Problem 140 - A Complete Resource Book in Chemistry for JEE Main

Question

The values of colligative properties of colloidal solution are of small order in comparison to those shown by true solutions of same concentration because of colloidal particles (a) Remain suspended in the dispersion medium (b) Form lyophilic colloids (c) Are comparatively less in number (d) Exhibit enormous surface area

Step-by-Step Solution

Answer

The correct answer is (c) because colloidal particles are fewer in number than particles in true solutions.

Step 1: Understanding Colligative Properties

Colligative properties, such as boiling point elevation and freezing point depression, depend on the number of particles in a solution. These properties apply to both true solutions and colloidal solutions.

Step 2: Characteristics of True Solutions

In a true solution, the solute particles are small and numerous, which means that they significantly affect colligative properties due to their high number.

Step 3: Characteristics of Colloidal Solutions

Colloidal solutions contain particles larger than those in true solutions. However, these particles are less numerous compared to solute particles in a true solution of the same concentration.

Step 4: Comparing Number of Particles

Because colligative properties are dependent on the total number of solute particles, colloidal solutions have smaller values for these properties compared to true solutions. This is primarily because the number of colloidal particles is lower, despite their larger size.

Step 5: Identifying the Correct Option

From the options given, (c) 'Are comparatively less in number' accurately explains why colligative properties of colloidal solutions are of smaller order compared to those of true solutions.

Key Concepts

Colloidal Solutions

Colloidal solutions are mixtures where tiny particles of one substance are dispersed throughout another, without dissolving entirely. These particles are larger than those found in true solutions and are typically in the range of 1 nm to 1000 nm. Because of their size, these particles remain suspended without settling out, thanks to constant collisions with molecules of the dispersion medium. This characteristic leads to unique behaviors and properties.
Examples of colloidal solutions include milk, jelly, and smoke. Despite appearing homogenous to the naked eye, under a microscope, the particles within a colloid are quite distinct.
In colloidal solutions, the particles have a large surface area relative to their volume. This gives them some special properties like the Tyndall effect, where light is scattered by the particles in the colloid, making a beam of light visible in the medium. Colloidal solutions do not settle on standing and they cannot be separated by ordinary filtration due to the size of their dispersed particles.

True Solutions

True solutions are homogeneous mixtures at a molecular or ionic level. Here, the solute completely dissolves in the solvent, forming a uniform composition. The particles in a true solution are typically no larger than 1 nm in diameter, which is incredibly small compared to those in colloidal solutions.
Due to the small size and the large number of particles, true solutions have a high degree of stability and do not scatter light. This means they do not exhibit the Tyndall effect. Notable examples include sugar in water or salt in water, where the solute is entirely dissolved and the solution appears clear and uniform.
True solutions are characterized by their ability to pass through ordinary filter paper without leaving any residue. The nature of true solutions allows them to significantly impact colligative properties.

Number of Particles

The number of particles in a solution is crucial in determining its colligative properties. These properties are dependent not on the nature of the dissolved particles, but on their quantity. Therefore, solutions with a greater number of solute particles, like true solutions, will have pronounced colligative properties.
For example, when a solute like salt is dissolved in water, it dissociates into ions, effectively increasing the number of particles in the solution. This dissociation isn't typically seen in colloidal solutions, where the solute particles remain intact and less abundant.
The impact of a solution’s number of particles is evident in phenomena like boiling point elevation and freezing point depression, which rely on disrupting the solvent's normal boiling or freezing process by introducing additional particles.

Boiling Point Elevation

Boiling point elevation is a colligative property where the boiling point of a solvent is increased by adding a non-volatile solute. This occurs because the added particles disrupt the formation of bubbles within the liquid, requiring more energy (heat) for the solvent to change into the gas phase.
The effect depends on the number of dissolved particles, not their size or chemical identity. Therefore, a true solution with many well-dissolved particles will exhibit a notable boiling point elevation compared to a colloidal solution.
To quantify this effect, we use the formula: \[ \Delta T_b = i \cdot K_b \cdot m \]Where:

• \( \Delta T_b \) is the boiling point elevation.
• \( i \) is the van 't Hoff factor (number of particles the solute forms).
• \( K_b \) is the ebullioscopic constant.
• \( m \) is the molality of the solution.

Freezing Point Depression

Freezing point depression is another key colligative property. It describes the process where the freezing point of a liquid (pure solvent) decreases when a solute is added. This occurs because the solute particles interfere with the formation of a solid crystalline structure, requiring the removal of more thermal energy to transition the liquid into a solid.
The degree of this depression correlates directly with the number of particles in the solution, making it more pronounced in true solutions where more numerous solute particles are present than in colloidal ones.
The formula to calculate freezing point depression is:\[ \Delta T_f = i \cdot K_f \cdot m \]Where:

• \( \Delta T_f \) is the freezing point depression.
• \( i \) is the van 't Hoff factor (indicating the number of particles created).
• \( K_f \) is the cryoscopic constant.
• \( m \) is the molality of the solution.