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II-07: Colligative properties and vapor pressure

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Module II-07 · Recommended before: Before solutions and phase changes

Colligative properties and vapor pressure

A dissolved solute can lower freezing temperature. The relationship uses molality and, when appropriate, a van ’t Hoff factor.

Learn the method

ΔT_f = i K_f m

  1. Identify ΔT_f = i K_f m.
  2. Use a correct value of i for the stated assumptions.
  3. Compute the positive magnitude of the freezing-point depression.
  4. Subtract this from the pure solvent freezing point.
  5. Include temperature units.

Common mistake: The temperature change is a positive depression magnitude, while the solution freezing point is lower.

Worked example

Problem: For an ideal nonelectrolyte with m = 0.50 mol/kg and water K_f = 1.86 °C·kg/mol, find ΔT_f.

Step-by-step solution: ΔT_f = (1)(1.86)(0.50) = 0.93 °C; freezing point becomes −0.93 °C.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Raoult’s law

For an ideal solution with solvent mole fraction 0.80 and pure solvent vapor pressure 25 mmHg, Psolvent = 0.80×25 = 20 mmHg.

Osmotic pressure

For an ideal nonelectrolyte at 0.100 M and 298 K, π = MRT = (0.100)(0.08206)(298) = 2.45 atm.

Henry’s law

In a consistent Henry-law convention where dissolved concentration C=kH×Pgas, increasing partial pressure doubles C if temperature and kH remain constant. Different texts define kH inversely; read the stated units.

Clausius–Clapeyron relation

ln(P₂/P₁)=−ΔHvap/R(1/T₂−1/T₁). Temperatures must be in kelvin and ΔHvap must use energy units consistent with R.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. For an ideal nonelectrolyte in water, find freezing-point depression at molality 0.5 m. Kf=1.86 °C/m.
Hint for question 1

First calculate magnitude of the depression.

Question 2. For an ideal nonelectrolyte in water, find freezing-point depression at molality 0.6 m. Kf=1.86 °C/m.
Hint for question 2

First calculate magnitude of the depression.

Question 3. For an ideal nonelectrolyte in water, find freezing-point depression at molality 0.7 m. Kf=1.86 °C/m.
Hint for question 3

First calculate magnitude of the depression.

Question 4. For an ideal nonelectrolyte in water, find freezing-point depression at molality 0.8 m. Kf=1.86 °C/m.
Hint for question 4

First calculate magnitude of the depression.

Question 5. For an ideal nonelectrolyte in water, find freezing-point depression at molality 0.9 m. Kf=1.86 °C/m.
Hint for question 5

First calculate magnitude of the depression.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

W3C WCAG 2.2 accessibility guidance.

Applied practice: Other colligative and vapor-pressure relationships

These ungraded questions extend the scored five-question check. Work each problem before opening its solution; progress records are not changed.

  1. Challenge 1. Estimate the boiling-point elevation of an ideal 0.400 m CaCl₂ solution with complete dissociation (i = 3) and water Kb = 0.512 °C/m.

    Show worked solution for challenge 1

    ΔTb = iKbm = 3(0.512 °C/m)(0.400 m) = 0.614 °C. This is an idealized result; real solutions may deviate from i = 3.

  2. Challenge 2. The mole fraction of a nonvolatile-solute solution’s solvent is 0.950, and pure solvent vapor pressure is 23.8 mmHg. Find the ideal solution vapor pressure.

    Show worked solution for challenge 2

    Raoult’s law: Psolvent = Xsolvent P°solvent = (0.950)(23.8 mmHg) = 22.6 mmHg.

IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.