Activity Coefficients at Infinite Dilution
Activity coefficients at infinite dilution () are important for:
- characterizing the behavior of liquid mixtures
- fitting gE-model parameters (e.g. Margules, van Laar, Wilson, NRTL, UNIQUAC)
- predicting the existence of an azeotrope
- the estimation of mutual solubilities
- providing incisive information for the statistical thermodynamicist (no solute-solute interactions)
- analytical chromatographers
- screening solvents for extraction and extractive distillation processes
- the calculation of limiting separation factors necessary for the reliable design of distillation processes
- the calculation of Henry constants and partition coefficients
- the development of predictive methods (mod. UNIFAC (Do),...)
Several methods were developed for the measurement of . The most important methods are: gas-liquid chromatography (GLC), non-steady-state gas-liquid chromatography, differential ebulliometry, static methods and the dilutor method. Chromatographic methods allow the determination of of volatile solutes in high (classical GLC) and low boiling (non-steady-state GLC) solvents. The dilutor method also allows the determination of in solvent mixtures. The addition of water to selective solvents (e.g. NMP + water) often increases the selectivity of the solvents used.
Fig.1 shows a scheme of the home-made GLC-apparatus, which can be used for "classical" as well as for "non-steady-state" gas-liquid chromatography <1, 2>. The calculation of from the obtained data and some typical -values can be seen in Fig. 2 and 3.
Fig. 1: Scheme of the gas-liquid chromatograph applicable
in the "classical" and the "non-steady-state" mode
Fig. 2: Evaluation of chromatographic data
Fig. 3: Typical -results
The GLC technique requires the careful preparation of the column and allows the measurement of a great number of in a rather short time. The amount of solvent in the column is determined gravimetrically. In order to check if solvent losses occur during the measurements, the liquid loading is determined before and after the measurement. This is taken into account assuming linear solvent loss during the isothermal measurements. With the use of presaturators the loss of solvent can be kept to a minimum. Furthermore the experimental conditions (gas flow, solvent loss, ...) are checked by measuring the retention time of a reference substance in regular intervals.
The experimental setup for the dilutor method is shown schematically in Fig. 4. and Fig. 5
Fig. 4: Scheme of the dilutor
Fig. 5: Scheme of the equilibrium cell
With a constant inert gas flow a highly diluted component (solute) is stripped from a liquid solution (solvent). The variation of solute concentration in the gaseous phase is measured with the help of a gas chromatograph <3>. In Fig. 6 values for are obtained from the graph. ln peak area versus time (concentration of the solute in the vapor phase).
Fig. 6 Evaluation of data from the dilutor method
A detailed description of the measurement procedure and the data analysis can be found by Leroi et al. (1977) and Duhem and Vidal (1978). The real behavior of the gas phase is taken into account with the help of fugacity coefficient of the solute in the saturated state. The values are calculated with the help of the second virial coefficient. For the vapor pressure calculation (Antoine, Wagner, DIPPR, ...) the equation with the smallest deviations to experimental vapor pressure data stored in the Dortmund Data Bank is used.
Figures 7 shows typical results for measurement in electrolyte systems with the help of the dilutor technique.
Fig. 7 Example for the value of ethanol in a water/sodium chloride mixtures