7-34 No. 1

A mixture of ethane, propane, and n-butane exists at -10°C at a total pressure of 3000 mm Hg. Determine the compositions of the vapor and liquid phases if the propane and n-butane compositions are equal in the liquid phase. Vapor pressures at -10 C are (in mm Hg): ethane: 14000, propane: 2700, and n-butane: 500.

In general, vapor-liquid equilibrium is achieved when the fugacities of a component are equal in both the liquid and the vapor. This is generally expressed as:

P F_i y_i= x_iP_i^satg_i

P is total pressure

F_i is fugacity coefficient for the vapor

y_i is vapor phase mole fraction of component i

x_i is liquid phase mole fraction of component i

P_i^sat is vapor pressure of component i

g_i is the liquid phase activity coefficient for component i

For ideal vapor phase (which is often approximately true), this becomes:

P y_i= x_iP_i^satg_i

The above form is the one usually involved in chemical engineering practice.

If both the liquid and the vapor are ideal, then

P y_i= x_iP_i^sat

This is almost never true, but it is often used in manual problems for the test because of the complexity of solving the equation using complex functions for g_i which themselves are functions of composition and temperature.

Obviously, it always pays to have any model validated by experimental data.

An illustration of this is an impressionist painting by Rene Magritte.

Is the tree really there, or is it an artifact of the model?