Regular solution

A regular solution is a solution that diverges from the behavior of an ideal solution only moderately ^[1].

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More precisely it can be described by Raoult's law modified with a Margules function with only one parameter α:

P₁= x₁P*₁f_1,M

P₂= x₂P*₂f_2,M

Where the Margules function is

f_1,M = exp(αx₂²)

f_2,M = exp(αx₁²)

Notice that the Margules function always contains the opposite mole fraction. It can also be shown that if the first Margules expression hold that the other one must have the same shape using the Gibbs-Duhem relation.

The value of α can be interpreted as W/RT, where W = 2U₁₂ -U₁₁ -U₂₂

represents the difference interaction between like and unlike neighbors.

In contrast to the case of ideal solutions, regular solutions do possess an enthalpy of mixing, due to the W term. If the unlike interactions are more infavorable than the like ones, we get competition between an entropy of mixing term that produces a minumum in the Gibbs free energy at x=0.5 and the enthalpy term that has a maximum there. At high temperatures the entropy wins and the system is fully miscible, at lower temperatures the G curve will have two minima and a maximum in between. This results in phase separation. In general there will be a temperature where the three extremes coalesce and the system becomes fully miscible. This point is known as the critical point of solubility or the consolute point.

In contrast to ideal solutions, the volumes in the case of regular solutions are no longer strictly additive but must be calculated from the partial molar volumes that are a function of x.

References