Raoult’s Law

1.0What is Raoult’s Law?

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

Mathematically, Raoult’s law is expressed as:

$P_{s}olution=X_{s}olvent\ast P{°}_{s}olvent$

Where:

• $P_{s}olution$ = Vapor pressure of the solution
• $X_{s}olvent$ = Mole fraction of the solvent
• $P{°}_{s}olvent$ = Vapor pressure of the pure solvent

2.0Principle of Raoult’s Law

Consider a solution of two  volatile liquids A and B in a container. Because both A and B are volatile, their particles exist in the vapor phase, contributing to the total pressure above the solution. Raoult’s law states that at equilibrium:

$P_A=x_A\ast P{°}_A{P}_B=x_B\ast P{°}_B$

Where:

• $P_A,P_B$ = Partial pressures of A and B
• $P{°}_A,P{°}_B$ = Vapor pressures of pure A and B at a given temperature
• $x_A,x_B$ = Mole fractions of A and B in the liquid phase

Thus, the total pressure of the solution is given by:

$P_{t}otal=P_A+P_B$

3.0Importance of Raoult’s Law

1. Understanding Vapor Pressure:

A closed container with a volatile liquid (A) reaches an equilibrium where the vapor particles exert pressure (vapor pressure).

Adding a solute (B) reduces the number of solvent (A) particles on the surface, thereby decreasing the vapor pressure of A.

If B is volatile, its vapor phase particles will also be lower than its pure state.

2. Relationship with Mole Fraction:

As the mole fraction of a component decreases, its partial pressure in the vapor phase also decreases.

Graphical Representation

Raoult’s law can be represented graphically, illustrating the relationship between vapor pressure and the mole fraction of components A and B. When plotted, the total vapor pressure exhibits a linear dependence on the mole fraction.

4.0Relationship with Other Laws

Raoult’s law is similar to the Ideal Gas Law, with the primary difference being that Raoult’s law applies to solutions. While the ideal gas law assumes no intermolecular forces, Raoult’s law assumes that the intermolecular forces between different and similar molecules are equal.

When combined with Dalton’s Law, Raoult’s law helps derive:

$y_i=(x_i\ast P{°}_i)/P_{t}otal$

Where:

• $x_i$ = Mole fraction of component i in the solution
• $y_i$ = Mole fraction in the gas phase

This equation indicates that components with higher pure vapor pressure dominate the gas phase in an ideal solution.

5.0Limitations of Raoult’s Law

1. Ideal Solutions Assumption: Raoult’s law is best suited for perfect solutions, which are rare because most solutions do not have uniform intermolecular forces.
2. Deviations from Raoult’s Law:

• Negative Deviation: Occurs when the vapor pressure is lower than expected. Example: Chloroform and Acetone, Water and HCl
• Positive Deviation: Occurs when cohesive forces are stronger than adhesive forces, leading to higher vapor pressure. Example: Benzene and Methanol, Ethanol and Chloroform