Chemical theory of vapor nonideality for strongly interacting substances

In systems that contain strongly interacting substances (such as those that contain carboxylic acids), the two interacting molecules tend to form a pair of stable weak bonds (such as hydrogen bonds for acid molecules in carboxylic acid systems). As a result, large negative deviations from vapor ideality occur even at low pressures. To account for the dimerization, Hayden and O'Connell developed expressions for the fugacity coefficients based on the thermodynamics of chemical equilibrium.

The chemical theory postulates that there is a dimerization equilibrium of the following type:

In this equilibrium reaction, i and j are two monomer molecules (that may or may not be chemically identical) that form a dimer ij. To describe this chemical equilibrium, we use a chemical equilibrium constant:

where

f is the fugacity of the true molecular species (monomer or dimer)

z is the true mole fraction

f" is the fugacity coefficient of the true molecular species

P is the total pressure

The following equation gives the fugacity coefficient of component i:

In this equation, zi and fi" refer to the monomer of species i while yi is the apparent mole fraction of component i, where apparent means that we neglect dimerization. To use this equation, we must first calculate the true fugacity coefficient, fi". We use the Lewis fugacity rule to calculate this value:

where

BiF is the free contribution to the second virial coefficient of component i

See Calculation of the second virial coefficient for the Hayden-O'Connell equation of state for more information.

After we calculate the true fugacity coefficient, we must then calculate the true mole fraction, zi. We simultaneously solve both the material balances (Sz = 1) and the chemical equilibria for all possible dimerization reactions to calculate the zi value.

We use the following relation to find the chemical equilibrium constant, Kij:

where

BijD is the dimerization contribution to the second virial coefficient

dij is the Kronecker delta

See Calculation of the second virial coefficient for the Hayden-O'Connell equation of state for more information.