The Ideal Solution and Roult's Law

As we know, the concept of ideal gas has been used to study a lot of thermodynamic properties, now it would be helpful to determine the similar type of concept in the case of Solutions.

What is an Ideal Solution?

In physical chemistry, an ideal solution is a solution in which the interactions between the solvent and the solute particles are the same as the interactions between the solvent-solvent and solute-solute particles.

This means that the solution exhibits ideal behavior, such as obeying Rouult's law and having a constant boiling point and a linear relationship between composition and vapor pressure.

An ideal solution can be thought of as a theoretical construct, since most real solutions do not behave ideally due to non-ideal interactions between the solute and solvent molecules.

Ideal solutions are important in the study of physical chemistry because they serve as a reference point for understanding the behavior of real solutions.

By comparing the behavior of a real solution to that of an ideal solution, scientists can gain insight into the nature of the intermolecular interactions between the solute and solvent molecules.

Let suppose, we have an Ideal Solution of two components, A and B, then the cohesive forces between A and A, B and B and A and B, will be be equal.

Characteristics of an Ideal Solution:

• An Ideal solution obeys Raoult's law and Henry's law. In an ideal solution, the vapor pressure of each component is directly proportional to its mole fraction in the solution.

• In an ideal solution, the boiling point of the solution remains constant throughout the distillation process.

• Ideal solutions have an entropy of mixing of zero. When two substances are mixed to form an ideal solution, the change in entropy (ΔS) is zero.

• Ideal solutions have a linear relationship between composition and vapor pressure.In an ideal solution, the vapor pressure of each component is directly proportional to its mole fraction in the solution, resulting in a linear relationship between composition and vapor pressure.

• Ideal solutions have no heat of mixing.

When two substances are mixed to form an ideal solution, the heat of mixing (ΔH) is zero.

• Ideal solutions have no volume change upon mixing. When two substances are mixed to form an ideal solution, the volume of the resulting solution is the same as the sum of the volumes of the individual components(∆V=0).

• In an ideal solution, the interactions between solute-solvent and solvent-solvent molecules are identical. This means that the solute molecules dissolve in the solvent without any change in intermolecular forces.

Examples of Ideal Solutions:

Here are some of the important examples of Ideal Solutions:

• Benzene and Toluene

• n-heptane and n-hexane

• Ether and Benzene

• Propyl Bromide and Ethyl Bromide

What is Roult's Law?

Roult's law was proposed by French chemist Francois-Marie Raoult in 1882.

Raoult was studying the behavior of solutions, particularly the vapor pressure of solutions containing volatile solutes.

He observed that when a volatile solute is dissolved in a liquid solvent, the vapor pressure of the solution is lower than that of the pure solvent.

Roult's Law: Defination

Raoult's Law states that the partial vapor pressure of a component in an ideal solution is equal to the product of the mole fraction of that component in the solution and the vapor pressure of the pure component.

An ideal Solution can obey Roult's law over a wide range of temperature.

This law is important in the study of colligative properties of solutions, such as boiling point elevation and freezing point depression, which depend on the concentration of solute particles in solution.

Derivation:

To derive the the equation of Roult's law, we consider a solution consisting of benzene A and toluene B, with mole fractions Xᴀ and Xʙ, respectively. The vapor pressure of pure benzene and toluene are P°ᴀ and P°ʙ, respectively.

According to Raoult's law, the partial vapor pressure of benzene in the solution, Pᴀ, can be calculated as follows:

Pᴀ = Xᴀ . P°ᴀ

Similarly, the partial vapor pressure of toluene in the solution, Pʙ, can be calculated as:

Pʙ = Xʙ . P°ʙ

The total vapor pressure of the solution, P(total), is the sum of the partial vapor pressures of benzene and toluene:

P(total) = Pᴀ + Pʙ

= P°ᴀ . Xᴀ + P°ʙ . Xʙ

Since Xᴀ+Xʙ=1

Then. Xᴀ = 1- Xʙ

By putting the value of Xᴀ in above given equation,

P(total) = P°ᴀ .(1-Xʙ) -- P°ʙ.Xʙ

This last equation represents the relationship between vapour pressure and composition of that hypothetical solution.

Raoult's law assumes that the interactions between the molecules in the solution are identical to those in the pure components. Nonetheless, Raoult's law is a useful approximation for dilute solutions of non-polar solutes in non-polar solvents.

Graphical Representation :

As we know,the the values of P°ᴀ and P°ʙ are constant at same temperature, this is clear from the equation that the total pressure is the linear function of mole fractions like Xᴀ or Xʙ .

Thus if a graph is plotted between mole fractions on x-axis and vapour pressures on y-axis then a straight line is obtained as shown in that figure given below.👇

In this figure, the full length be gives total pressure - mole fraction and dotted lines refer to the partial pressure versus composition.

This dotted line passes through the origin which indicates that both components are behaving ideally.

When Xᴀ =1 and Xʙ = 0 i.e., Solution contains only B then

P = P°ᴀ.Xᴀ + P°ʙ.Xʙ

Since the values of Xᴀ=0 and Xʙ=1

Therefore,

P = P°(0) + P°ʙ.(1)

P = Pʙ

Similarly,when Xᴀ=1 and Xʙ=0 then

P = P°ᴀ.Xᴀ + P°ʙ.Xʙ

P = P°ᴀ.(1) + P°ʙ.(0)

P = P°ᴀ

At any concentration, the total pressure is the sum of the partial pressures of those two components at constant temperature.

Commercial Importance:

Ideal solutions and Roult's law have significant commercial importance in various industries, including chemical, pharmaceutical, and food.

An ideal solution is a mixture of two or more substances that behaves like a single substance in terms of physical properties such as vapor pressure, boiling point, and freezing point. This property is essential in the chemical industry for designing and manufacturing products that require specific physical properties. For example, the manufacture of automotive antifreeze requires a mixture of ethylene glycol and water, which is an ideal solution that can resist freezing at low temperatures.

Roult's law is crucial in the pharmaceutical industry for the development of drugs and their dosage forms. It helps in predicting the behavior of drug molecules in various formulations and their efficacy in the body.

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In the food industry, ideal solutions and Roult's law are used to design and produce food products with desirable physical properties.

For example, the creation of low-calorie sweeteners requires the mixing of two or more substances to produce an ideal solution that can mimic the sweetness of sugar without adding calories. The properties of the solution are determined by Roult's law, which allows manufacturers to optimize the formulation and produce a product with consistent properties.

Frequently Asked Questions-FAQs

1. What is Ideal Solution?

An ideal solution is a solution in which the interactions between the solvent and the solute particles are the same as the interactions between the solvent-solvent and solute-solute particles.For example, an ideal solution of Benzene and Toluene etc.

2. What are three examples of Ideal Solution?

Below are three main examples of some ideal solutions.

• Benzene and Toluene

• n-heptane and n-hexane

• Ether and Benzene

The Ideal Solution | Roult's Law - Explanation and Derivation

The Ideal Solution and Roult's Law

What is an Ideal Solution?