Non-Ideal Solutions: Raoult’s Law and Examples

Non-Ideal Solutions: We know that a solution is made up of a solvent and a solute. The major component of a solution is the solvent (i.e. water, air), while the minor component of a solution is the solute (sugar, carbon dioxide, etc.). A concrete example would be lemonade. The water acts as the solvent, and the salt or sugar added to the water is the solute.

At a given temperature and pressure, no solution is ideal and results in non-ideal solutions. A variety of forces act on non-ideal solutions, making it difficult to predict the properties of such solutions. These solutions are identified by determining the strength and specifics of the intermolecular forces between the different molecules in that particular solution. Let us explore more about non-ideal solutions in this article.

Non-Ideal Solutions: Raoult’s Law

In \(1986,\) a French Chemist named Francois Marte Raoult proposed a quantitative relationship between partial pressure and the mole fraction of volatile liquids. Raoult’s law in its general form can be stated as, for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction. It is expressed by the formula:

\({{\text{P}}_{{\text{solution}}}} = {{\text{X}}_{{\text{solvent}}}} \times {\text{P}}{^\circ _{{\text{solvent}}}}\)

where
\({{\text{P}}_{{\text{solution}}}}\) is the vapour pressure of the solution
\({{\text{X}}_{{\text{solvent}}}}\) is the mole fraction of the solvent
\({\text{P}}{^\circ _{{\text{solvent}}}}\) is the vapour pressure of the pure solvent

In a binary solution, if a volatile solute is added to the volatile solvent, each solute’s and solvent’s component is added to the total pressure.

\({{\text{P}}_{{\text{solution}}}} = \left({{{\text{X}}_{{\text{solvent}}}} \times {\text{P}}{^\circ _{{\text{solvent}}}}} \right) + \left({{{\text{X}}_{{\text{solute}}}} \times {\text{P}}{^\circ _{{\text{solute}}}}} \right)\)

Raoult’s Law is akin to the ideal gas law, except as it relates to the properties of a solution. Raoult’s Law assumes ideal behaviour in which the intermolecular forces between dissimilar molecules of a solution equals forces between similar molecules.

Based on Raoult’s Law, liquid-liquid solutions are classified into two types of solutions, they are:

1. Ideal Solutions
2. Non-ideal Solutions

Let us look at some of the differences between ideal and non-ideal solution:

What is Ideal Solution?

The solutions that obey Raoult’s Law at every concentration range and at all temperatures are called Ideal Solutions.

1. An ideal solution is obtained by mixing two ideal components, that is, solute and a solvent with similar molecular size, structure and identical intermolecular forces. 
2. The resulting solution obtained by mixing two identical liquids \({\text{A}}\) (solvent) and \({\text{B}}\) (solute), will experience several intermolecular forces of attractions as summarised below:
   a. \({\text{A}} – {\text{A}}\) intermolecular forces of attraction (solvent-solvent)
   b. \({\text{B}} – {\text{B}}\) intermolecular forces of attraction (solute-solute)
   c. \({\text{A}} – {\text{B}}\) intermolecular forces of attraction (solvent-solute)
3. In an ideal solution, the intermolecular forces of attraction between \({\text{A}} – {\text{A,}}\,{\text{B}} – {\text{B}}\) and \({\text{A}} – {\text{B}}\) are nearly equal, i.e., \({\text{A}} – {\text{A}} \approx {\text{B}} – {\text{B}} \approx {\text{A}} – {\text{B}}\)

According to Raoult’s Law, the partial vapour pressure of two components of the solution may be given as:

\({{\text{P}}_{\text{A}}} = {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}}\)

\({{\text{P}}_{\text{B}}} = {{\text{X}}_{\text{B}}}{\text{P}}{^\circ _{\text{B}}}\)

Total pressure \({\text{P}}\) is given by-

\({\text{P}} = {{\text{P}}_{\text{A}}} + {{\text{P}}_{\text{B}}}\)

\({\text{P}} = {{\text{X}}_{\text{A}}} \times {\text{P}}{^\circ _{\text{A}}} + {{\text{X}}_{\text{B}}} \times {\text{P}}{^\circ _{\text{B}}}\)

