Ideality of solutions is analogous to ideality for gases, with the important difference that intermolecular interactions in liquids are strong and can not 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, the interactions between unlike neighbors (UAB) and like neighbors UAA and UBB must be of the same average strength i.e. 2UAB=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 ideal. Since the interaction energies between A and B are the same, it follows that there is no 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.
An ideal mix is defined as a mix that satisfies:
Since the definition of fugacity in a pure substance is:
If we derivative this last equation with respect to at constant we get:
These last two equations put together give:
Applying the first equation of this section to this last equation we get
Prociding in a similar way but derivative with respect of we get to a similar result with enthalpies
Meaning that the enthalpy of the mix is equal to the sum of its components.
Since and :
At last we can calculate the entropy of mixing since and
Note that this free energy of mixing is always negative (since each is positive and each must be negative) i.e. ideal solutions are always completely miscible.
The equation above can be expressed in terms of chemical potentials of the individual components
If the chemical potential of pure liquid is denoted , then the chemical potential of in an ideal solution is
Any component of an ideal solution obeys Raoult's Law over the entire composition range:
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.
Reply to the discussion by Chapuis et al. on "Network model for hydraulic conductivity of sand--bentonite mixtures" (1).(DISCUSSION / DISCUSSION)
Jan 01, 2006; The writers are grateful for the interest and the feedback provided by the discussers. Answers and responses to their concerns...