## Thermodynamic Basis

The second law of thermodynamics tells us that the chemical potential of each component must be equal in both liquid and vapor phases at phase equilibrium. A somewhat simplified equation representing this condition is:

where

Xj = mol fraction of/th component in liquid yj = mol fraction of/th component in vapor PT = total system pressure pressure constant

x and y

FIGURE 2.11

### Bubble point and dew point at constant pressure

Pj = vapor pressure of _/th component at the temperature of the system yy = activity coefficient of thej'th component in the liquid phase at the conditions of temperature and composition of the liquid

This activity coefficient is a "fudge factor" that is used to account for nonideality. If the components are chemically quite similar, there is little attraction or repulsion of neighboring molecules of different types. The system is "ideal" and obeys Raoult's law (y} = 1).

Nonideality will be discussed in more detail in Section 2.3. We will assume ideal VLE behavior for the rest of this section for purposes of simplicity.

In the petroleum industry, distribution coefficients or "K values" are customarily used. The K value (K, ) of the jth component is defined as the ratio of vapor composition (y,j to liquid composition (x/).

If the system is "ideal" (yj = I), the K value is simply the vapor pressure divided by the total system pressure.

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