Raoult's law
Proposed by French chemist François-Marie Raoult in 1887,[1][2] it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component (liquid or solid) multiplied by its mole fraction in the mixture.
Mathematically, Raoult's law for a single component in an ideal solution is stated as where
Raoult's law is a phenomenological relation that assumes ideal behavior based on the simple microscopic assumption that intermolecular forces between unlike molecules are equal to those between similar molecules, and that their molar volumes are the same: the conditions of an ideal solution.
Raoult's law is instead valid if the physical properties of the components are identical.
For example, if the two components differ only in isotopic content, then Raoult's law is essentially exact.
Comparing measured vapor pressures to predicted values from Raoult's law provides information about the true relative strength of intermolecular forces.
If the vapor pressure is less than predicted (a negative deviation), fewer molecules of each component than expected have left the solution in the presence of the other component, indicating that the forces between unlike molecules are stronger.
For a solution of two liquids A and B, Raoult's law predicts that if no other gases are present, then the total vapor pressure
above the solution is equal to the weighted sum of the "pure" vapor pressures
Raoult's law was first observed empirically and led François-Marie Raoult[1][2] to postulate that the vapor pressure above an ideal mixture of liquids is equal to the sum of the vapor pressures of each component multiplied by its mole fraction.
[4]: 325 Taking compliance with Raoult's Law as a defining characteristic of ideality in a solution, it is possible to deduce that the chemical potential of each component of the liquid is given by where
That is, Substituting the formula for chemical potential gives as the gas-phase mole fraction depends on its fugacity,
in equilibrium with its vapor is Subtracting these equations and re-arranging leads to the result[4]: 326 For the ideal gas, pressure and fugacity are equal, so introducing simple pressures to this result yields Raoult's law: 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.
It can be shown using the Gibbs–Duhem equation that if Raoult's law holds over the entire concentration range
If deviations from the ideal are not too large, Raoult's law is still valid in a narrow concentration range when approaching
The solute also shows a linear limiting law, but with a different coefficient.
Consequently, both its pedagogical value and utility have been questioned at the introductory college level.
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.
In elementary applications, Raoult's law is generally valid when the liquid phase is either nearly pure or a mixture of similar substances.
[7] Raoult's law may be adapted to non-ideal solutions by incorporating two factors that account for the interactions between molecules of different substances.
The first factor is a correction for gas non-ideality, or deviations from the ideal-gas law.
[4]: 326 This modified or extended Raoult's law is then written as[8] In many pairs of liquids, there is no uniformity of attractive forces, i.e., the adhesive (between dissimilar molecules) and cohesive forces (between similar molecules) are not uniform between the two liquids.
For example, the system of chloroform (CHCl3) and acetone (CH3COCH3) has a negative deviation[9] from Raoult's law, indicating an attractive interaction between the two components that have been described as a hydrogen bond.
[10] The system HCl–water has a large enough negative deviation to form a minimum in the vapor pressure curve known as a (negative) azeotrope, corresponding to a mixture that evaporates without change of composition.
[11] When these two components are mixed, the reaction is exothermic as ion-dipole intermolecular forces of attraction are formed between the resulting ions (H3O+ and Cl–) and the polar water molecules so that ΔHmix is negative.
When the adhesion is weaker than cohesion, which is quite common, the liquid particles escape the solution more easily that increases the vapor pressure and leads to a positive deviation.
If the deviation is large, then the vapor pressure curve shows a maximum at a particular composition and forms a positive azeotrope (low-boiling mixture).
When these pairs of components are mixed, the process is endothermic as weaker intermolecular interactions are formed so that ΔmixH is positive.
