Question

Solution-1 : \(2.025\,\text{g}\) glucose, \(125\,\text{mL}\)
Solution-2 : \(9\,\text{g}\) urea, \(500\,\text{mL}\)
Solution-3 : \(1.9\,\text{g}\) CaCl$_2$, \(250\,\text{mL}\)
Solution-4 : \(20.5\,\text{g}\) Al$_2$(SO$_4$)$_3$, \(750\,\text{mL}\)
[2mm] Order of \(\Delta T_b\) is:

• A. Al$_2$(SO$_4$)$_3$ > Urea > CaCl$_2$ > Glucose
• B. Al$_2$(SO$_4$)$_3$ > CaCl$_2$ > Urea > Glucose
• C. Glucose > Al$_2$(SO$_4$)$_3$ > CaCl$_2$ > Urea
• D. CaCl$_2$ > Urea > Glucose > Al$_2$(SO$_4$)$_3$

Hint:

For colligative properties, always compare \(\boldsymbol{i \times m}\). Electrolytes dominate due to higher van’t Hoff factor.

Answer 1

The Correct Option is A

Concept:
Elevation in boiling point is a colligative property and is given by: \[ \Delta T_b = i K_b m \] where \(i\) = van’t Hoff factor, \(m\) = molality of the solution. Thus, \(\Delta T_b \propto i \times m\).
Step 1: Calculate Molality of Each Solution
(1) Glucose (non-electrolyte, \(i=1\))
Moles of glucose: \[ \frac{2.025}{180} = 0.01125\,\text{mol} \] Mass of solvent: \[ 125\,\text{mL} \approx 0.125\,\text{kg} \] \[ m = \frac{0.01125}{0.125} = 0.09 \] \[ i \times m = 0.09 \] (2) Urea (non-electrolyte, \(i=1\))
Moles of urea: \[ \frac{9}{60} = 0.15\,\text{mol} \] Mass of solvent: \[ 500\,\text{mL} = 0.5\,\text{kg} \] \[ m = \frac{0.15}{0.5} = 0.30 \] \[ i \times m = 0.30 \] (3) CaCl$_2$ (strong electrolyte, \(i=3\))
Moles of CaCl$_2$: \[ \frac{1.9}{111} \approx 0.0171\,\text{mol} \] Mass of solvent: \[ 250\,\text{mL} = 0.25\,\text{kg} \] \[ m = \frac{0.0171}{0.25} \approx 0.0684 \] \[ i \times m \approx 3 \times 0.0684 = 0.205 \] (4) Al$_2$(SO$_4$)$_3$ (strong electrolyte, \(i=5\))
Moles of Al$_2$(SO$_4$)$_3$: \[ \frac{20.5}{342} \approx 0.06\,\text{mol} \] Mass of solvent: \[ 750\,\text{mL} = 0.75\,\text{kg} \] \[ m = \frac{0.06}{0.75} = 0.08 \] \[ i \times m = 5 \times 0.08 = 0.40 \]
Step 2: Compare \(i \times m\)
\[ \text{Al}_2(\text{SO}_4)_3\ (0.40)>\text{Urea}\ (0.30)>\text{CaCl}_2\ (0.205)>\text{Glucose}\ (0.09) \]
Final Conclusion:
\[ \boxed{\text{Al}_2(\text{SO}_4)_3>\text{Urea}>\text{CaCl}_2>\text{Glucose}} \]