Ideal and Non-Ideal Solutions Raoult's Law - JEE

In 1986, a French Chemist named Francois Marte Raoult proposed a quantitative relation between partial pressure and mole fraction of volatile liquids. The law states that the mole fraction of the solute component is directly proportional to its partial pressure. On the basis of Raoult’s Law, liquid–liquid solutions are classified into two types of solutions, they are Ideal Solutions and Non-ideal Solutions. Now in this article, we will be discussing three important concepts, they are Raoult Law, Ideal Solution, and Non-Ideal Solution.

Raoult's Law

Raoult's law states that the partial vapour pressure of a solvent in a solution (or mixture) is equal to or identical to the vapour pressure of the pure solvent multiplied by its mole fraction in the solution. 

Mathematically, Raoult’s law equation is given by the following formula.

\[{{P}_{solvent}}~=\text{ }{{x }_{solvent}}\times {{P}^{0}}_{solvent}\]

where

\[{{P}_{solvent}}~\]= vapour pressure of the solvent in the solution

\[{{x }_{solvent}}\]= mole fraction of the solvent

\[{{P}^{0}}_{solvent}\]= vapour pressure of the pure solvent

In general, Raoult's law is only applicable to ideal solutions. That is the solution for which there is no interaction between the molecules of the solvent and those of the solute. In reality, however, most solutions do exhibit some degree of intermolecular interactions. As a result, Raoult's law typically overestimates or underestimates the actual vapour pressure lowering that occurs in non-ideal solutions.

Representing the Interaction of Solution

Ideal Solution

The solutions which obey Raoult’s Law at every range of concentration and at all temperatures are called Ideal Solutions. Ideal solutions can be obtained by mixing two ideal components, i.e., solute and a solvent having similar molecular size and structure.  For instance, let us consider two liquids, i.e., liquid A and liquid B, and mix them. The formed solution will experience several intermolecular forces of attractions inside it, which will be like:

• A – A intermolecular force of attraction

• B – B intermolecular forces of attraction

• A – B intermolecular forces of attraction

Thus, the solution is said to be an ideal solution, only when the intermolecular forces of attraction between A – A, B – B, and A – B are almost equal. 

Examples: n-hexane and n-heptane, Bromoethane and Chloroethane, Benzene and Toluene, \[CC{{l}_{4}}~and~\text{ }SiC{{l}_{4}}\], Chlorobenzene and Bromobenzene, Ethyl Bromide and Ethyl Iodide, n-Butyl Chloride and n-Butyl Bromide are some examples of Ideal Solution.

General Characteristics of Ideal Solutions 

• Ideal Solution Raoult’s Law example, which means partial pressure of components A and B in a solution will be \[{{P}_{A}}~=\text{ }{{P}_{A}}^{0}~{{x}_{A}}~and\text{ }{{P}_{B}}~=\text{ }{{P}_{B}}^{0}~{{x}_{B\text{ }~}}\]

where \[{{P}_{A}}^{0}~and\text{ }{{P}_{B}}^{0}~\]are respective vapour pressure in pure form and \[{{x}_{A}}~and\text{ }{{x}_{B}}\] are respective mole fractions of components A and B.

• Enthalpy of mixing of two components should be zero, that is, \[{{\Delta }_{mix}}~H\text{ }=\text{ }0\]. This particularly signifies that no heat is absorbed or released during the mixing of two pure components to form an ideal solution.

• Volume of mixing of two components should be zero, that is, \[{{\Delta }_{mix}}~V\text{ }=\text{ }0\]. This means that the total volume of solution is equal to the sum of the volume of solute and solution. Adding further, it also signifies that there is no occurrence of contraction or expansion of volume while mixing two components.

• The solvent-solvent and solute-solute interaction are nearly equal to the solute-solvent interaction.

Non-Ideal Solution

Solutions which don’t obey Raoult’s law at every range of concentration and at all temperatures are called Non-Ideal Solutions. 

General characteristics of Non-ideal Solutions are as follows:

• Solute-solute and solvent-solvent interactions are different from that of solute-solvent interactions.

• Enthalpy of mixing that is, \[{{\Delta }_{mix}}~H\text{ }\ne \text{ }0\], which means that heat might have released if enthalpy of mixing is negative \[\left( {{\Delta }_{mix}}~H\text{ }<\text{ }0 \right)\] or the heat might have observed if enthalpy of mixing is positive \[\left( {{\Delta }_{mix}}~H\text{ }>\text{ }0 \right)\].

