Problem 62 - A Complete Resource Book in Chemistry for JEE Main

Question

The rise in the boiling point of a solution containing \(1.8 \mathrm{~g}\) of glucose in \(100 \mathrm{~g}\) of solvent is \(0.1^{\circ} \mathrm{C}\). The molal elevation constant of the liquid is (a) \(1 \mathrm{~K} / \mathrm{m}\) (b) \(0.1 \mathrm{~K} / \mathrm{m}\) (c) \(0.01 \mathrm{~K} / \mathrm{m}\) (d) \(10 \mathrm{~K} / \mathrm{m}\)

Step-by-Step Solution

Answer

The correct answer is (a) \(1 \mathrm{~K/m}\).

Step 1: Understand the Problem

We need to determine the molal elevation constant, given the rise in boiling point when a certain mass of glucose is dissolved in a solvent. We are given the mass of glucose, the mass of solvent, and the rise in boiling point.

Step 2: Apply the Formula for Boiling Point Elevation

The formula for boiling point elevation is \(\Delta T = K_b \cdot m\), where \(\Delta T\) is the change in boiling point, \(K_b\) is the molal elevation constant, and \(m\) is the molality of the solution.

Step 3: Calculate Moles of Solute

The molar mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol. The number of moles of glucose is given by \( \frac{1.8\, \text{g}}{180\, \text{g/mol}} = 0.01\, \text{moles}\).

Step 4: Calculate Molality of the Solution

Molality \(m\) is calculated as moles of solute per kilogram of solvent. The mass of the solvent is 100 g, which is 0.1 kg. Thus, \( m = \frac{0.01\, \text{moles}}{0.1\, \text{kg}} = 0.1\, m\).

Step 5: Solve for the Molal Elevation Constant

We know \(\Delta T = 0.1\, ^\circ C\) and \( m = 0.1\, m\). Substituting in \(\Delta T = K_b \cdot m\), we get \(0.1 = K_b \cdot 0.1\). Solving for \(K_b\), we find \(K_b = 1\, \text{K/m}\).

Key Concepts

Molality

Molality is a measure of the concentration of a solution. It is focused on the amount of solute dissolved in a given mass of solvent. Unlike molarity, which uses volume, molality is defined as the number of moles of solute per kilogram of solvent. This makes it particularly useful in situations where the temperature and pressure may change, such as boiling point elevation. To calculate the molality of a solution, you need to know two things:

• The number of moles of the solute
• The mass of the solvent in kilograms

Knowing these, you can use the formula:\[m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]This measure ensures consistency even when environmental conditions fluctuate, making it ideal for studying solution properties like boiling point elevation.

Molal Elevation Constant

The molal elevation constant, often denoted as \(K_b\), is a unique property of each solvent. It describes how much the boiling point of a solution increases for a molal concentration of solute. The elevation in boiling point, \(\Delta T\), is calculated using the formula:\[\Delta T = K_b \cdot m\]where \(m\) is the molality of the solution. This constant is essential for calculating the change in boiling point when a solute is added, and it depends on the solvent's own characteristics. For example:

• Each solvent has its own value of \(K_b\), which is determined experimentally.
• In the given problem, knowing the molal elevation constant allows us to find how much the presence of glucose raises the boiling point of the solution.

Understanding \(K_b\) means understanding how solutions behave when solutes are added, which is critical for applications in solution chemistry.

Solution Chemistry

Solution chemistry is the study of different substances and how they interact when mixed to form a solution. A solution consists of a solute (substance to be dissolved) and a solvent (substance in which the solute dissolves). The interactions between solute and solvent molecules are what define the properties of the solution, like boiling point elevation. Key aspects include:

• Solubility: The ability of a solute to dissolve in a solvent.
• Concentration: The amount of solute present in a given quantity of solvent or solution, represented by molality, molarity, and other units.
• Colligative Properties: These include boiling point elevation and depend on the number of solute particles rather than their identity.

In practical terms, understanding how these factors work together allows chemists to predict and manipulate the behavior of solutions in various conditions, such as in industrial processes and biological systems.