We know the total mole fraction of a solution is equal to \(1\). So,

\({{\text{X}}_{\text{A}}} + {{\text{X}}_{\text{B}}} = 1\)

\({{\text{X}}_{\text{A}}} = 1 – {{\text{X}}_{\text{B}}}\)

Hence, total pressure \({\text{P}}\) is given by-

\({\text{P}} = \left({1 – {{\text{X}}_{\text{B}}}}  \right){\text{P}}{^\circ _{\text{A}}} + {{\text{X}}_{\text{B}}} \times {\text{P}}{^\circ _{\text{B}}}\)

\({\text{P}} = {\text{P}}{^\circ _{\text{A}}} – {{\text{X}}_{\text{B}}}\left({{\text{P}}{^\circ _{\text{A}}} – {\text{P}}{^\circ _{\text{B}}}} \right)\)

The characteristics of Ideal Solutions are as follows:

1. Ideal solutions follow Raoult’s Law, which means partial pressure of components \({\text{A}}\) and \({\text{B}}\) in a solution will be \({{\text{P}}_{\text{A}}} = {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}}\) and \({{\text{P}}_{\text{B}}} = {{\text{X}}_{\text{B}}}{\text{P}}{^\circ _{\text{B}}}\) where \({\text{P}}{^\circ _{\text{A}}}\) and \({\text{P}}{^\circ _{\text{B}}}\) are respective vapour pressures in pure form. \({{\text{X}}_{\text{A}}}\) and \({{\text{X}}_{\text{B}}}\) are respective mole fractions of components \({\text{A}}\) and \({\text{B}}\).
2. In an ideal solution, the enthalpy of mixing of two components should be zero, that is, \({\Delta _{{\text{mix}}}}{\text{H}} = 0\). This means that no heat is released or absorbed during the mixing of two pure components to form an ideal solution.
3. The volume of mixing of two components in an ideal solution should be zero, that is, \({\Delta _{{\text{mix}}}}{\text{V}} = 0\) This means that in an ideal solution the total volume of solution is equal to the sum of the volume of solute and solvent. It also signifies that there is no contraction or expansion of volume while mixing two components.
4. The solute-solute \((\mathrm{B}-\mathrm{B})\) interaction and solvent-solvent \((\mathrm{A}-\mathrm{A})\) interaction is nearly equal to solute-solvent \((\mathrm{A}-\mathrm{B})\) interaction.

Note: There are very few solutions that are ideal, only some solutions show ideal behaviour.

Example of Ideal Solutions
1. \({\text{n}}\)-hexane and \({\text{n}}\)-heptane
2. Bromoethane and Chloroethane
3. Benzene and Toluene
4. \({\text{CC}}{{\text{l}}_4}\) and \({\text{SiC}}{{\text{l}}_4}\)
5. Chlorobenzene and Bromobenzene
6. Ethyl Bromide and Ethyl lodide
7. \({\text{n}}\) – Butyl Chloride and \({\text{n}}\) – Butyl Bromide

Non-ideal Solutions

1. The solutions that do not follow Raoult’s Law at every concentration range and at all temperatures and deviate from it are called Non-Ideal Solutions. 
2. The resulting solution obtained by mixing two liquids, \({\text{A}}\) (solvent) and \({\text{B}}\) (solute), will experience several intermolecular forces of attractions as summarised below:
   a. \({\text{A}} – {\text{A}}\) intermolecular forces of attraction (solvent-solvent)
   b. \({\text{B}} – {\text{B}}\) intermolecular forces of attraction (solute-solute)
   c. \({\text{A}} – {\text{B}}\) intermolecular forces of attraction (solvent-solute)
3. In a non-ideal solution, the intermolecular forces of attraction between \({\text{A}} – {\text{A,}}\,{\text{B}} – {\text{B}}\) and \({\text{A}} – {\text{B}}\) are not equal, i.e., \({\text{A}} – {\text{A}} \ne {\text{B}} – {\text{B}} \ne {\text{A}} – {\text{B}}\).

