Problem 136 - A Complete Resource Book in Chemistry for JEE Main

Question

The colligative properties of electrolytes require a slightly different approach than the one used for the colligative properties of non- electrolytes. The electrolytes dissociate into ions in solution. It is the number of solute particles that determine the colligative properties of a solution. The electrolyte solutions, therefore show abnormal colligative properties. To account for this effect we define a quantity; called the van't Hoff factor which is given by [solution] \(i=\) \(\frac{\text { Actual number of particles in solution after dissociation }}{\text { Number of formula units initally dissolved in solution }}\) \(\mathrm{i}=1\) (for non - electrolytes); \(\mathrm{i}>1\) (for electrolytes, undergoing dissociation) \(\mathrm{i}<1\) (for solute, undergoing association) For a solution of a non electrolyte in water, the van't Hoff factor is (a) Always equal to 2 (b) Always equal to 0 (c) \(>1\) but \(<2\) (d) \(\leq 1\)

Step-by-Step Solution

Answer

For a non-electrolyte, the van't Hoff factor \( i \) is always equal to 1, thus option (d) \( \leq 1 \) is correct.

Step 1: Understanding Van't Hoff Factor

The van't Hoff factor, denoted as \( i \), is crucial in determining the colligative properties of solutions. It accounts for the dissociation or association of solute particles in a solution. Non-electrolytes do not dissociate into ions once dissolved in a solution, hence their van't Hoff factor is \( i = 1 \).

Step 2: Non-Electrolyte Characteristics

Non-electrolytes, when dissolved in a solvent like water, do not split into ions or form additional particles. This means the number of particles before and after dissolution remains constant.

Step 3: Evaluating the Options

Considering the nature of non-electrolytes, the van’t Hoff factor should reflect that the number of particles remains unchanged, thus \( i \) is equal to 1.

Step 4: Selecting the Correct Answer

Since the van't Hoff factor for non-electrolytes is always \( i = 1 \), it cannot be 2, 0, or any value greater than 1 but less than 2. Therefore, the correct choice given the options is (d) \( \leq 1 \).

Key Concepts

Colligative Properties

Colligative properties are intriguing because they depend solely on the number of solute particles present in a solution, rather than the identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. When a solute is added to a solvent, these properties change in predictable ways, primarily due to the disruption of the solvent’s natural chemical environment.
Colligative properties are especially important when dealing with solutions because they help us understand how solutes, whether electrolytes or non-electrolytes, influence things like the boiling and freezing points of a solvent. For example, adding salt to ice can change the freezing point of water, a common practice in de-icing. The key takeaway is that it's the number of particles, not what they are composed of, that truly matters.

• Boiling Point Elevation: The temperature at which the liquid's vapor pressure equals the atmospheric pressure rises when more solute particles are introduced.
• Freezing Point Depression: The freezing point of the solution is lower than that of the pure solvent, crucial for phenomena like antifreeze working in car engines.
• Vapor Pressure Lowering: With solute particles present, there are fewer solvent molecules escaping into vapor, reducing vapor pressure.
• Osmotic Pressure: Pressure required to prevent water from diffusing through a semipermeable membrane separating two solutions of different solute concentration.

Electrolytes and Non-Electrolytes

Understanding the difference between electrolytes and non-electrolytes is vital when studying colligative properties. Electrolytes are substances that dissociate into ions when dissolved in water, creating solutions that can conduct electricity. On the other hand, non-electrolytes dissolve but do not form ions, thus they do not conduct electricity.
Electrolytes are further classified based on how completely they dissociate:

• Strong Electrolytes: Completely dissociate into ions, like sodium chloride or hydrochloric acid.
• Weak Electrolytes: Partially dissociate, such as acetic acid.

For non-electrolytes, the van't Hoff factor (\( i = 1 \) describes that there is no change in the particle count upon dissolution.
By breaking into more particles, electrolytes can significantly alter colligative properties because their dissociation increases the number of particles in the solution. For example, a strong electrolyte like sodium chloride, when dissolved, doubles the number of particles, because each unit produces two ions: Na\(^+\) and Cl\(^-\).

Dissociation and Association in Solutions

In the chemistry of solutions, dissociation and association are two key processes that affect colligative properties. Dissociation refers to the process where molecules or compounds break down into simpler constituents, typically ions. This is common in electrolyte solutions, where a compound like NaCl dissociates into Na\(^+\) and Cl\(^-\) ions. The degree of dissociation can greatly affect the solution's properties.
Association, on the other hand, is less common than dissociation. It occurs when particles adhere together to form larger aggregates, which reduces the number of particles in the solution. This usually reduces colligative properties.
Understanding these processes is critical for predicting how a solution will behave when solutes are added. When electrolytes dissolve and dissociate into more ions, the solution can exhibit greater changes in its colligative properties because of the increase in particles. Conversely, if the process of association were to happen, such as when molecules pair up, the number of effective particles would decrease, causing a different impact on colligative properties.

• Dissociation: Increases the number of particles, leading to a stronger impact on properties like boiling and freezing points.
• Association: Decreases the number of effective particles, which might reduce the expected effects on these properties.