Editing Raoult's law (section)

===Ideal mixing===
An ideal solution would follow Raoult's law, but most solutions deviate from ideality. Interactions between gas molecules are typically quite small, especially if the vapor pressures are low. However, the interactions in a liquid are very strong. For a solution to be ideal, the interactions between unlike molecules must be of the same magnitude as those between like molecules.<ref>Rock, Peter A. ''Chemical Thermodynamics'' (MacMillan 1969), p. 261. {{ISBN|1891389327}}.</ref> This approximation is only true when the different species are almost chemically identical. One can see that from considering the [[Gibbs free energy of mixing|Gibbs free energy change of mixing]]:

: <math>\Delta_\text{mix} G = nRT (x_1 \ln x_1 + x_2 \ln x_2).</math>

This is always negative, so mixing is spontaneous. However, the expression is, apart from a factor <math>-T</math>, equal to the entropy of mixing. This leaves no room at all for an enthalpy effect and implies that <math>\Delta_\text{mix} H</math> must be equal to zero, and this can only be true if the interactions between the molecules are indifferent.

It can be shown using the [[Gibbs–Duhem equation]] that if Raoult's law holds over the entire concentration range <math>x \in [0,\ 1]</math> in a binary solution then, for the second component, the same must also hold.

If deviations from the ideal are not too large, Raoult's law is still valid in a narrow concentration range when approaching <math>x \to 1</math> for the majority phase (the ''solvent''). The solute also shows a linear limiting law, but with a different coefficient. This relationship is known as [[Henry's law]].

The presence of these limited linear regimes has been experimentally verified in a great number of cases, though large deviations occur in a variety of cases.  Consequently, both its pedagogical value and utility have been questioned at the introductory college level.<ref name="Hawkes 1995">{{cite journal|last = Hawkes|first = Stephen J.|year = 1995|title = Raoult's Law Is a Deception|journal = [[J. Chem. Educ.]]|volume = 72|issue = 3|pages = 204–205|doi = 10.1021/ed072p204| s2cid=95146940 |doi-access = free| bibcode=1995JChEd..72..204H }}</ref> In a perfectly ideal system, where ideal liquid and ideal vapor are assumed, a very useful equation emerges if Raoult's law is combined with [[Dalton's Law]]:

: <math>x_i = \frac{y_i p_\text{total}}{p_i^\star},</math> <!-- Please do not completely delete from article. Very valuable equation. -->

where <math>x_i</math> is the [[mole fraction]] of component <math>i</math> in the ''solution'', and <math>y_i</math> is its [[mole fraction]] in the ''gas phase''. This equation shows that, for an ideal solution where each pure component has a different vapor pressure, the gas phase is enriched in the component with the higher vapor pressure when pure, and the solution is enriched in the component with the lower pure vapor pressure. This phenomenon is the basis for [[distillation]].