Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

When non-zero volatile solute is dissolved in a solvent, the relative lowering of vapour pressure is equal to (a) molar fraction of solute (b) molar fraction of solvent (c) concentration of the solute in grams per liter (d) concentration of the solute in gram per \(100 \mathrm{~mL}\).

Step-by-Step Solution

Answer

The relative lowering of vapor pressure is equal to the mole fraction of the solute (option a).

Step 1: Understanding the Concept

The relative lowering of vapor pressure in a solution is defined as the decrease in the vapor pressure of the solvent due to the presence of a non-volatile solute. This concept is based on Raoult's Law for non-volatile solutes.

Step 2: Statement of Raoult's Law

According to Raoult's Law, the relative lowering of vapor pressure is given by the equation: \( \frac{P^0 - P}{P^0} = x_2 \), where \( P^0 \) is the vapor pressure of the pure solvent, \( P \) is the vapor pressure of the solution, and \( x_2 \) is the mole fraction of the solute.

Step 3: Interpreting the Equation

From the equation \( \frac{P^0 - P}{P^0} = x_2 \), we see that the relative lowering of vapor pressure \( \frac{P^0 - P}{P^0} \) is directly equal to the mole fraction of the solute \( x_2 \).

Step 4: Evaluating the Options

The problem lists four options, and by the statement of Raoult's Law, the correct answer is the mole fraction of the solute, which is option (a).

Key Concepts

Relative Lowering of Vapor Pressure

The term 'relative lowering of vapor pressure' describes a phenomenon observed when a non-volatile solute is added to a solvent. This causes the vapor pressure of the solvent to decrease. Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form. When a solute is added, it occupies space at the surface of the liquid, reducing the number of solvent molecules that can escape into the vapor phase.
The decrease in vapor pressure due to the solute is expressed as the relative lowering of vapor pressure. This is calculated using the equation: \( \frac{P^0 - P}{P^0} \), where \( P^0 \) is the vapor pressure of the pure solvent and \( P \) is the vapor pressure of the solution. The relative lowering of vapor pressure is an important concept as it helps in understanding how various factors affect the boiling and freezing points of solutions.

Mole Fraction of Solute

The mole fraction of the solute in a solution is a way of expressing its concentration. It indicates the ratio of the number of moles of a solute to the total number of moles in the solution. Mathematically, it is expressed as:

• \( x_2 = \frac{{n_2}}{{n_1 + n_2}} \)

where \( x_2 \) is the mole fraction of the solute, \( n_2 \) is the number of moles of solute, and \( n_1 \) is the number of moles of solvent.
Understanding mole fractions helps determine how much of a solute is present compared to everything else in the solution. In relation to Raoult's Law, the relative lowering of vapor pressure is directly proportional to the mole fraction of the solute, described by the equation \( \frac{P^0 - P}{P^0} = x_2 \). This proportionality means that as more solute is added, the vapor pressure decreases further.

Non-Volatile Solute

In solutions, a non-volatile solute is one that does not readily evaporate into the vapor phase. As a result, when such a solute is added to a solvent, the vapor pressure of the solvent decreases significantly. This happens because non-volatile solutes typically do not contribute to the vapor above the solution since they have very low or negligible vapor pressures themselves.
Non-volatile solutes are crucial for applications where modification of boiling and freezing points are needed; for instance, in antifreeze solutions and culinary applications. By understanding how non-volatile solutes affect vapor pressure through Raoult's Law, scientists and engineers can predict other properties of solutions. The presence of non-volatile solutes is a key factor in the mathematical relation: \( \frac{P^0 - P}{P^0} = x_2 \), illustrating their effect on the vapor pressure lowering of a solvent.