Raoult’s Law

Raoult’s Law in chemistry relates partial pressures of volatile liquid components to their mole fractions in a liquid solution. It states that the partial pressure of each component in the solution is directly proportional to its mole fraction. Thus, it helps us to calculate the total vapour pressure of the solution. Based on Raoult’s law, liquid solutions are classified as Ideal Solutions and Non-Ideal Solutions.

In this article, we will discuss the definition of Raoult’s law, ideal and non-ideal solutions, Raoult’s law for non-volatile solutes and some solved numerical problems based on Raoult’s law.

Raoult’s Law Definition

Raoult’s law states that,

For a liquid solution having volatile components, the partial vapour pressure of a component is directly propotional to its mole fraction in the solution.

For example, consider a solution having two volatile components 1 and 2, then by Raoult’s law, partial pressure of 1 is written as,

p₁ = p₁⁰x₁ and p₂ = p₂⁰x₂

where,

• p₁ is Partial Pressure of Component 1
• p₂ is Partial Pressure of Component 2
• p₁⁰ is Vapour Pressure of Component 1 in Pure Form
• p₂⁰ is Vapour Pressure of Component 2 in pure form
• x₁ is Mole Fraction of Component 1 in Solution
• x₂ is Mole Fraction of Component 2 in Solution

Now, according to Dalton’s law of partial pressures which states the total vapour pressure of a solution is the sum of partial pressures of its constituents. Thus,

p_{Total =} p₁⁰x₁ + p₂⁰x₂

where,

• p_Total is Total Vapour Pressure of Solution

Thus, we can determine the total vapour pressure of a liquid solution using Raoult’s law and Dalton’s law of partial pressures.

Raoult’s Law Formula

Raoult’s law equation mathematically is written as:

P_solution = Χ_solventP⁰_solvent

where,

• P_solution is Vapour pressure of Solution
• Χ_solvent is Mole Fraction of Solvent
• P⁰_solvent is Vapour Pressure of Pure Solvent

Classification of Solutions based on Raoult’s law

Liquid Solutions are classified into two types on the basis of whether they obey the Raoult’s law or not. The classification is discussed as follows:

Ideal Solutions

Solutions which obey Raoult’s law irrespective of concentration in which the components are mixed are known as ideal solutions. There are two more properties followed by ideal solutions, i.e. there is no change in the enthaply or volume before and after mixing of solution components.

An ideal solution results from mixing of such components which have similar intermolecular and intramolecular forces of attraction. This can be understood by taking example of A and B as components of a solution. The solution would be ideal if A-A and B-B interactions are similar to those of A-B. Perfectly ideal solutions are rare.

Examples of some nearly ideal solutions include solutions of:

• Benzene and Toluene
• n-hexane and n-heptane
• bromoethane and chloroethane

Non Ideal Solutions

Solutions which don’t obey Raoult’s law for entire range of concentration are known as non-ideal solutions. These solutions show positive or negative deviation from the Raoult’s law depending upon whether the actual vapour pressure of the solution higher or lower than that determined by Raoult’s law.

These deviations occur due to intramolecular interactions of components being weaker or stronger than their intermolecular interactions. There are a variety of non-ideal solutions.

Some examples of non-ideal solutions include solutions of:

• Ethanol and Acetone
• Chloroform and Acetone
• Phenol and Aniline

Raoult’s law for Non-Volatile Solutes

For solutions having non volatile solutes, vapour pressure is only due to the solvent as non volatile solutes do not exert any pressure. Thus, Raoult’s law for non volatile solutes is defined as

Vapour pressure of the solution is directly propotional to the mole fraction of the solvent.

Mathematically,

p_Total ∝ x_s

p_Total = p_s⁰x_s

where,

• p_Total is Total Vapour Pressure of Solution
• p_s⁰ is Vapour Pressure of Solvent in Pure Form
• x_s is Mole Fraction of Solvent

Raoult’s Law with Other Laws

Raoult’s law can be related to various other laws to deduce some important relations.

• Dalton’s law of partial pressures states that the total vapour pressure of a solution is sum of the partial pressures of its components and Raoult’s law gives a way to calculate partial pressure of a component of the solution. Thus, Raoult’s law alongwith Dalton’s law of partial pressures can be used to find the total vapour pressure of a solution.

• Raoult’s law is closely related to the Ideal Gas law which states that different gaseous particles do not exert any force on each other. And for ideal solutions, Raoult’s law assumes that the intermolecular forces between the involved particles are same before mixing and after mixing to form the solution.

