Calculate molarity, work out how much solute a solution needs, and plan a dilution with C1V1 = C2V2.
Why this matters
Almost every lab procedure starts with "prepare a 0.1 M solution" or "dilute the stock 1 in 10". Clinical labs dilute patient samples that read above an instrument's range, biotech technicians make buffers and media, and water-treatment engineers dose chemicals by concentration. Getting the concentration wrong silently ruins an experiment or a result, so these calculations are checked again and again on the job.
Vocabulary
- Solute: the substance being dissolved (salt).
- Solvent: the substance doing the dissolving, usually water.
- Solution: the uniform mixture of the two. "Aqueous" (aq) means dissolved in water.
- Concentration: how much solute is in a given amount of solution.
Molarity
The most common concentration unit in chemistry is molarity (M), moles of solute per litre of solution:
molarity (M) = moles of solute / litres of solution
moles = molarity × litres
Note "litres of solution", not "litres of water added". When you make a solution properly, you dissolve the solute and then add solvent up to the final volume mark.
Worked example 1: how much salt?
You need 500 mL of 0.200 M sodium chloride (NaCl, 58.44 g/mol).
moles = 0.200 mol/L × 0.500 L = 0.100 mol
grams = 0.100 mol × 58.44 g/mol = 5.84 g
In a lab you would weigh 5.84 g of NaCl, dissolve it in less than 500 mL of water in a 500 mL volumetric flask, then fill to the mark and mix.
Worked example 2: what is the concentration?
9.0 g of glucose (180.16 g/mol) is dissolved to make 250 mL of solution.
moles = 9.0 / 180.16 ≈ 0.0500 mol
molarity = 0.0500 mol / 0.250 L = 0.200 M
Other units you will meet
| unit | meaning | where it shows up |
|---|---|---|
| % w/v | grams of solute per 100 mL of solution | saline: 0.9% w/v NaCl = 0.9 g per 100 mL |
| mg/mL or mg/L | mass per volume | clinical results, drug doses, water quality |
| ppm | parts per million (about mg/L in dilute water) | environmental testing |
| mM, µM | millimolar (10⁻³ M), micromolar (10⁻⁶ M) | biology and biochemistry |
Converting between them always goes through molar mass and unit prefixes. For example, 0.9% w/v NaCl is 9 g/L, and 9 / 58.44 ≈ 0.154 M.
Dilution: C₁V₁ = C₂V₂
When you add solvent, the amount of solute does not change; it is just spread through more volume. Moles before = moles after:
C1 × V1 = C2 × V2
C1, V1 are the stock concentration and the volume of stock you take; C2, V2 are the final concentration and final volume. Any volume unit works as long as both sides use the same one.
Worked example 3: a 1-in-10 dilution
Make 250 mL of 0.10 M from a 1.0 M stock.
V1 = C2 × V2 / C1 = 0.10 × 250 / 1.0 = 25 mL
Take 25 mL of stock and add solvent to a final volume of 250 mL (that is about 225 mL of solvent, but you fill to the mark, you do not add exactly 225 mL).
Worked example 4: from a concentrated stock
Make 100 mL of 0.50 M hydrochloric acid from 6.0 M stock.
V1 = 0.50 × 100 / 6.0 ≈ 8.33 mL
Dilution factor
The dilution factor is V₂ / V₁ (or C₁ / C₂). A 1-in-10 dilution has a factor of 10. Serial dilutions repeat a step: three 1-in-10 dilutions in a row give 1-in-1000. Clinical labs multiply a diluted sample's reading by the dilution factor to report the original value.
Safety note
This lesson is paper calculation only. Preparing solutions, especially from concentrated acids and bases, must be learned in a teaching or workplace lab with your instructor or supervisor and the lab's own procedures; employer or institution training is required before you do it for real. One rule you will hear on day one: when diluting concentrated acid, add acid to water, never water to acid, because the heat released can make the liquid boil and spatter. Do not experiment with household chemicals at home. See OSHA's laboratory safety guidance. Checked on 2026-10-23.
Common mistakes
- Dividing by the volume of solvent added instead of the final solution volume.
- mL vs L. Molarity needs litres: 250 mL = 0.250 L.
- Swapping C₁ and C₂. The stock is always the more concentrated one; if V₁ comes out larger than V₂, you swapped them.
- Adding V₁ + V₂. V₂ is already the final volume, stock included.
Quick recap
- Molarity = moles of solute per litre of solution.
- grams = molarity × litres × molar mass.
- C₁V₁ = C₂V₂ because dilution keeps the moles of solute the same.
- Fill to the final volume; add acid to water; learn the hands-on part under supervision.
Try it
Open the Do tab: you will finish a Python dilution calculator, then take the quiz.