6' Ideal Liquid Solutions

1
6. Ideal Liquid Solutions

• We have already developed a model for the
  chemical potential of ideal solutions.
• Acknowledges the fact that molecules have finite
  volume and strong interactions, but assumes that
  these interactions are the same for all
  components of the mixture.
• This are the same assumptions used for ideal
  mixtures of real gases.
• The chemical potential of species i in an ideal
  solution is given by
• (11.26)11.75
• where Gil (T,P) represents the pure liquid Gibbs
  energy at T,P.
• This reference state can be shifted to (T,unit
  pressure) using
• (11.37)11.31

2
Ideal Liquid Solutions

• Substituting for Gil (T,P) yields
• To estimate the chemical potential of component i
  in an ideal liquid solution, all we require is
  the composition (xi) and the pure liquid fugacity
  (fil ).
• The fugacity of a pure liquid can be calculated
  using
• (11.41)11.44
• For those cases in which the ideal solution model
  applies, we require only pure component data to
  estimate the chemical potentials and total Gibbs
  energy of the liquid phase.

3
Non-Ideal Liquid Solutions

• Relatively few liquid systems meet the criteria
  required by ideal solution theory. In most cases
  of practical interest, molecular interactions are
  not uniform between components, resulting in
  mixture behaviour that deviates significantly
  from the ideal case.
• The approach for handling non-ideal liquid
  solutions is exactly the same as that adopted for
  non-ideal gas mixtures. We define a solution
  fugacity, fil as
• (11.42)11.46
• To use this approach, we require experimental
  data or correlations pertaining to the specific
  mixture of interest

4
Lewis-Randall Rule

• The ideal solution model developed in earlier is
  known (in a slightly different form) as the
  Lewis-Randall equation
• (11.80)11.83
• The solution fugacity of component i in an ideal
  solution (gas or liquid) can be represented by
  the product of the pure component fugacity and
  the mole fraction.
• Whenever you apply an ideal solution model, you
  are using the Lewis-Randall rule.
• This is an approximation that yields reasonable
  results for similar compounds (benzene/toluene,
  ethanol/propanol)
• However, it is important that you appreciate the
  limitations of this rule. When you cannot find
  mixture data, you may need to use it (but I
  suggest you look harder).

5
Liquid Phase Activity Coefficients

• Based on our definition of solution fugacity
• (11.42)11.46
• we could define a liquid phase solution fugacity
  coefficient
• that reflects deviations of the solution fugacity
  from a perfect gas mixture.
• A more logical approach is to measure the
  deviations of the solution fugacity from ideal
  solution behaviour. For this purpose, we define
  the activity coefficient
• (11.87)11.90
• this convenient parameter is used to correlate
  non-ideal liquid solution data, just as ?i is
  used for gas mixtures

6
Excess Properties of Non-Ideal Liquid Solutions

• Most of the information needed to describe
  non-ideal liquid solutions is published in the
  form of the excess Gibbs energy, GE.
• Excess properties are defined as the difference
  between the actual property value of a solution
  and the ideal solution value at the same T, P,
  and composition.
• ME(T,P, xn) M(T,P, xn) - Mid(T,P,
  xn) (11.82)11.85
• In defining excess properties, we use ideal
  solution behaviour as our reference. Pure
  components cannot have excess properties.
• Partial excess properties can also be defined
• MiE(T,P, xn) Mi(T,P, xn) - Miid(T,P,
  xn)(11.86)11.88
• where

7
Excess Properties of Non-Ideal Liquid Solutions

• The partial excess Gibbs energy is of primary
  interest
• where the actual partial molar Gibbs energy is
  provided by equation 11.42 11.46
• and the ideal solution chemical potential is
• Leaving us with the partial excess Gibbs energy
• (11.88)11.91

8
Excess Properties of Non-Ideal Liquid Solutions

• Why do we define excess properties for liquid
  solutions?
• They are more easily applied to experimental data
• Activity coefficients can be treated as partial
  molar properties with respect to excess
  properties. Three important results follow
• (11.92)11.96
• The Gibbs-Duhem equation
• (11.14)
• The summability relation, providing GE from ln?i
  data
• (11.95)11.99