Educational explanation, not professional design advice. Last reviewed 11 November 2026. Disclaimer
In plain English
Chemists count tiny particles in groups, much as a shop counts eggs in dozens. The group is called a mole, and it is a very large number of particles. Weighing a substance tells you its mass; dividing by the mass of one mole (its molar mass) tells you how many moles you have.
Molarity is the number of moles of a substance dissolved in each litre of solution. It is the usual way to describe how strong a laboratory or process solution is. Dilution makes a weaker solution from a stronger one by adding water or another solvent: the amount of substance stays the same, but it is spread through a larger volume.
Technical definition
The amount of substance n is measured in moles (mol). One mole contains exactly 6.022 140 76 × 10²³ specified particles (the Avogadro constant). The molar mass M (g/mol) is the mass of one mole; it is the sum of the atomic masses in the formula, for example 58.44 g/mol for sodium chloride (NaCl). Molar concentration (molarity) c is the amount of solute per volume of solution, in mol/L (also written M). Note that the volume is that of the final solution, not of the water added.
How it works and where it is used
To prepare a solution of known molarity, you calculate the mass of solute needed, weigh it, dissolve it in part of the solvent, and then make up to the final volume in a volumetric flask. Purity matters: if the solid is only 99.5% pure, you need slightly more of it.
When a solution is diluted, the number of moles of solute does not change. So the concentration times the volume is the same before and after: C₁V₁ = C₂V₂. This is used to make working solutions from a concentrated stock. A serial dilution repeats the same dilution several times, for example taking 1 part and adding 9 parts water (a 1 : 10 dilution) three times to reach one thousandth of the original concentration — more accurate than trying to measure a very small volume once.
| Quantity | Symbol and unit | Relation |
|---|---|---|
| Amount of substance | n, mol | n = m ÷ M |
| Molar mass | M, g/mol | sum of atomic masses |
| Molarity | c, mol/L | c = n ÷ V |
| Mass concentration | g/L (or mg/L) | c × M |
Formula
n = m × P ÷ M c = n ÷ V m = c × V × M ÷ P
C₁V₁ = C₂V₂ Serial dilution: Cn = C₀ ÷ DFn
m = mass weighed (g), P = purity as a fraction, M = molar mass (g/mol), n = amount (mol), V = final solution volume (L), c = molarity (mol/L). C₁, V₁ = concentration and volume of stock taken; C₂, V₂ = final concentration and total volume; DF = dilution factor per step; n = number of steps.
Worked example
Example 1 — preparing a solution. Make 250 mL of 0.50 mol/L sodium chloride (M = 58.44 g/mol).
- n = 0.50 mol/L × 0.250 L = 0.125 mol
- m = 0.125 × 58.44 = 7.305 g of pure NaCl
- If the salt is 99.5% pure: m = 7.305 ÷ 0.995 = 7.342 g
Dissolve it in about 200 mL of water, then make up to the 250 mL mark.
Example 2 — diluting a stock. Make 500 mL of 0.10 mol/L solution from a 1.0 mol/L stock: V₁ = C₂V₂ ÷ C₁ = 0.10 × 500 ÷ 1.0 = 50 mL of stock, made up to 500 mL (about 450 mL of water).
Example 3 — serial dilution. Three 1 : 10 dilutions of a 1.0 mol/L stock give 1.0 ÷ 10³ = 0.001 mol/L.
In the workshop and in practice
These calculations are used every day in quality-control laboratories, water treatment, electroplating baths, cleaning-in-place systems and cooling-water dosing. In water treatment, concentrations are often given in mg/L, which for dilute water solutions is practically the same as parts per million (ppm). Write down the units at every step: most mistakes come from mixing mL and L, or g and mg.
Common mistakes and misconceptions
- Adding the solute to the full volume of water. The final volume will then be more than intended; make up to the mark after dissolving.
- Using the formula mass of the wrong form. Hydrated salts such as CuSO₄·5H₂O have a larger molar mass than the dry salt.
- Mixing up volume units. Molarity uses litres; 250 mL is 0.250 L.
- Treating C₁V₁ = C₂V₂ as a reaction. It applies to dilution only, not to mixing substances that react.
Safety note
Read the safety data sheet before handling any chemical. When diluting concentrated acids, always add the acid slowly to water, never water to acid, and wear eye protection and gloves.
Related calculators
- Molarity Calculator — Molarity from mass, molar mass and volume — or the mass or volume needed for a chosen molarity, with purity.
- Solution Dilution Calculator (C₁V₁ = C₂V₂) — Solve C₁V₁ = C₂V₂ for any value, the diluent volume to add, or the result of a serial dilution.
- Chemical Concentration Converter — Convert a concentration between molarity, g/L, mg/L, % w/v, % w/w, ppm, ppb, molality and mole fraction.
- Stoichiometry & Limiting Reagent Calculator — Limiting reagent, theoretical product and excess reactant left over, from the balanced equation coefficients and reactant masses or moles.
Related topics
- pH and pOH Explained — A logarithmic scale for how acidic or basic a water solution is.
References
- IUPAC: Quantities, Units and Symbols in Physical Chemistry (the Green Book)
- BIPM: The International System of Units (SI Brochure), definition of the mole
- Harris, Quantitative Chemical Analysis