The vapor pressures of the solvent and solute obey Raoult's law and Henry's law, respectively,[3] and the activity coefficient (which measures deviation from ideality) is equal to one for each component.
Instead we assume that the mean strength of the interactions are the same between all the molecules of the solution.
More formally, for a mix of molecules of A and B, then the interactions between unlike neighbors (UAB) and like neighbors UAA and UBB must be of the same average strength, i.e., 2 UAB = UAA + UBB and the longer-range interactions must be nil (or at least indistinguishable).
If the molecular forces are the same between AA, AB and BB, i.e., UAB = UAA = UBB, then the solution is automatically ideal.
If the molecules are almost identical chemically, e.g., 1-butanol and 2-butanol, then the solution will be almost ideal.
The more dissimilar the nature of A and B, the more strongly the solution is expected to deviate from ideality.
Different related definitions of an ideal solution have been proposed.
[5][6][7] This definition depends on vapor pressure, which is a directly measurable property, at least for volatile components.
The thermodynamic properties may then be obtained from the chemical potential μ (which is the partial molar Gibbs energy g) of each component.
If the vapor is an ideal gas, The reference pressure
= 1 bar, or as the pressure of the mix, whichever is simpler.
from Raoult's law, This equation for the chemical potential can be used as an alternate definition for an ideal solution.
However, the vapor above the solution may not actually behave as a mixture of ideal gases.
Some authors therefore define an ideal solution as one for which each component obeys the fugacity analogue of Raoult's law
[8][9] Since the fugacity is defined by the equation this definition leads to ideal values of the chemical potential and other thermodynamic properties even when the component vapors above the solution are not ideal gases.
constant we get: Since we know from the Gibbs potential equation that: with the molar volume
, these last two equations put together give: Since all this, done as a pure substance, is valid in an ideal mix just adding the subscript
, with optional overbar, standing for partial molar volume: Applying the first equation of this section to this last equation we find: which means that the partial molar volumes in an ideal mix are independent of composition.
we get a similar result for molar enthalpies: Remembering that
, similarly It is also easily verifiable that Finally since we find that Since the Gibbs free energy per mole of the mixture
Hence the molar Gibbs free energy of mixing is or for a two-component ideal solution where m denotes molar, i.e., change in Gibbs free energy per mole of solution, and
Note that this free energy of mixing is always negative (since each
must be negative (infinite)), i.e., ideal solutions are miscible at any composition and no phase separation will occur.
The equation above can be expressed in terms of chemical potentials of the individual components where
of an ideal solution obeys Raoult's Law over the entire composition range: where
is the equilibrium vapor pressure of pure component
Deviations from ideality can be described by the use of Margules functions or activity coefficients.
A single Margules parameter may be sufficient to describe the properties of the solution if the deviations from ideality are modest; such solutions are termed regular.
In contrast to ideal solutions, where volumes are strictly additive and mixing is always complete, the volume of a non-ideal solution is not, in general, the simple sum of the volumes of the component pure liquids and solubility is not guaranteed over the whole composition range.
By measurement of densities, thermodynamic activity of components can be determined.