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

Concept: Boiling point elevation depends on the colligative property: \[ \Delta T_b = i \cdot K_b \cdot m \] where \(i\) = van’t Hoff factor (number of particles), \(m\) = molality.
Step 1: Calculate molality for each solution. - \(\mathbf{I: Glucose}\) (non-electrolyte, \(i=1\)) \[ M(\ce{C6H12O6}) = 180 \,\text{g mol}^{-1}, \quad n = \frac{2.2}{180} \approx 0.0122 \,\text{mol} \] \[ m = \frac{0.0122}{0.125} \approx 0.0976 \,\text{mol L}^{-1} \] - \(\mathbf{II: CaCl2}\) (\(i=3\), dissociates into \(\ce{Ca^{2+}}\) + 2\(\ce{Cl^-}\)) \[ M(\ce{CaCl2}) = 40 + 71 = 111 \,\text{g mol}^{-1}, \quad n = \frac{1.9}{111} \approx 0.0171 \,\text{mol} \] \[ m = \frac{0.0171}{0.25} = 0.0684 \,\text{mol L}^{-1} \] Effective molality = \(i \cdot m = 3 \times 0.0684 = 0.205\). - \(\mathbf{III: Urea}\) (non-electrolyte, \(i=1\)) \[ M(\ce{CH4N2O}) = 60 \,\text{g mol}^{-1}, \quad n = \frac{9}{60} = 0.15 \,\text{mol} \] \[ m = \frac{0.15}{0.5} = 0.30 \,\text{mol L}^{-1} \] - \(\mathbf{IV: Al2(SO4)3}\) (\(i=5\), dissociates into 2\(\ce{Al^{3+}}\) + 3\(\ce{SO4^{2-}}\)) \[ M(\ce{Al2(SO4)3}) = 2(27) + 3(32 + 64) = 342 \,\text{g mol}^{-1} \] \[ n = \frac{20.5}{342} \approx 0.0599 \,\text{mol} \] \[ m = \frac{0.0599}{0.75} \approx 0.0799 \,\text{mol L}^{-1} \] Effective molality = \(i \cdot m = 5 \times 0.0799 = 0.399\).
Step 2: Compare effective molalities. \[ \text{I: } 0.0976, \quad \text{II: } 0.205, \quad \text{III: } 0.30, \quad \text{IV: } 0.399 \]
Step 3: Increasing order of boiling point. \[ \text{III (0.30)<I (0.0976)<II (0.205)<IV (0.399)} \] Thus, the correct order is: \[ \text{III<I<II<IV} \]