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Raoult’s Law was proposed by the famous French chemist Francois Marie Raoult in 1887. During an experiment, the chemist found that when substances are mixed in a solution, the vapour pressure of that solution is simultaneously decreased. From this observation, Raoult explained the relationship between partial pressure and mole fractions of two different components. 

The law has great importance in physical chemistry, and it is viewed as the law of thermodynamics. Let’s look at an in-depth study of Raoult’s Law as well as its importance and limitations. 

Raoult’s Law 

According to Raoult’s law, the solvent’s partial vapour pressure in a mixture is always equal to the vapour pressure of the pure solvent, multiplied by its mole fraction in that solution. In simple terms, the vapour pressure of a solution depends on the mole fraction of the solute dissolved into the solution. That means when a substance is added to a solution, the vapour pressure of the solution will ultimately decrease. 

It depends on two variables : 

  • The present mole fraction of the amount of added solute. 
  • The original vapour pressure of the pure solvent. 

Raoult’s Law Formula 

Mathematically, the law is written as

nt1

It is to be noted that when more than one solute is dissolved in the solution, each solvent’s component is added to the total pressure of the solution. 

Explanation of Raoult’s Law 

For a volatile solute

Suppose there are one solvent and two different types of solutes in a solution. Then, both components are volatile in nature. 

So, here, Solvent = Component 1

               Solute2 = Component 2

               Solute3 = Component 3 

For each component, the partial pressure will be

          P¹ = P1⁰x¹ 

          P² = P2⁰x²                    (P⁰ – vapour pressure of pure component)   

          P³ = P3⁰ x³ 

So, according to Dalton’s law of partial pressure, the total vapour pressure of the solution will be                  

          (PT = P1 + P2 + P3)  

Let’s see how Raoult’s law works in a binary solution. 

There are two components, A and B 

So, partial pressure will be 

PA = P⁰A • xA 

PB = P⁰B • xB

So, PT = PA + PB

          = P⁰A xA + P⁰B xB 

As we all know that the mole fraction = (xA + xB = 1)

Hence,  P⁰A (1- xB) + P⁰B xB 

  • Therefore, at a given temperature in a volatile solution, the partial vapour pressure of each component is always equal to the multiplication of the vapour pressure of the pure component and its mole fraction.         

For a non-volatile solute     

Here, P⁰B = 0   

Here, B means solute.

0 represents no vapour pressure.   

So, PT = P⁰A xA + P⁰B xB 

PT = P⁰A xA + 0 

Thus, PT = PA   

  • Hence, by adding a non-volatile solute, the vapour pressure of a solution is always equal to the vapour pressure of the pure solvent and multiplied by its mole fraction at a given temperature.

Deviations from Raoult’s Law 

If there are adhesive or cohesive forces present in between two components, then deviations from this law can be worked. The deviations are of two types.

Negative Deviation 

It occurs in a non-ideal solution when the vapour pressure is lower than that what is anticipated by the law. This implies negative deviation. It happens when the forces between molecules are stronger than the molecules in pure liquids. 

For example: Solution of chloroform and acetone, solution of water and hydrochloric acid, etc. In both of these cases, hydrogen bonds create deviations. 

Positive Deviation

It occurs when in a non-ideal solution, the vapour pressure is greater than what is predicted by the law. It happens when the molecular forces of two components (A-B) are weaker than the A-A or B-B interaction forces. Consequently, it is easier for molecule A to escape as compared to a pure solution. 

For example: Solution of ethanol and acetone, solution of chloroform and ethanol, etc are considered as positive deviations. 

Raoult’s Law’s Relationship with Other Laws 

The relationship between Raoult’s Law with other important laws is as follows: 

  • In physical chemistry, Raoult’s law is quite identical to the ideal gas law. However, the difference is that the former is applicable to solutions only. The ideal gas law is applicable to show the ideal behaviour of gases, and here, the intermolecular forces which are present in between the dissimilar substance molecules are zero. On the other hand, in Raoult’s law, the intermolecular forces prevailing between the similar as well as the different molecules are always equal. 
  • Raoult’s law can also be applicable to non-ideal solutions. However, this is done by considering the molecular interactions between different substances. 
  • By containing ideal liquid and ideal vapour in an ideal system, we can get a very useful equation by combining Raoult’s law and Dalton’s law. 

X¹ = Y¹ Ptotal / P⁰1 

Here, 

X¹ = mole fraction of component 1 in the solution 

Y¹ =  mole fraction in the vapour phase 

What we get from the equation is that in an ideal solution containing pure components, each and every substance will have a different vapour pressure. Moreover, in the gas phase, the substances will have a higher vapour pressure but the solution will have a lower vapour pressure.  

  • Raoult’s law is considered to be a special case of Henry’s Law.
nt2

Raoult’s Law’s Association with Colligative Properties 

Raoult’s Law and the colligative properties are discussed below. 

  • The effect of this law is observed in lowering the vapour pressure. When a non-volatile substance is dissolved into a volatile solvent, the vapour pressure of the end product becomes lower than that of the pure solvent. 
  • Adding a non-volatile solute to a pure solvent actually lowers the vapour pressure of the solution, and consequently, the heat is supplied to the solution to bring the vapour pressure up to the atmospheric pressure so that the pure solvent supplies the boiling point advancement.
  • When we add a non-volatile solute to a pure solvent, it results in the lowering of the vapour pressure of the solution. As a consequence, a depression in the freezing point of the solution occurs as compared to its solvent. 

Limitations of Raoult’s Law 

There are certain limitations to Raoult’s law. They are as follows:

  • The law is applicable to ideal solutions only. This is because the forces of attraction between the solvent molecules are exactly the same as those between the solvent and solute in a solution which implies that in an ideal solution, it takes the same proportion of energy for solvent molecules to escape from the surface of the solution. 
  • The nature of a solution is another important thing. It is noteworthy that the law only works for those solutes which do not change their characteristics when they dissolve. The solutes must not create ions or associates. The main concern is not the number of moles of the component in the solution but the number of moles in the component formed. 
  • The law works well in extremely dilute or in less concentrated solutions. 
  • Sometimes in the case of attractive forces, many of the components in the solution do not have the same consistency. These types of solutions refrain from following Raoult’s law properly. 

Conclusion 

Raoult’s law plays a pivotal role in determining the nature as well as the properties of a solution. It has great implications in thermodynamics also. It measures the intermolecular strength of liquids, and by adding non-volatile solutes, it lowers the vapour pressure of the solution. Through this article, we have learned the important points regarding Raoult’s law. We have also discussed how this law works with the colligative properties of a solution.