Non-ideal solutions depict characteristics as follows:

1. Non-ideal solutions do not abide by Raoult’s Law. The partial pressure of components \(\mathrm{A}\) and \(\mathrm{B}\) in a non-ideal solution will be \({{\text{P}}_{\text{A}}} \ne {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}}\) and \({{\text{P}}_{\text{B}}} \ne {{\text{X}}_{\text{B}}}{\text{P}}{^\circ _{\text{B}}}\) where \({\text{P}}{^\circ _{\text{A}}}\) and \({\text{P}}{^\circ _{\text{B}}}\) are respective vapour pressures in pure form. \({{\text{X}}_{\text{A}}}\) and \({{\text{X}}_{\text{B}}}\) are respective mole fractions of components \({\text{A}}\) and \({\text{B}}.\)
2. The solute-solute \(\left( {{\text{B}} – {\text{B}}} \right)\) and solvent-solvent \(\left( {{\text{A}} – {\text{A}}} \right)\) interactions are different from that of the solute-solvent \(\left( {{\text{A}} – {\text{B}}} \right)\) interaction.
3. The enthalpy of mixing is \({\Delta _{{\text{mix}}}}{\text{H}} \ne 0.\) This means that heat might have released if the enthalpy of mixing is negative \(\left( {{\Delta _{{\text{mix}}}}{\text{H}} < 0} \right),\) or the heat might have been absorbed if the enthalpy of mixing is positive \(\left( {{\Delta _{{\text{mix}}}}{\text{H}} > 0} \right).\)
4. The volume of mixing that is \({\Delta _{{\text{mix}}}}{\text{V}} \ne 0.\) This depicts that there will be some expansion \(\left(\Delta_{\operatorname{mix}} V>0\right)\) or contraction \(\left(\Delta_{\operatorname{mix}} V<0\right)\) on the dissolution of liquids.

Difference between ideal and non ideal solution

Non-ideal solutions can occur in two ways:

1. When the intermolecular forces of attraction between solute and solvent molecules is weaker than between similar (of the same type) molecules. This results in positive deviation from Raoult’s Law.

2. When the intermolecular forces of attraction between dissimilar molecules are greater than those between similar molecules. This results in negative deviation from Raoult’s Law.

Positive Deviation from Raoult’s Law

Positive Deviation from Raoult’s Law is observed when the vapour pressure of the components is greater than what is expected in Raoult’s Law. 

These solutions result when forces of attraction between dissimilar molecules \(\left({{\text{A}} – {\text{B}}} \right)\) are weaker than between similar molecules (\({\text{A-A}}\) or \({\text{B-B}}\)). The resulting solution has a larger enthalpy than its pure components , causing the process to be endothermic, i.e, heat is absorbed to make the reaction move forward.

Characteristics of Non-Ideal Solution Showing Positive Deviation:

In a non-ideal liquid-liquid binary solution, the vapour pressure of \({\text{A}}\) can be represented as-

\({{\text{P}}_{\text{A}}} > {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}}\)

And vapour pressure of \({\text{B}}\) can be represented as-

\({{\text{P}}_{\text{B}}} > {{\text{X}}_{\text{B}}}{\text{P}}{^\circ _{\text{B}}}\)

where \({\text{P}}{^\circ _{\text{A}}}\) and \({\text{P}}{^\circ _{\text{B}}}\) are respective vapour pressures in pure form. \({{\text{X}}_{\text{A}}}\) and \({{\text{X}}_{\text{B}}}\) are respective mole fractions of components \({\text{A}}\) and \({\text{B}}.\)

Hence, the total vapour pressure of the non-ideal solution showing positive deviation is given by-

\({\text{P}} > {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}} + {{\text{X}}_{\text{B}}}{\text{P}}{^\circ _{\text{B}}}\)

