Balance Equations for Binary Systems

The balance equations to be solved take the same form for both vapors and liquids. The liquid equations will be shown, and the reader should recognize the vapor equations by analogy. First, the true mole fractions must sum to unity:

In a binary system, a balance equation can be written for either component to match the apparent mole fraction:

Dividing numerator and denominator by the true number of moles, n_T,

Rearranging Eqn. 19.21 to facilitate implementation of the balance, multiply by the denominator,

and collecting the true mole fraction results in a form of Eqn. 19.21 that is easier to implement:

Eqns. 19.20 and 19.22 are not yet ready to implement because all of the true mole fractions are unknown and only two equations have been developed. In the next section, we show that the true mole fractions can be written in terms of an equilibrium constant and the monomer mole fractions, which will provide sufficient information once the equilibrium constants are known.