Problem 10 - A Complete Resource Book in Chemistry for JEE Main

Question

According to Raoult's law, relative lowering of vapour pressure for a solution is equal to (a) mole fraction of the solute (b) mole fraction of a solvent (c) moles of a solute (d) moles of a solvent

Step-by-Step Solution

Answer

(a) mole fraction of the solute

Step 1: Understanding Raoult's Law

Raoult's Law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of solvent present in the solution.

Step 2: Relative Lowering of Vapor Pressure Formula

The relative lowering of vapor pressure is given by the formula: \( \frac{{P^0_A - P_A}}{{P^0_A}} = X_B \), where \(P^0_A\) is the vapor pressure of pure solvent, \(P_A\) is the vapor pressure of the solution, and \(X_B\) is the mole fraction of the solute.

Step 3: Identifying the Correct Option

According to the formula, the relative lowering of vapor pressure (\( \frac{{P^0_A - P_A}}{{P^0_A}} \)) is equal to \(X_B\), the mole fraction of the solute. Thus, the correct answer is option (a).

Key Concepts

Relative Lowering of Vapor Pressure

In the simple scenario of mixing substances, Raoult's Law plays a significant role in understanding how vapor pressures behave in solutions. When a solute is dissolved in a solvent, the vapor pressure of the solvent above the solution is less than the vapor pressure of the pure solvent. This is what we describe as the relative lowering of vapor pressure.

It is shown mathematically as \( \frac{P^0_A - P_A}{P^0_A} \), where \( P^0_A \) is the vapor pressure of the pure solvent and \( P_A \) is that of the solution. This difference is due to the presence of solute particles which occupy space on the liquid's surface, thereby reducing the number of solvent molecules that can escape into vapor phase.

The key takeaway is that this relative lowering is actually equal to the mole fraction of the solute in an ideal solution. Thus, more solute means a greater effect on lowering the vapor pressure.

Mole Fraction of Solute

To comprehend solutions and their behaviors, it's crucial to grasp the idea of the mole fraction. It is simply the ratio of moles of solute to the total moles in the solution. For instance, if we have a solution, the mole fraction of the solute can be derived as:

• Calculate the number of moles of solute.
• Calculate the total number of moles (i.e., moles of solute plus moles of solvent).
• The mole fraction of solute \( X_B \) is therefore \( \frac{\text{moles of solute}}{\text{total moles in solution}} \).

This fraction is a dimensionless quantity and plays a pivotal role in phenomena like vapor pressure lowering. For ideal solutions, which closely follow Raoult's Law, the relationship between vapor pressure and mole fractions becomes straightforward. Here, the relative lowering of vapor pressure equals the mole fraction of the solute, simplifying calculations.

Ideal Solution

When studying Raoult’s Law, it's beneficial to understand what constitutes an ideal solution. An ideal solution adheres closely to Raoult's Law, meaning the interactions between the molecules of the solute and solvent are similar to those in the pure substances.

In essence, these solutions show no change in enthalpy when mixed, and they also present linear relationships between vapor pressure and mole fractions.

Here's what characterizes an ideal solution:

• Energy remains consistent: There is no heat absorbed or evolved during mixing.
• Compatible molecules: Solute-solvent interactions are very similar to solute-solute and solvent-solvent interactions.
• Perfect adherence: The solution's vapor pressure behavior aligns perfectly with Raoult's Law, implying the calculated properties reflect actual behaviors efficiently.

Understanding ideal solutions helps us simplify many complex chemical calculations and properly predict the behavior of solutions in a controlled environment.