1. The solute-solvent forces of attraction are stronger than solute-solute and solvent-solvent interaction, \({\text{A}} – {\text{B}} < {\text{A}} – {\text{A}}\) or \({\text{B}} – {\text{B}}\). Due to the strong \({\text{A}} – {\text{B}}\) attraction, the escaping tendency of the \({\text{A}} – {\text{B}}\) type of molecules is less. This decreases the vapour pressure of the solution.
2. In such solutions, the enthalpy of mixing is negative, that is, \({\Delta _{{\text{mix}}}}{\text{H}} > 0\). This is because heat is released to form new molecular interaction. As there is an increase in the magnitude of the intermolecular forces of \({\text{A}} – {\text{B}}\) molecules, the volume of mixing is negative, that is, \({\Delta _{{\text{mix}}}}{\text{V}} > 0\). This is because, on the dissolution of components \({\text{A}}\) and \({\text{B}}\), the molecules of \({\text{A}} – {\text{B}}\) are held strongly to each other, resulting in the decrease of the volume.

Example:

A non-ideal solution of carbon disulphide and acetone exhibits positive deviation from Raoult’s Law. Carbon disulfide is a non-polar molecule whereas acetone is a polar molecule. As carbon disulfide is non-polar, the intermolecular forces of attraction are London dispersion forces. These forces are weak compared to other types of intermolecular forces. At the same time, acetone being polar has dipole-dipole forces, which are very strong compared to London dispersion forces.

Putting these two types of intermolecular forces together in a mixture results in dipole-induced dipole interactions. But dipole-dipole induced forces are not nearly as strong as the dipole-dipole interactions between the acetone molecules. Hence, carbon disulfide-acetone solution is a non-ideal solution showing positive deviation.

Few more example of non-ideal solutions showing positive deviation-

1. Acetone and Carbon disulphide
2. Acetone and Benzene
3. Carbon Tetrachloride and Toluene or Chloroform
4. Methyl Alcohol and Water
5. Acetone and Ethanol
6. Ethanol and Water
    

Negative Deviation from Raoult’s Law

Negative Deviation from Raoult’s Law is observed when the vapour pressure of the components is less than what is expected in Raoult’s Law. 

These solutions result when forces of attraction between dissimilar molecules \(\left( {{\text{A}} – {\text{B}}} \right)\) are stronger than between similar molecules (\({\text{A-A}}\) or \({\text{B-B}}\)). The resulting solution has less enthalpy of solution than pure components of the solution, causing the process to be exothermic (heat is released to make the reaction move forward).

Characteristics of Non-Ideal Solution Showing Negative Deviation

In a non-ideal liquid-liquid binary solution exhibiting negative deviation, the vapour pressure of \({\text{A}}\) can be represented as-

\({{\text{P}}_{\text{A}}} < {{\text{X}}_{\text{A}}} \times {\text{P}}{^\circ _{\text{A}}}\)

And vapour pressure of \({\text{B}}\) can be represented as-

\({{\text{P}}_{\text{B}}} < {{\text{X}}_{\text{B}}} \times {\text{P}}{^\circ _{\text{B}}}\)

where \({\text{P}}{^\circ _{\text{A}}}\) and \({\text{P}}{^\circ _{\text{B}}}\) are respective vapour pressures in pure form. \({{\text{X}}_{\text{A}}}\) and \({{\text{X}}_{\text{B}}}\) are respective mole fractions of components \({\text{A}}\) and \({\text{B}}\).

Hence, the total vapour pressure of the non-ideal solution showing negative deviation is given by-

\({\text{P}} < {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}} + {{\text{X}}_{\text{B}}}{\text{P}}{^\circ _{\text{B}}}\)

1. The solute-solvent forces of attraction are stronger than solute-solute and solvent-solvent interaction, \({\text{A}} – {\text{B}} > {\text{A}} – {\text{A}}\) or \({\text{A-B}}\). Due to the strong \({\text{A-B}}\) attraction, the escaping tendency of the \({\text{A-B}}\) type of molecules is less. This decreases the vapour pressure of the solution.
2. In such solutions, the enthalpy of mixing is negative, that is, \({\Delta _{{\text{mix}}}}{\text{H}} < 0.\) This is because heat is released to form new molecular interaction.
3. As there is an increase in the magnitude of the intermolecular forces of \({\text{A-B}}\) molecules, the volume of mixing is negative, that is, \({\Delta _{{\text{mix}}}}{\text{V}} < 0.\) This is because, on the dissolution of components \({\text{A}}\) and \({\text{B}}\), the molecules of \({\text{A-B}}\) are held strongly to each other, resulting in the decrease of the volume.

