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II-05: Concentrations, mole fractions and units

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Module II-05 · Recommended before: Before colligative properties and equilibrium

Concentrations, mole fractions and units

Concentration units are not interchangeable. Molality uses kilograms of solvent; molarity uses liters of solution.

Learn the method

molality = mol solute / kg solvent

  1. Write the definition of the requested unit.
  2. Convert mass to kilograms if needed.
  3. Distinguish solvent from solution.
  4. Compute the ratio with units.
  5. Check whether the question asks for m, M or mole fraction.

Common mistake: Molality divides by solvent mass; molarity divides by solution volume.

Worked example

Problem: Dissolve 0.50 mol solute in 2.00 kg solvent. Find molality.

Step-by-step solution: m = 0.50 mol / 2.00 kg solvent = 0.25 mol/kg.

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

More applications of this mathematics

Try each extension before expanding its solution.

Molarity

0.200 mol dissolved to make 0.500 L of final solution gives 0.400 M.

Mole fraction

Mix 2.0 mol A and 3.0 mol B. Mole fraction of A = 2.0/(2.0+3.0)=0.40; the fractions sum to one.

Mass percent and ppm

Mass percent=100×mass solute/mass solution. For 2.0 mg solute in 1.00 kg solution, mass fraction is 2.0×10⁻⁶, about 2.0 ppm by mass.

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. 0.6 mol solute is dissolved in 1.5 kg of solvent. Find molality.
Hint for question 1

Molality has kilograms of solvent in the denominator.

Question 2. 0.8 mol solute is dissolved in 4 kg of solvent. Find molality.
Hint for question 2

Molality has kilograms of solvent in the denominator.

Question 3. 1 mol solute is dissolved in 5 kg of solvent. Find molality.
Hint for question 3

Molality has kilograms of solvent in the denominator.

Question 4. 1.2 mol solute is dissolved in 3 kg of solvent. Find molality.
Hint for question 4

Molality has kilograms of solvent in the denominator.

Question 5. 1.5 mol solute is dissolved in 6 kg of solvent. Find molality.
Hint for question 5

Molality has kilograms of solvent in the denominator.

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: Molality and mole fractions

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

  1. Challenge 1. A solution contains 0.500 mol solute in 0.250 kg of solvent. Calculate molality.

    Show worked solution for challenge 1

    Molality = 0.500 mol / 0.250 kg = 2.00 mol/kg, often written 2.00 m.

  2. Challenge 2. A mixture contains 0.200 mol A and 0.800 mol B. Find the mole fraction of A.

    Show worked solution for challenge 2

    Total moles = 0.200 + 0.800 = 1.000 mol. Xₐ = 0.200/1.000 = 0.200 (unitless).

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.