Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following solutions will exhibit highest boiling point? (a) \(0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) (b) \(0.01 \mathrm{M} \mathrm{KNO}_{3}\) (aq) (c) \(0.015 \mathrm{M}\) urea (aq) (d) \(0.015 \mathrm{M}\) glucose (aq)

Step-by-Step Solution

Answer

The solution with \( 0.01 \mathrm{M} \mathrm{Na}_2\mathrm{SO}_4 \) exhibits the highest boiling point.

Step 1: Understanding Boiling Point Elevation

The boiling point of a solution is higher than that of the pure solvent. The increase in boiling point is directly proportional to the molal concentration of the solute particles in the solution based on 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 dissociates into), \( k_b \) is the ebullioscopic constant, and \( m \) is the molality of the solution.

Step 2: Determining the Van 't Hoff Factor

Calculate the van 't Hoff factor \( i \) for each solute: - For \( \mathrm{Na}_2\mathrm{SO}_4 \), \( i = 3 \) (Na\(^+\) ions + SO\( _4^{2-} \) ion)- For \( \mathrm{KNO}_3 \), \( i = 2 \) (K\( ^+ \) ion + NO\( _3^- \) ion)- For urea and glucose (nonelectrolytes), \( i = 1 \).

Step 3: Calculating Effective Concentration

The effective concentration of solute particles in molarity is the product of molarity and van 't Hoff factor for each solution:- \( \mathrm{Na}_2\mathrm{SO}_4 \): \( 0.01 \times 3 = 0.03 \)- \( \mathrm{KNO}_3 \): \( 0.01 \times 2 = 0.02 \)- Urea: \( 0.015 \times 1 = 0.015 \)- Glucose: \( 0.015 \times 1 = 0.015 \).

Step 4: Comparing Effective Concentrations

Compare the effective concentrations calculated for each solution. The highest effective concentration indicates the highest boiling point:- \( \mathrm{Na}_2\mathrm{SO}_4 \): \( 0.03 \)- \( \mathrm{KNO}_3 \): \( 0.02 \)- Urea: \( 0.015 \)- Glucose: \( 0.015 \).The solution with \( 0.03 \) is the highest.

Key Concepts

van 't Hoff Factor Explained

When a solute dissolves in a solvent, it can dissociate into multiple particles. The van 't Hoff factor (\( i \)) represents the number of particles into which a single solute molecule dissociates. It plays a crucial role in determining how much the boiling point of a solution will increase.

Here's how it works:

• For nonelectrolytes like urea and glucose, which don't dissociate in solution, \( i = 1 \).
• For electrolytes like \( \text{Na}_2\text{SO}_4 \), the compound dissociates into three ions in water: two sodium ions (\( \text{Na}^+ \)) and one sulfate ion (\( \text{SO}_4^{2-} \)). Therefore, \( i = 3 \).
• Similarly, \( \text{KNO}_3 \) dissociates into two ions, potassium ion (\( \text{K}^+ \)) and nitrate ion (\( \text{NO}_3^- \)), hence \( i = 2 \).

By applying the van 't Hoff factor in calculations, we can effectively determine how many particles a solute will contribute to a solution, which directly impacts colligative properties like boiling point elevation.

Understanding Molal Concentration

Molal concentration, also known as molality (\( m \)), is a way to express the concentration of a solution. Unlike molarity, which is dependent on volume, molality is defined as the number of moles of solute per kilogram of solvent.

Molality is particularly useful in calculations involving colligative properties because it doesn't change with temperature. Here's why it's significant:

• It allows for accurate determination of how much a non-volatile solute will raise the boiling point of a solution, independent of temperature fluctuations.
• Using molality can simplify the mathematics involved in calculating changes in boiling point and freezing point.

When applying the formula for boiling point elevation (\( \Delta T_b = i \cdot k_b \cdot m \)), the molal concentration (\( m \)) acts as a key factor in quantifying the effect of the solute on the boiling point. This makes understanding molality essential for dealing with colligative properties.

Exploring Colligative Properties

Colligative properties are physical properties of solutions that depend on the concentration of solute particles, rather than the identity of the solute molecules or ions.

Boiling point elevation is one such property. Let's explore why these properties are so important:

• These properties include not just boiling point elevation, but also freezing point depression, vapor pressure lowering, and osmotic pressure.
• In boiling point elevation, adding a solute to a solvent increases the boiling temperature because more energy is needed for the liquid to change into vapor.

Colligative properties highlight the collective effect of the number of solute particles in a solution. This means they are directly tied to factors like the van 't Hoff factor and molal concentration, both of which are critical in accurately predicting how a solution behaves when a solute is introduced. Understanding these properties provides insight into the natural tendency of solutions to stabilize by diluting the effects of solutes, causing changes in properties like boiling and freezing points.