Reply #17: Determination of NRTL Parameters for the Water, Formic Acid,

[PVnRT]

and n-Butyl Acetate System at Subatmospheric Pressure

A material balance requires that the change in moles of one component must equal the change in moles of the component in any phase <2> if any reactions taking place have a stoichiometric ratio of 1:1, i.e.,

Σdn_i,α = 0 (4)

If the general criterion for equilibrium is used, that is, dG_total = 0, this simplifies equation (3), assuming only two phases are present, to:

Σ ( μ_i,α - μ_i,β ) = 0 (5)

In order for equation (5) to be true, μ_i,α must be equal to μ_i,β. Since, in this case, the partial molar Gibbs free energy is defined as the chemical potential μ, the following holds true <2>:

dμ_i = RTd(ln f_i) (6)

Indefinite integration yields:

μ_i = RT ln f_i + Θ_i (7)

Since Θ_i is a constant only dependent on temperature, and, at equilibrium, all phases are at the same temperature and pressure, substituting equation (7) into the result for equation (5), it is seen that the fugacity of each component is equal across all phases.

Written four years ago for a master's thesis.