Molarity and Dilutions
How to express solution concentration in mol L⁻¹, how to calculate the volumes needed for a dilution, and the practical steps for making a standard solution in the lab.
Primary sources: Khan Academy Chemistry · NIST Chemistry WebBook
01 · Molarity
Moles of solute per litre of solution.
Molarity (symbol c) is the most widely used measure of concentration in chemistry:
where c is concentration (mol L⁻¹), n is amount of solute (mol) and V is volume of solution (L). The unit mol L⁻¹ is also written M or mol dm⁻³.
Key point: molarity refers to the solution volume, not the solvent volume alone. When a solid is dissolved, the volume changes slightly — always make up to the final volume in a calibrated volumetric flask. See our moles and molar mass guide for how to convert between mass and moles.
02 · Dilutions
Same moles, more solvent.
When you dilute a solution you add more solvent, increasing the volume. The amount of solute (moles) stays the same — only the concentration changes. This gives the dilution equation:
where subscript 1 = initial (concentrated) solution and subscript 2 = final (diluted) solution. If you know any three of these four values you can find the fourth.
Serial dilutions — a chain of successive dilutions — are used when very low concentrations are needed (e.g. 10⁻⁹ mol L⁻¹ in pharmacology). Each step multiplies the dilution factor. Use our dilution calculator to compute any dilution instantly.
03 · Worked examples
Three standard problems.
What mass of NaOH to make 250 mL of 0.100 mol L⁻¹?
n = c × V = 0.100 × 0.250 = 0.0250 mol
m = n × M = 0.0250 × 40.00 = 1.00 g NaOH
Dilute 10.0 mL of 6.00 mol L⁻¹ HCl to 150 mL. Final concentration?
c₁V₁ = c₂V₂ → c₂ = (6.00 × 10.0) / 150
c₂ = 0.400 mol L⁻¹ HCl
50.0 mL of 0.200 mol L⁻¹ H₂SO₄ contains how many moles?
n = c × V = 0.200 × 0.0500
n = 0.0100 mol H₂SO₄
04 · Standard solutions
Making a solution of known concentration.
A standard solution has an accurately known concentration. It is used in titrations and calibration. To prepare one from a solid:
- Calculate the mass needed: m = c × V × M
- Weigh to 4 decimal places on an analytical balance.
- Dissolve in ~50 mL of distilled water in a beaker; stir until fully dissolved.
- Allow to cool to room temperature (dissolution can be exothermic).
- Transfer quantitatively to a volumetric flask — rinse the beaker and stirring rod three times, adding washings to the flask.
- Make up to the graduation mark with distilled water, using a dropper for the last few mL.
- Stopper and invert to mix.
Primary standards (e.g. anhydrous sodium carbonate, potassium hydrogen phthalate) are substances that can be weighed and dissolved directly because they are pure, stable, non-hygroscopic and have a high molar mass. NaOH is not a primary standard — it absorbs CO₂ and moisture.
Questions about molarity and dilutions
- Molarity (c) = n / V, where n is moles of solute and V is volume in litres. Units are mol L⁻¹ (= mol dm⁻³ = M). Example: dissolving 0.10 mol NaCl in 500 mL (0.500 L) gives c = 0.10 / 0.500 = 0.200 mol L⁻¹. See our moles and molar mass guide for how to calculate moles from mass.
- When a solution is diluted, the number of moles of solute does not change — you just add more solvent. So c₁V₁ = c₂V₂. Example: dilute 25.0 mL of 2.00 mol L⁻¹ HCl to 100.0 mL. c₂ = (2.00 × 25.0) / 100.0 = 0.500 mol L⁻¹. Use our dilution calculator to check any dilution.
- Calculate the required mass: m = c × V × M (where M is molar mass).
- Weigh accurately using a 4-decimal-place balance.
- Dissolve in a small volume of distilled water in a beaker (with stirring).
- Allow to cool to room temperature.
- Transfer quantitatively to a volumetric flask (rinse beaker 3×).
- Add distilled water until the meniscus is at the graduation mark.
- Concentration can be expressed in many units: g L⁻¹, ppm (mg L⁻¹), %, mol L⁻¹. Molarity specifically means mol L⁻¹ and is the most useful unit for stoichiometry because reactions occur in mole ratios. Mass concentration (g L⁻¹) is converted to molarity by dividing by molar mass: c (mol L⁻¹) = ρ (g L⁻¹) / M (g mol⁻¹).
Try the dilution calculator
Enter stock concentration, desired final concentration and volume — the tool calculates exactly how much to measure out.