Questions: Osmotic Pressure and Colligative Properties

Question 1

A student predicts that a 0.1 M sucrose solution should have a lower osmotic pressure than a 0.1 M glucose solution because sucrose molecules are larger. According to the van't Hoff equation, which statement is correct?

• A. Both solutions have the same osmotic pressure, because osmotic pressure depends on particle count, not molecular size or identity.
• B. The glucose solution has higher osmotic pressure because smaller molecules move more freely across the membrane.
• C. The sucrose solution has higher osmotic pressure because larger molecules exert more force on the membrane.
• D. The osmotic pressures differ because the two solutes have different chemical identities.

Answer: (A)

Osmotic pressure is a colligative property — it depends only on the number of dissolved particles per unit volume (molarity), not on the chemical identity or size of the solute. Both solutions are 0.1 M, so both produce Π = MRT ≈ 2.4 atm at room temperature. The student's reasoning confuses molecular identity with particle count.

Question 2

Why does the van't Hoff equation for osmotic pressure (Π = MRT) have the same mathematical structure as the ideal gas law (PV = nRT)?

• A. Both equations describe gases in different physical states — one gaseous, one dissolved.
• B. Dissolved solute particles exert a 'pressure' on the membrane analogous to gas molecules hitting container walls, and at dilute concentrations solute particles behave independently just as ideal gas molecules do.
• C. The similarity is a mathematical coincidence with no physical significance.
• D. Both equations apply only when particles are non-interacting and at high temperature.

Answer: (B)

Van't Hoff recognized that dissolved solute particles in dilute solutions behave analogously to ideal gas molecules: they are sparsely distributed and interact minimally. Their collective tendency to move toward lower concentration creates a pressure on the membrane equivalent to the pressure ideal gas molecules exert on container walls. The analogy breaks down in concentrated solutions, just as the ideal gas law fails at high pressures.

Question 3

Osmotic pressure is the most sensitive colligative property for determining the molar mass of a large protein such as hemoglobin, even at very low concentrations.

• T. True
• F. False

Answer: True

Even a dilute 1 g/L solution of a protein with molar mass ~64,000 g/mol has a molarity of about 1.5 × 10⁻⁵ M. This produces a boiling point elevation of only ~0.00003°C — unmeasurable — but an osmotic pressure of about 0.4 mmHg, which is detectable with an osmometer. Osmotic pressure scales with MRT, and M does not depend on the molar mass of the solute.

Question 4

Adding the same mass (in grams) of glucose and NaCl to separate equal volumes of water produces solutions with equal osmotic pressures, since the same amount of solute was added.

• T. True
• F. False

Answer: False

Osmotic pressure depends on the number of dissolved particles, not mass. NaCl (molar mass ~58 g/mol) dissociates into two ions (Na⁺ and Cl⁻), giving a van't Hoff factor i ≈ 2. Glucose (molar mass ~180 g/mol) does not dissociate, so i = 1. Per gram added, NaCl produces far more moles of particles (~1/58 × 2 vs. 1/180 × 1), yielding roughly 6× more osmotic pressure per gram.

Question 5

Why must the van't Hoff factor i be included when calculating the osmotic pressure of an electrolyte solution like NaCl, but not for a molecular solute like glucose?

Model answer: The van't Hoff factor accounts for the fact that electrolytes dissociate into multiple ions when dissolved, increasing the number of solute particles beyond what the initial molarity suggests. NaCl dissociates into Na⁺ and Cl⁻, so a 0.1 M NaCl solution effectively has ~0.2 M particles, giving i ≈ 2 and doubling the osmotic pressure compared to a non-dissociating 0.1 M solute. Glucose remains as intact molecules in solution (i = 1), so no correction is needed.

The key is that osmotic pressure depends on total particle concentration. Dissociation multiplies particle count; i captures this multiplier. For strong electrolytes like NaCl, i approaches 2; for weak electrolytes it is between 1 and 2 depending on degree of dissociation.