## Bubblepoint Calculations

The most common VLE problem is to calculate the temperature and vapor composition y that is in equilibrium with a liquid at a known total pressure of the system P and with a known liquid composition (all the xj values). At phase equilibrium the "chemical potential" m of each component in the liquid and vapor phases must be equal:

The liquid-phase chemical potential of component j can be expressed in terms of liquid mole fraction Xj, vapor pressure Pj, and activity coefficient g:

m=xjpsgj

The vapor-phase chemical potential of component j can be expressed in terms of vapor mole fraction yj, the total system pressure P, and fugacity coefficient sj mj = yjps

Therefore the general relationship between vapor and liquid phases is yjps = XjpSg

If the pressure of the system is not high, the fugacity coefficient is unity. If the liquid phase is "ideal" (i.e., there is no interaction between the molecules), the activity coefficient is unity. The latter situation is much less common than the former because components interact in liquid mixtures. They can either attract or repulse. Section 1.7 discusses nonideal systems in more detail.

Let us assume that the liquid and vapor phases are both ideal (g = 1 and sj = 1). In this situation the bubblepoint calculation involves an iterative calculation to find the temperature T that satisfies the equation