Study guides & original practice
Dilution calculations with M1V1 = M2V2
Dilution adds solvent while keeping the amount of dissolved solute unchanged, provided none is lost or reacts. Start with conservation of solute, not memorization of a rearranged formula.
By ExamCat · Original study lesson · Published September 24, 2026
Understand the method
Because n = MV, the same solute amount before and after dilution gives M₁V₁ = M₂V₂. Both volumes can be in milliliters if their units match. This relation alone does not describe mixing two different nonzero-concentration solutions.
Worked example, step by step
Prepare 200 mL of 0.15 M solution from a 1.0 M stock.
- List the stock concentration as M₁ = 1.0 M and the target as M₂ = 0.15 M.
- Solve V₁ = M₂V₂/M₁ = 0.15 × 200 ÷ 1.0 = 30 mL.
- Measure 30 mL of stock, then add solvent until the final solution reaches 200 mL.
- Check the amount: 1.0 × 0.030 = 0.030 mol, matching 0.15 × 0.200 = 0.030 mol.
A mistake to watch for
The final volume is 200 mL; it is not an instruction to add 200 mL of solvent to the stock. For classroom preparation, follow the specified equipment and lab procedure.
Try it yourself: three questions
Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.
1. Dilute 40 mL of 0.50 M stock to 100 mL. Find the concentration.
Show answer and explanation
M₂ = 0.50 × 40/100 = 0.20 M. More volume distributes the same solute amount more widely.
2. Can dilution alone turn 0.10 M stock into 0.30 M solution?
Show answer and explanation
No. Adding solvent lowers concentration. The calculation would demand less final volume, which is not dilution by solvent addition.
3. What happens to solute moles during ideal dilution?
Show answer and explanation
They stay constant. Solvent amount and total volume change; confusing those quantities with solute amount leads to the wrong model.
Build your next practice session
Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.
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Further reading
OpenStax Chemistry 2e provides textbook background. The worked scenario and practice questions on this page were written independently for ExamCat.
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