Question

For different aqueous solution of 0.1 M NaCl, 0.1 M urea, 0.1 M $Na_3PO_4$ and 0.1 M $Na_2SO_4$ solution at 27°C, the correct statement is:

• A. The order of osmotic pressure is, urea > NaCl > $Na_2SO_4$ > $Na_3PO_4$
• B. The order of vapour pressure is, $Na_3PO_4$ > $Na_2SO_4$ > NaCl > urea
• C. The order of boiling point is, urea > NaCl > $Na_2SO_4$ > $Na_3PO_4$
• D. The order of freezing point is, urea > NaCl > $Na_2SO_4$ > $Na_3PO_4$

Answer 1

Answer: (D)

The order of freezing point is, urea > NaCl > $Na_2SO_4$ > $Na_3PO_4$

Answer 2

The problem requires comparing colligative properties (osmotic pressure, vapour pressure, boiling point, and freezing point) for different aqueous solutions of the same molar concentration (0.1 M). Colligative properties depend on the number of solute particles in the solution, which is quantified by the van't Hoff factor ($i$). Assuming complete dissociation for strong electrolytes:

1. Urea (CO(NH₂)₂): Non-electrolyte, $i = 1$.
2. NaCl: Strong electrolyte, dissociates into Na⁺ and Cl⁻. So, $i = 2$.
3. Na₂SO₄: Strong electrolyte, dissociates into 2Na⁺ and SO₄²⁻. So, $i = 3$.
4. Na₃PO₄: Strong electrolyte, dissociates into 3Na⁺ and PO₄³⁻. So, $i = 4$.

The order of van't Hoff factors is: $i_{\text{Urea}} (1) < i_{\text{NaCl}} (2) < i_{\text{Na₂SO₄}} (3) < i_{\text{Na₃PO₄}} (4)$

Now, let's analyze each colligative property:

• Osmotic Pressure ($\pi$): $\pi = iCRT$. Osmotic pressure is directly proportional to $i$. Therefore, the order of osmotic pressure is: Urea < NaCl < Na₂SO₄ < Na₃PO₄. The given option states: urea > NaCl > Na₂SO₄ > Na₃PO₄. This is incorrect.

• Vapour Pressure ($P_s$): Vapour pressure lowering ($\Delta P$) is directly proportional to $i$. $\Delta P = P_0 - P_s$. A higher $i$ leads to a greater lowering of vapour pressure, and thus a lower vapour pressure of the solution ($P_s$). So, $P_s$ is inversely proportional to $i$. Therefore, the order of vapour pressure is: Na₃PO₄ < Na₂SO₄ < NaCl < Urea. The given option states: Na₃PO₄ > Na₂SO₄ > NaCl > urea. This is incorrect.

• Boiling Point ($T_b$): Elevation in boiling point ($\Delta T_b$) is directly proportional to $i$. $\Delta T_b = iK_bm$. A higher $i$ leads to a greater elevation in boiling point, and thus a higher boiling point of the solution ($T_b = T_b^0 + \Delta T_b$). So, $T_b$ is directly proportional to $i$. Therefore, the order of boiling point is: Urea < NaCl < Na₂SO₄ < Na₃PO₄. The given option states: urea > NaCl > Na₂SO₄ > Na₃PO₄. This is incorrect.

• Freezing Point ($T_f$): Depression in freezing point ($\Delta T_f$) is directly proportional to $i$. $\Delta T_f = iK_fm$. A higher $i$ leads to a greater depression in freezing point, and thus a lower freezing point of the solution ($T_f = T_f^0 - \Delta T_f$). So, $T_f$ is inversely proportional to $i$. Therefore, the order of freezing point is: Urea > NaCl > Na₂SO₄ > Na₃PO₄. The given option states: urea > NaCl > Na₂SO₄ > Na₃PO₄. This is correct.

The van't Hoff factors ($i$) for the given solutes are: Urea ($i=1$), NaCl ($i=2$), Na₂SO₄ ($i=3$), Na₃PO₄ ($i=4$).

Colligative properties like osmotic pressure, boiling point elevation ($\Delta T_b$), and freezing point depression ($\Delta T_f$) are directly proportional to $i$.

Vapour pressure of the solution ($P_s$) and freezing point of the solution ($T_f$) are inversely proportional to $i$. Boiling point of the solution ($T_b$) is directly proportional to $i$.

Order of $i$: Urea < NaCl < Na₂SO₄ < Na₃PO₄ Order of osmotic pressure: Urea < NaCl < Na₂SO₄ < Na₃PO₄ Order of vapour pressure: Na₃PO₄ < Na₂SO₄ < NaCl < Urea Order of boiling point: Urea < NaCl < Na₂SO₄ < Na₃PO₄ Order of freezing point: Urea > NaCl > Na₂SO₄ > Na₃PO₄

Comparing these with the options, only the statement regarding the order of freezing point is correct.