Question

Consider the following aqueous solutions. I. 2.2 g Glucose in 125 mL of solution. II. 1.9 g Calcium chloride in 250 mL of solution. III. 9.0 g Urea in 500 mL of solution. IV. 20.5 g Aluminium sulphate in 750 mL of solution. The correct increasing order of boiling point of these solutions will be: [Given: Molar mass in g mol\(^{-1}\): H = 1, C = 12, N = 14, O = 16, Cl = 35.5, Ca = 40, Al = 27 and S = 32]

• A. I<III<IV<II
• B. III<I<II<IV
• C. I<II<III<IV
• D. III<II<I<IV

Hint:

For colligative properties: - Always calculate effective molality using van’t Hoff factor \(i\). - Strong electrolytes dissociate into multiple ions, increasing particle count and effect.

Answer 1

The Correct Option is B

To determine the correct increasing order of the boiling points of the given solutions, we need to understand the concept of boiling point elevation, a colligative property that depends on the number of solute particles in a solution.

The boiling point elevation can be calculated using the formula:

\(\Delta T_b = i \cdot K_b \cdot m\)

where:

• \(\Delta T_b\) = boiling point elevation
• \(i\) = Van't Hoff factor (number of particles the solute dissociates into)
• \(K_b\) = ebullioscopic constant (depends on the solvent, here water is the solvent)
• \(m\) = molality of the solution

Let's calculate the molality and Van't Hoff factor for each solution:

Solution I: Glucose

- Molar mass of glucose (C₆H₁₂O₆) = 180 g/mol

- Number of moles = \(\frac{2.2\ \text{g}}{180\ \text{g/mol}} = 0.0122\ \text{mol}\)

- Volume of solution = 125 mL = 0.125 L

- Molality \(m = \frac{0.0122\ \text{mol}}{0.125\ \text{kg}} = 0.0976\ \text{mol/kg}\)

- Van't Hoff factor \(i = 1\) (no dissociation)

Solution II: Calcium chloride (CaCl₂)

- Molar mass of CaCl₂ = 40 + 2 \times 35.5 = 111 g/mol

- Number of moles = \(\frac{1.9\ \text{g}}{111\ \text{g/mol}} = 0.0171\ \text{mol}\)

- Volume of solution = 250 mL = 0.25 L

- Molality \(m = \frac{0.0171\ \text{mol}}{0.25\ \text{kg}} = 0.0684\ \text{mol/kg}\)

- Van't Hoff factor \(i = 3\) (dissociates into 1 Ca²⁺ and 2 Cl^-)

Solution III: Urea

- Molar mass of urea (NH₂CONH₂) = 60 g/mol

- Number of moles = \(\frac{9\ \text{g}}{60\ \text{g/mol}} = 0.15\ \text{mol}\)

- Volume of solution = 500 mL = 0.5 L

- Molality \(m = \frac{0.15\ \text{mol}}{0.5\ \text{kg}} = 0.3\ \text{mol/kg}\)

- Van't Hoff factor \(i = 1\) (urea does not dissociate)

Solution IV: Aluminium sulphate (Al₂(SO₄)₃)

- Molar mass of Al₂(SO₄)₃ = 2(27) + 3(32 + 4(16)) = 342 g/mol

- Number of moles = \(\frac{20.5\ \text{g}}{342\ \text{g/mol}} = 0.0599\ \text{mol}\)

- Volume of solution = 750 mL = 0.75 L

- Molality \(m = \frac{0.0599\ \text{mol}}{0.75\ \text{kg}} = 0.0799\ \text{mol/kg}\)

- Van't Hoff factor \(i = 5\) (dissociates into 2 Al³⁺ and 3 SO₄^2-)

Now, calculate the relative boiling point elevation (since \(K_b\) is the same for all aqueous solutions, it can be ignored for the order):

• Solution I: \(\Delta T_b = 1 \times 0.0976 = 0.0976\)
• Solution II: \(\Delta T_b = 3 \times 0.0684 = 0.2052\)
• Solution III: \(\Delta T_b = 1 \times 0.3 = 0.3\)
• Solution IV: \(\Delta T_b = 5 \times 0.0799 = 0.3995\)

Thus, the increasing order of boiling point elevation (i.e., boiling points) is III < I < II < IV.