Question

The following solutions were prepared by dissolving 10 g of glucose (C₆H₁₂O₆ ) in 250 ml of water (P₁), 10 g of urea (CH₄N₂O) in 250 ml of water (P₂ ) and 10 g of sucrose (C₁₂H₂₂O₁₁) in 250 ml of water (P₃). The right option for the decreasing order of osmotic pressure of these solutions is

• A. P₃ > P₁ > P₂
• B. P₂ > P₁ > P₃
• C. P₁ > P₂ > P₃
• D. P₂ > P₃ > P₁

Answer 1

The Correct Option is A

To determine the decreasing order of osmotic pressure of the solutions, we can use the concept of osmotic pressure which is given by the formula:

\[\Pi = i \cdot C \cdot R \cdot T\]

where:

• \(\Pi\) is the osmotic pressure.
• \(i\) is the van 't Hoff factor, which is 1 for glucose, urea, and sucrose as they do not ionize in solution.
• \(C\) is the concentration of the solute in moles per liter.
• \(R\) is the universal gas constant.
• \(T\) is the temperature in Kelvin.

The osmotic pressure depends on the concentration of solute particles. Let's calculate the concentration for each solution:

1. Glucose (P₁): The molar mass of glucose (C₆H₁₂O₆) is 180 g/mol.
2. The number of moles of glucose = \(\frac{10}{180} = 0.0556 \, \text{mol}\)
3. Concentration of glucose = \(\frac{0.0556}{0.25} = 0.2224 \, \text{mol/L}\)
4. Urea (P₂): The molar mass of urea (CH₄N₂O) is 60 g/mol.
5. The number of moles of urea = \(\frac{10}{60} = 0.1667 \, \text{mol}\)
6. Concentration of urea = \(\frac{0.1667}{0.25} = 0.6668 \, \text{mol/L}\)
7. Sucrose (P₃): The molar mass of sucrose (C₁₂H₂₂O₁₁) is 342 g/mol.
8. The number of moles of sucrose = \(\frac{10}{342} = 0.0292 \, \text{mol}\)
9. Concentration of sucrose = \(\frac{0.0292}{0.25} = 0.1168 \, \text{mol/L}\)

Since osmotic pressure is directly proportional to the concentration of solute particles, the solution with higher concentration will exert more osmotic pressure. Therefore, compare the concentrations:

• Urea (P₂): 0.6668 mol/L
• Glucose (P₁): 0.2224 mol/L
• Sucrose (P₃): 0.1168 mol/L

The correct decreasing order of osmotic pressure is P₂ > P₁ > P₃. However, this is different from the given correct answer in the question. It appears that there may be an error in the provided correct answer, as based on these calculations, the order should be based on concentration levels derived from molar mass calculations.