## Thermodynamics and Equilibrium Data

Accurate and reliable thermodynamic data for vapour-liquid equilibrium is essential to distillation

Figure 1 Simple distillation - a still.

design. For binary mixtures, these data are generally presented in the form of tables containing the liquid and vapour equilibrium compositions over a range of temperatures for a fixed pressure. The same information can also be plotted in what is called an x-y diagram. For multicomponent mixtures, however, vapour liquid equilibrium data are difficult to represent in graphical or tabular form. In such case, K values are used instead.

K value and relative volatility The K value of a component i is a measure of the tendency of such component to vaporize. A K value is defined by:

where yi is the equilibrium composition of the vapour phase for a composition Xi of the liquid phase. K values are a function of temperature, pressure and composition, and they are widely reported for binary and multicomponent mixtures. An associated concept is the relative volatility, a,-, which is a measure of the ease of separation of components i and j by distillation:

Ideal and nonideal systems An ideal system is one in which the liquid phase obeys Raoult's Law and the vapour phase obeys the ideal gas law. For such systems, the K value is given by:

where pi is the vapour pressure of pure component i and P is the pressure of the system. Note that pi is a function of temperature.

For a nonideal system, the K values can also depend upon the composition of the mixture and are expressed in terms of fugacity coefficients, where éi is the vapour phase fugacity coefficient and yL is the liquid phase activity coefficient, as given below:

Azeotropic systems represent examples of nonideal mixtures for which eqn [5] has to be used.

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