• The volume of mixing, i.e., \[{{\Delta }_{mix}}~V\text{ }\ne \text{ }0\], which depicts that there will be some expansion or contraction in dissolution of liquids.

Types of Non-Ideal Solution

Non-ideal solutions are of two types:

• Non-ideal solutions showing positive deviation from Raoult’s Law

• Non-ideal solutions showing negative deviation from Raoult’s Law

a) Positive Deviation from Raoult’s Law

Positive deviation from Raoult’s Law occurs when the vapour pressure of the component is greater than what is expected in Raoult’s Law.

Positive Deviation from Raoult's Law Examples

Here let's discuss the positive deviation from Raoult's law examples. For instance, let us consider two components A and B to form non-ideal solutions. Let the vapour pressure, pure vapour pressure, and mole fraction of component A be \[{{P}_{A}}~,\text{ }{{P}_{A}}^{0}~and\text{ }{{x}_{A}}~\], respectively, and same with that of component B be \[{{P}_{B}}~,\text{ }{{P}_{B}}^{0}~and\text{ }{{x}_{B}}\], respectively.

These liquids will show positive deviation when Raoult’s Law (conditions for positive deviation from Raoult's law):

• \[{{P}_{A}}~>\text{ }{{P}_{A}}^{0}~{{x}_{A}}~and\text{ }{{P}_{B}}~>\text{ }{{P}^{0}}_{B}~{{x}_{B}},\]as the total vapour pressure \[\left( {{P}_{A}}^{0}~{{x}_{A}}~+\text{ }{{P}^{0}}_{B}~{{x}_{B}} \right)\] is greater than what it should be according to Raoult’s Law.

• The solute-solvent forces of attraction is weaker than solute-solute and solvent-solvent interaction that is, \[A\text{ }\text{ }B\text{ }<\text{ }A\text{ }\text{ }A\text{ }or\text{ }B\text{ }\text{ }B\]

• The enthalpy of mixing is positive that is, \[{{\Delta }_{mix}}~H\text{ }>\text{ }0\], because the heat absorbed to form new molecular interaction is less than the heat released on breaking of original molecular interaction.

• The volume of mixing is positive, that is, \[{{\Delta }_{mix}}~V\text{ }>\text{ }0\], as the volume expands on dissolution of components A and B.

b) Negative Deviation from Raoult’s Law

Negative Deviation occurs when the total vapour pressure is less than what it should be according to Raoult’s Law. Now again considering the same A and B components to form a non-ideal solution, it will show a negative deviation from Raoult’s Law only when:

• \[{{P}_{A}}~<\text{ }{{P}_{A}}^{0}~{{x}_{A}}~and\text{ }{{P}_{B}}~<\text{ }{{P}^{0}}_{B}~{{x}_{B}}~\]as the total vapour pressure \[\left( {{P}_{A}}^{0}~{{x}_{A}}~+\text{ }{{P}^{0}}_{B}~{{x}_{B}} \right)\]is less than what it should be with respect to Raoult’s Law.

• The solute-solvent interaction is stronger than solute-solute and solvent-solvent interaction that is, \[A\text{ }\text{ }B\text{ }>\text{ }A\text{ }\text{ }A\text{ }or\text{ }B\text{ }\text{ }B\].

• The enthalpy of mixing is negative, that is \[{{\Delta }_{mix}}~H\text{ }<\text{ }0\] because more heat is released when new molecular interactions are formed.

• The volume of mixing is negative, that is, \[{{\Delta }_{mix}}~V\text{ }<\text{ }0\] as the volume decreases on dissolution of components A and B.

Summary

In this article, we have discussed Raoult's and ideal and non-ideal solutions. Let us summarise the article with the key points. Raoult’s law states that the mole fraction of the solute component is directly proportional to its partial pressure. Solution that obeys Raoult’s law is known as the ideal solution and the solution that doesn’t obey Raoult's law is known as the non-ideal solution. The non-ideal solutions are divided into two more types, they are non-ideal solutions showing positive deviation from Raoult’s Law and non-ideal solutions showing negative deviation from Raoult’s Law.