 8.2, for which the Nernst equation is... 

Mention should be made of polystyrenesulfcmic add and its salts. In the concentration rai in which the isopiestic method was used (17), the mean activity coefficient was found to increase with increasing concentration and the cube-root rule was not valid. This is due to strong solute-solvent interaction, specifically hydrophobic influences on water molecules. However, in a concentration range in vhich this interaction is not so intense, it is expected that the cube-root rule holds. As a matter of fact, the y values of polystyrenesulfonic add [reported by Dolar and Leskovsek (36)] fitted this rule at lowconcentrations, as is shown in Fig. 2. ... 

Fig. 16. The mean activity coefficient of sodium poly-Iy-glataniate at a degree of neutralization of 0.3 as a fiinction of the cube root of concentiatknt at 2S . O. A emf method , A isopiestic method...

The isopiestic and manometric methods (units A2j A2.4) for determination of water activity have the limitation of being dependent on fixed laboratory equipment. The electronic-type sensors have advantages of portability, speed, and simplicity of measurement. The characteristics of a sensor depend upon the manufacturer and each instrument must be calibrated separately. The anodized sensors have advantages of ruggedness, small dimensions, and fast response, as well as freedom from large temperature coefficients and less susceptibility to contamination of the lithium chloride conductivity sensors (Smith, 1971). 

---