Problem 58 - A Complete Resource Book in Chemistry for JEE Main

Question

The elevation in boiling point for \(13.44 \mathrm{~g}\) of \(\mathrm{CuCl}_{2}\) dissolved in \(1 \mathrm{~kg}\) of water as solvent will be \(\left(\mathrm{K}_{\mathrm{b}}=0.52 \mathrm{~kg} / \mathrm{J}\right.\), molar mass of \(\left.\mathrm{CuCl}_{2}=134.4 \mathrm{~g} / \mathrm{mol}\right)\) (a) \(0.05\) (b) \(0.10\) (c) \(0.16\) (d) \(0.20\).

Step-by-Step Solution

Answer

The boiling point elevation is approximately 0.16; therefore, the correct option is (c).

Step 1: Calculate Moles of Solute

First, determine the number of moles of \( \text{CuCl}_2 \). Use the formula: \[ \text{moles} = \frac{\text{mass of solute}}{\text{molar mass of solute}} \] Substitute the given values: \[ \text{moles of CuCl}_2 = \frac{13.44 \text{ g}}{134.4 \text{ g/mol}} \approx 0.1 \text{ mol} \]

Step 2: Determine van't Hoff Factor

\( \text{CuCl}_2 \) dissociates into 3 ions (1 Cu\(^{2+}\) and 2 Cl\(^{-}\)). Thus, the van't Hoff factor, \( i \), is 3.

Step 3: Use Boiling Point Elevation Formula

The boiling point elevation \( \Delta T_b \) is calculated using the formula: \[ \Delta T_b = i \times K_b \times m \] where \( m \) is the molality of the solution.

Step 4: Calculate Molality

Molality \( m \) is calculated as the moles of solute per kilogram of solvent: \[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{0.1}{1} = 0.1 \text{ mol/kg} \]

Step 5: Calculate the Boiling Point Elevation

Substitute the values into the boiling point elevation formula: \[ \Delta T_b = 3 \times 0.52 \times 0.1 = 0.156 \]

Step 6: Determine Correct Option

The calculated boiling point elevation is approximately \(0.16\). So, the correct answer is option (c), \(0.16\).

Key Concepts

van't Hoff Factor

The **van't Hoff factor** is a concept that helps us understand how solutes affect various colligative properties, such as boiling point elevation, by accounting for the degree of dissociation of a substance in solution. When a solute dissolves in a solvent, it may break apart or dissociate into multiple particles or ions. This splitting increases the number of solute particles in the solution, thus enhancing the effect on the boiling point elevation.
To determine the van't Hoff factor, you simply count the total number of particles the solute forms after dissociation. For example, in the case of \(\text{CuCl}_2\), when it dissolves in water, it dissociates into one \(\text{Cu}^{2+}\) ion and two \(\text{Cl}^{-}\) ions. So, the van't Hoff factor \(i\) for \(\text{CuCl}_2\) becomes 3 as you add up the number of each type of ion formed.

• The formula to determine the van't Hoff factor is given as:\[i = \text{number of particles after dissociation} \]
• A key function of the van't Hoff factor is to adjust the colligative properties calculation, such as boiling point elevation.

Understanding and correctly determining the van't Hoff factor is crucial because it directly influences the magnitude of the boiling point elevation.

Molality

**Molality** is a measure of the concentration of a solute in a solution, typically used when temperature changes are involved. Unlike molarity, which depends on the volume of the solution, molality focuses on the mass of the solvent, making it temperature-independent.
Molality \(m\) is defined as the number of moles of solute per kilogram of solvent. This measurement provides a consistent way to express concentration, regardless of temperature shifts that might affect volume. In the boiling point elevation problem, molality is used to determine how the solute affects the solution's boiling point.

• To calculate molality, use the equation:\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
• For the \(\text{CuCl}_2\) solution, we've identified 0.1 moles of solute dissolved in 1 kg of water, giving a molality of 0.1 mol/kg.

Molality is especially useful for boiling point elevation calculations because it remains constant regardless of temperature changes, ensuring accurate and dependable results.

Moles Calculation

The **calculation of moles** is a fundamental concept in chemistry that helps us determine the amount of a substance in a given mass. To accurately calculate the moles of a solute like\(\text{CuCl}_2\), you need to know both its mass and its molar mass.
The equation used for finding the number of moles is:\[ \text{moles} = \frac{\text{mass of solute}}{\text{molar mass of solute}} \]
In this exercise, you have 13.44 g of \(\text{CuCl}_2\) with a molar mass of 134.4 g/mol.

• Plug the values into the moles formula:\[ \text{moles of CuCl}_2 = \frac{13.44 \text{ g}}{134.4 \text{ g/mol}} \approx 0.1 \text{ mol} \]
• This calculation reveals that you have approximately 0.1 moles of \(\text{CuCl}_2\).

Having the correct number of moles is essential for proceeding with further calculations, such as determining the solution's molality and subsequently applying it to find the boiling point elevation.