*According to Raoult’s Law, for a solution of volatile liquids, the partial vapor pressure of each component (volatile) of the solution is proportional to the mole fraction of that component present in the solution.*

## Understanding Raoult’s law?

The study of colligative properties has been one of the most advanced subjects of research in physical chemistry. The properties of solutions such as partial pressure and vapor pressure and their subsequent variation due to varying parameters have been a pivotal point for the developments in this field. Raoult’s Law gives us a quantitative relation between the partial vapor pressure of components present in vapor solution phase above a liquid solution and the mole fraction of that component in the solution. Raoult’s Law is defined as a solution that has one or more volatile liquids in it.

Let us try to understand what exactly Francois Marie Raoult wanted to describe through his statement given as Raoult’s Law. As for now suppose we have a liquid binary solution consisting of a solvent 1 and a volatile solute 2. Note that this law is defined only for volatile components of a solution. Let Ptotal be the total vapor pressure of the two components and P1 and P2 be the partial vapor pressures of component 1 and component 2 respectively, and the mole fraction of component 1 and 2 be x1 and x2 in the solution phase and y1 and y2 in the vapor phase respectively.

### Raoult’s law Equation

So, for component 1:

**P _{1 }**

**α**

**x**

_{1}**P _{1 }= P_{1}^{o }x_{1}**,……………………………. (1)

Where P_{1}^{o} is the vapor pressure of component 1 in a pure state.

Similarly for component 2:

**P _{2 }= P_{2 }^{o }x_{2, }**…………………………….. (2)

From Dalton’s Law of partial pressures we know that,

**P _{total }= P_{1}+P_{2}**

Using the values of P_{1} and P_{2} from equation (1) and (2) respectively we have:

**P _{total }= P_{1}^{o}x_{1} + P_{2}^{o}x_{2}**

=>** P _{total }= P_{1}^{o}(1-x_{2}) + P_{2}^{o}x_{2}**

=>** P _{total }= P_{1}^{o} + (P_{2}^{o}-P_{1}^{o})x_{2}**

We can draw following inferences from the above equation:

- The above equation is a straight line between
**P**and_{total}**x**whose slope is given by_{2}**(P**and the y-intercept is equal to_{2}^{o}-P_{1}^{o})**P**._{1}^{o} - The total vapor pressure above a solution varies linearly with the mole fraction of component 2.
- The total vapor pressure above a solution depends on the vapor pressure of Component 1 and 2 in their pure state and the mole fraction of component 2 in the solution.

### Limitations of Raoult’s Law

The above-discussed topic finds application in many industries, but developments in science and technology have rendered even **Raoult’s Law** some limitations.

- It is applicable only to ideal liquid solutions.
- The results obtained for some complex, concentrated solutions that have significant intermolecular forces varying considerably from the law.

Nevertheless, the law applies to most ideal solutions and has been a base for further studies in this field.

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