Ideality of solutions is analogous to ideality for gases, with the important difference that intermolecular interactions in liquids are strong and cannot simply be neglected as they can for ideal gases. 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. Since the interaction energies between A and B are almost equal, it follows that there is a very small overall energy (enthalpy) change when the substances are mixed. 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. The simplest definition is that an ideal solution is a solution for which each component (i) obeys Raoult's law for all compositions. Here is the vapor pressure of component i above the solution, is its mole fraction and is the vapor pressure of the pure substance i at the same temperature.
This definition depends on vapor pressures which are a directly measurable property, at least for volatile components. The thermodynamic properties may then be obtained from the chemical potential μ (or partial molarGibbs energy g) of each component, which is assumed to be given by the ideal gas formula
The reference pressure may be taken as = 1 bar, or as the pressure of the mix to ease operations.
On substituting the value of 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 ,
Here is the fugacity of component in solution and is the fugacity of as a pure substance. 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. An equivalent statement uses thermodynamic activity instead of fugacity.
If we differentiate this last equation with respect to at constant we get:
but we know from the Gibbs potential equation that:
It can also be shown that volumes are strictly additive for ideal solutions.
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.