IntoChemistry

I-10: Solution concentration and dilution

IntoChemistry | General Chemistry I Math Readiness

Free of subscriptions • Self-paced • Text-based and keyboard accessible

Course home

Module I-10 · Recommended before: Before solution reactions and titration stoichiometry

Solution concentration and dilution

Molarity is moles of dissolved solute per liter of final solution. Dilution adds solvent but conserves solute moles.

Learn the method

M = n/V; M₁V₁ = M₂V₂

  1. Convert all volumes to liters.
  2. For molarity use M = n/V.
  3. For dilution use M₁V₁ = M₂V₂.
  4. Compare the resulting concentration with the starting concentration.

Common mistake: The volume is final solution volume, not just solvent volume.

Worked example

Problem: Find the molarity of 0.50 mol solute in 2.00 L of solution.

Step-by-step solution: M = 0.50 mol / 2.00 L = 0.25 mol/L = 0.25 M.

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

More applications of this mathematics

Try each extension before expanding its solution.

Dilution calculation

Dilute 25.0 mL of 2.00 M stock to 0.500 M. V₂=(2.00×25.0)/0.500=100. mL final volume.

Solution stoichiometry

A 1:1 reaction requires 0.020 mol base to react with 0.020 mol acid. At 0.100 M base, V = n/M = 0.200 L = 200 mL.

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. What is the molarity of 0.90 mol solute in 1.5 L final solution?
Hint for question 1

Use liters of total solution.

Question 2. What is the molarity of 2.45 mol solute in 3.5 L final solution?
Hint for question 2

Use liters of total solution.

Question 3. What is the molarity of 3.20 mol solute in 4 L final solution?
Hint for question 3

Use liters of total solution.

Question 4. What is the molarity of 4.05 mol solute in 4.5 L final solution?
Hint for question 4

Use liters of total solution.

Question 5. What is the molarity of 5.00 mol solute in 5 L final solution?
Hint for question 5

Use liters of total solution.

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.

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.