• Raoult’s law can also be seen as an extension of Henry’s law. According to Henry’s law, concentration of a gas dissolved in a liquid is directly proportional to its partial pressure in the solution and According to Raoult’s law, partial pressure of a component in the solution is directly proportional to its mole fraction. Thus, the two laws are correlated.

Significance of Raoult’s Law

Importance of Raoult’s law can be expressed in terms of following points:

• Raoult’s law helps us to calculate the total vapour pressure of a solution which means the pressure exerted by the vapours on the liquid solvent when they are in equilibrium.

• Raoult’s law is also used to determine vapour pressure of the solution in case of non volatile solutes.
• If partial pressures of components of a solution are known, we can determine the composition of the solution using Raoult’s law.

• Raoult’s law is also used to determine some of the colligative properties of the solution, i.e. the properties which depend on the concentration of solute particles in the solution such as elevation in boiling point, depression in freezing point, etc.

• Raoult’s law can also be applied to ideal gas mixtures.

Limitations of Raoult’s law

Although there are many useful applications of Raoult’s law, it has some limitations discussed as follows:

• Raoult’s law is applicable to ideal solutions only but majority of solutions are non ideal in nature, thus we may not get an accurate estimate for vapour pressure of non ideal solutions by using Raoult’s law only.

• Raoult’s law assumes that the vapour pressure of solution remains unchanged with temperature but for various substances vapour pressure changes with temperature. So, Raoult’s law may not give accurate results for the cases where temperature changes significantly.

Read More,

• Colligative Properties
• Ideal and Non-Ideal Solutions
• Vapour Pressure

Raoult’s Law Examples

Some examples of Raoult’s Law are,

Example 1: 2 moles of P are mixed with 4 moles of Q to form a liquid solution, determine the total vapour pressure of the solution given that vapour pressures of P and Q in pure form are 70 torr and 40 torr respectively.

Solution:

Here, mole fraction of P, x_p = 2/(2+4) = 1/3 and mole fraction of Q, x_q = 4/(2+4) = 2/3

According to Raoult’s law,

p_Total = p₁⁰x₁ + p₂⁰x₂

p_Total = 70×(1/3) + 40×(2/3)

p_Total = 50

Thus, total vapour pressure of the solution is 50 torr as determined by Raoult’s law.

Example 2: Determine the vapor pressure of a solution containing 600 g of n-heptane and 288 g of n-pentane at 25^oC. The vapor pressure of n-heptane and n-pentane are 46 mm Hg and 512 mm Hg respectively.

Solution:

We know that,

Molecular weight of n-heptane = 100 g

No. of Moles of n-heptane in the solution = 600/100 = 6

Molecular weight of n-pentane = 72

No. of moles of n-pentane in the solution = 288/72 = 4

Now,

Mole Fraction of n-heptane = 6/(6+4) = 6/10 = 0.6

Mole Fraction of n-pentane = 4/(6+4) = 4/10 = 0.4

As solution of n-pentane and n-heptane forms a nearly ideal solution, using Raoult’s Law here,

According to Raoult’s law,

p_Total = p₁⁰x₁ + p₂⁰x₂

p_Total = 0.6×46 + 0.4×1400

p_Total = 587.6 mm Hg

Thus, total vapour pressure of the solution is obtained as 587.6 mm Hg using Raoult’s law.

Raoult’s Law Frequently Asked Questions

What is Raoult’s Law?

Raoult’s law states that partial pressure of a component in a liquid solution is directly propotional to its mole fraction in the solution.

What is Partial Pressure of a Component?

Partial pressure of a component is the pressure which would be exerted by it if only that component is present in the solution’s volume at same temperature.

Do All Solutions Follow Raoult’s Law?

No, only ideal solutions obey Raoult’s law for which enthalpy change and volume change is zero before and after mixing. The vapour pressure of such solutions can be directly determined by Raoult’s law.

What does a Positive Deviation from Raoult’s Law imply?

A positive deviation from Raoult’s law means that vapour pressure of the solution will be higher than that determined by using Raoult’s law. This is due to intramolecular forces between molecules in solution being weaker than the intermolecular forces of the components.

What does a Negative Deviation from Raoult’s Law Imply?

A negative deviation from Raoult’s law means that vapour pressure of the solution will be lower than that determined by using Raoult’s law. This is due to intramolecular forces between molecules in solution being stronger than the intermolecular forces of the components.

Is Raoult’s Law Applicable to Gaseous Mixtures?

Raoult’s law is applied to determine vapour pressure of liquid solution, it may be used for some gaseous mixtures such as ideal gases.

What is Raoult’s Law and Henry’s Law?

• According to Henry’s Law solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

• According to Rault’s Law partial vapor pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.