Equilibrium of distillation

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 

Here is the chemical potential of the volatile solvent in the vapor phase, ix[,. .. are the chemical potentials of the solvent in the various cups, filled with the samples, and the standard solutions, respectively. After establishment of the isopiestic equilibration, the solutions are reweighed. From the equilibrium concentrations, the activity coefficients can be calculated. 

Consider a system consisting of a distillation flask, a condenser, and a receiving flask. In the distillation flask, there is a volatile component (1) that is subject to the distillation process and a nonvolatile component (2) dissolved in the volatile component at a mole fraction JC2. We have 1 = Xi+X2- The distillation flask is kept at some temperature T + AT. 

In the condenser, a temperature gradient is maintained from T +AT to T. When the volatile component moves from the distillation flask to the receiving flask, it is ideally cooled down to temperature T of the pure volatile liquid component in the receiving flask and vice versa. 

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