Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

A solution is obtained by dissolving \(6 \mathrm{~g}\) of urea (mol. wt \(=60\) ) in a litre solution, another solution is prepared by dissolving \(34.2 \mathrm{~g}\) of cane sugar (mol. \(\mathrm{wt}=342\) ) in a litre of solution at the same temperature The lowering of vapour pressure in the first solution is (a) same as that of second solution (b) double that of second solution (c) half that of second solution (d) nearly one fifth of the second solution

Step-by-Step Solution

Answer

(a) same as that of second solution

Step 1: Understand the concept

The lowering of vapor pressure of a solution is a colligative property, which depends on the number of solute particles in the solution. To compare the lowering of vapor pressure between two solutions, we need to compare their molar concentrations.

Step 2: Calculate the number of moles of urea

Urea has a molecular weight of 60 g/mol. The number of moles of urea in the solution is calculated using the formula: \( \text{moles of urea} = \frac{\text{mass of urea}}{\text{molecular weight of urea}} = \frac{6 \, \text{g}}{60 \, \text{g/mol}} = 0.1 \, \text{moles} \).

Step 3: Calculate the number of moles of cane sugar

Cane sugar has a molecular weight of 342 g/mol. The number of moles of cane sugar in the solution is calculated using the formula: \( \text{moles of cane sugar} = \frac{\text{mass of cane sugar}}{\text{molecular weight of cane sugar}} = \frac{34.2 \, \text{g}}{342 \, \text{g/mol}} = 0.1 \, \text{moles} \).

Step 4: Compare lowering of vapor pressure

Both solutions have the same number of moles of solute (0.1 moles). Since the lowering of vapor pressure depends on the moles of solute, both solutions will have the same lowering of vapor pressure.

Key Concepts

Vapor Pressure Lowering

Vapor pressure lowering is an important concept in chemistry and a key colligative property. It occurs when a solute is dissolved in a solvent, thereby reducing the number of solvent molecules at the surface. This reduction in surface molecules leads to a decrease in the rate of evaporation of the solvent. As a result, the equilibrium vapor pressure above the liquid decreases.

This concept is crucial for understanding solutions because it is not determined by the type of solute, but by the quantity of solute particles present. Thus, it is directly related to solute concentration rather than the specific properties of the solute itself. This makes vapor pressure lowering a unique area of study in solutions, focusing on particle count rather than chemistry specifics.

Molar Concentration

Molar concentration describes the amount of a solute in a given volume of solution, usually expressed in moles per liter (mol/L). It is also known as molarity. Calculating molarity involves determining the number of moles of a solute and the volume of the solution.

Consider the solutions mentioned in the exercise: both urea and cane sugar solutions were prepared with different masses of solutes, yet their molar concentrations turned out to be the same. This is because the number of moles is also dependent on the molecular weight of each solute. Dividing the mass of the solute by its molar mass yields the number of moles, which then determines the molarity in a set volume of solution. Equal molar concentrations of different solutes result in the same colligative effects when dissolved in solvents.

Colligative Property Calculations

Colligative properties are properties of solutions that depend on the concentration of solute particles rather than their identity. Key colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

• To calculate colligative properties, one must first determine the number of solute particles in the solution through molarity.
• For vapor pressure lowering, the comparison focuses on how many solute particles disrupt the solvent molecules at the liquid's surface.

In our example, both solutions were calculated to have the same solute concentration because they have the same number of moles (0.1 moles). Thus, the colligative property, i.e., lowering of vapor pressure, was found to be the same for both solutions.

Molecules in Solution

Understanding molecules in solution is foundational for grasping why colligative properties occur. When substances dissolve, the solute molecules or ions spread throughout the solvent, often separating into individual particles. The solute particles interfere with the solvent molecules, affecting various properties of the solution.

• In the exercise, urea and cane sugar dissolve in water, dispersing evenly among the water molecules.
• This dispersion affects how the water molecules are distributed at the surface, impacting evaporation rates and vapor pressure.

Bringing it back to colligative properties, it’s the number of these dispersed particles that determines the extent of effects like vapor pressure lowering. The nature of the particles – whether molecule or ion – is less significant than the sheer count when evaluating colligative properties.