Example-

A non-ideal solution of chloroform and acetone exhibits negative deviation from Raoult’s Law. The molecules of acetone and chloroform bond with each other through hydrogen bonding. The formation of hydrogen bonding reduces the escaping tendency of acetone-chloroform molecules. Therefore, the vapour pressure of the solution is less than that expected for an ideal solution.

Few more examples of non-ideal solutions showing positive deviation-

1. Chloroform and Benzene
2. Chloroform and Diether
3. Acetone and Aniline
4. Nitric Acid \(\left({{\text{HN}}{{\text{O}}_3}} \right)\) and water
5. Acetic Acid and pyridine
6. Hydrochloric Acid \(\left({{\text{HCl}}} \right)\) and water

Azeotropes

Binary mixtures that have a constant composition in the liquid and vapour phase at all temperatures are called azeotropes. Azeotropes do not follow Raoult’s Law. These mixtures cannot be separated by fractional distillation. This is because the composition of the vapour phase remains the same after boiling, hence azeotropes are also known as Constant Boiling Mixtures. In these mixtures, one component has a higher or lower boiling point than the other component. 

There are two types of Azeotropes:

1. Negative Azeotrope or Maximum Boiling Azeotrope
2. Positive Azeotrope or Minimum Boiling Azeotrope

Negative Azeotrope or Maximum Boiling Azeotrope

When two non-ideal solutions mixed at some specific composition shows a large negative deviation from Raoult’s Law results in the formation of Negative Azeotrope or Maximum Boiling Azeotrope. These mixtures have a boiling point lower than the boiling point of their constituents. Negative azeotropes have the highest vapour pressure and lowest boiling point.

Examples:

1. \(68 \%\) of Nitric Acid \(\left({{\text{HN}}{{\text{O}}_3}} \right)\) and \(32 \%\) of water form maximum boiling azeotrope, with boiling temperature of \(393.5\,{\text{K}}.\)
2. \(20.24 \%\) of Hydrochloric Acid \(\left({{\text{HCl}}} \right)\) and water form maximum boiling azeotrope, with boiling temperature of \(373\,{\text{K}}.\)

Positive Azeotrope or Minimum Boiling Azeotrope

When two non-ideal solutions mixed at some specific composition shows a large negative deviation from Raoult’s Law results in the formation of Positive Azeotrope or Maximum Boiling Azeotrope. These mixtures have a boiling point higher than the boiling point of its constituents. Positive azeotropes have the lowest vapour pressure and highest boiling point.

Example:

1. \(95.5 \%\) of Ethanol and \(4.5 \%\) of water form minimum boiling azeotrope at a boiling temperature of \(351.5\,{\text{K}}.\)

Summary

In this article, we learnt the different types of solutions based on Raoult’s Law. We also learnt the types of non-ideal solution and their deviation from Raoult’s Law. We also learnt the difference between Ideal and Non-ideal solutions. In this article, we also learnt about Azeotropes and its two types, i.e., Negative Azeotrope or Maximum Boiling Azeotrope and positive Azeotrope or Minimum Boiling Azeotrope

FAQs About Non-Ideal Solutions

Let us look at some of the commonly asked questions about the topic:

Q.1: What is a non-ideal solution with examples?
Ans: The solutions that do not abide by the rules of Raoult’s Law at every concentration range and at all temperatures and deviate from it are called Non-Ideal Solutions. In these types of solutions, the intermolecular forces of attraction between \({\text{A}} – {\text{A}},\,{\text{B}} – {\text{B}}\) and \({\text{A-B}}\) are not equal, i.e., \({\text{A}} – {\text{A}} \ne {\text{B}} – {\text{B}} \ne {\text{A}} – {\text{B}}.\) Example – Acetone and carbon disulphide solution, acetone and chloroform solution.

Q.2: What is the ideal and non-ideal solution?
Ans: Ideal solutions obey Raoult’s Law at every range of concentration and at all temperatures. The intermolecular forces of attraction between \({\text{A}} – {\text{A}},\,{\text{B}} – {\text{B}}\) and \({\text{A-B}}\) are nearly equal, i.e., \({\text{A}} – {\text{A}} = {\text{B}} – {\text{B}} = {\text{A}} – {\text{B}}\). Example – Benzene and Toluene.
Non-ideal solutions do not obey Raoult’s Law at every range of concentration and at all temperatures and deviate from it. In these types of solutions, the intermolecular forces of attraction between \({\text{A}} – {\text{A}},\,{\text{B}} – {\text{B}}\) and \({\text{A-B}}\) are not equal, i.e., \({\text{A}} – {\text{A}} \ne {\text{B}} – {\text{B}} \ne {\text{A}} – {\text{B}}\). Example – Acetone and carbon disulphide.

Q.3: What are the types of non-ideal solutions?
Ans: Based on the type of solute-solvent interaction, non-ideal solutions are of two types-
1. When the intermolecular forces of attraction between solute and solvent molecules is weaker than between similar (of the same type) molecules. This results in a positive deviation from Raoult’s Law.
2. When the intermolecular forces of attraction between dissimilar molecules are greater than those between similar molecules. This results in a negative deviation from Raoult’s Law.

Q.4: What are the characteristics of a non-ideal solution?
Ans: Non-ideal solutions depict characteristics as follows:
1. Non-ideal solutions do not abide by Raoult’s Law. The partial pressure of components \({\text{A}}\) and \({\text{B}}\) in a solution will be \({{\text{P}}_{\text{A}}} \ne {{\text{X}}_{\text{A}}}{\text{P}}{^\circ _{\text{A}}}\) and \({{\text{P}}_{\text{R}}} \ne {{\text{X}}_{\text{R}}}{\text{P}}{^\circ _{\text{R}}}\) where \({\text{P}}{^\circ _{\text{A}}}\) and \({\text{P}}{^\circ _{\text{B}}}\) are respective vapour pressures in pure form. \({{\text{X}}_{\text{A}}}\) and \({{\text{X}}_{\text{B}}}\) are respective mole fractions of components \({\text{A}}\) and \({\text{B}}.\)
2. The solute-solute \(\left( {{\text{B}} – {\text{B}}} \right)\) and solvent-solvent \(\left( {{\text{A}} – {\text{A}}} \right)\) interaction is different from that of the solute-solvent \(\left( {{\text{A}} – {\text{B}}} \right)\) interaction.
3. The enthalpy of mixing is \({\Delta _{{\text{mix}}}}{\text{H}} \ne 0.\) This means that heat might have released if the enthalpy of mixing is negative \(({\Delta _{{\text{mix}}}}{\text{H}} < 0),\) or the heat might have absorbed if the enthalpy of mixing is positive \(({\Delta _{{\text{mix}}}}{\text{H}} > 0).\)
4. The volume of mixing that is \({\Delta _{{\text{mix}}}}{\text{V}} \ne 0.\) This depicts that there will be some expansion \(({\Delta _{{\text{mix}}}}{\text{V}} > 0)\) or contraction \(({\Delta _{{\text{mix}}}}{\text{V}} < 0)\) on the dissolution of liquids.

Q.5: What type of liquid form a non-ideal solution?
Ans: Solutions in which the intermolecular forces of attraction between \({\text{A}} – {\text{A}},\,{\text{B}} – {\text{B}}\) and \({\text{A-B}}\) are not equal, i.e, \({\text{A}} – {\text{A}} \ne {\text{B}} – {\text{B}} \ne {\text{A}} – {\text{B}}\) form non-ideal solutions. Example – Acetone and carbon disulphide.

Q.6: What makes a solution non-ideal?
Ans: A solution is non-ideal if its solute-solvent interaction is not equal to the solute-solute or solvent-solvent interaction.

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