What Molarity Is
Molarity is the number of moles of solute per litre of solution — not per litre of solvent. The distinction matters: dissolving something increases the volume, so 1 mole added to 1 litre of water produces slightly more than 1 litre of solution.
M = moles of solute ÷ litres of solution
moles = mass (g) ÷ molar mass (g/mol)
Combining them: M = mass ÷ (molar mass × litres). The unit is written M and read "molar", so 0.5 M is "half molar".
Worked Example
Sodium chloride has a molar mass of 58.44 g/mol. To find the molarity of 5.85 g dissolved to make 1 litre:
- moles = 5.85 ÷ 58.44 = 0.1001 mol
- M = 0.1001 ÷ 1 = 0.1 M
Making a Solution Correctly
The procedure matters as much as the arithmetic:
- Calculate the mass needed: grams = molarity × litres × molar mass.
- Weigh it accurately and transfer it into a volumetric flask.
- Add solvent to roughly two-thirds of the final volume and dissolve completely.
- Then make up to the graduation mark.
Never add the stated volume of solvent to the solid. Adding 250 mL of water to 1.46 g of salt gives a solution of slightly more than 250 mL, and therefore slightly the wrong concentration.
Concentration Units
| Unit | Definition | Depends on temperature? |
|---|---|---|
| Molarity (M) | Moles per litre of solution | Yes — volume expands when heated |
| Molality (m) | Moles per kilogram of solvent | No — mass does not change |
| Normality (N) | Gram equivalents per litre | Yes |
| Mass percent (% w/w) | Grams solute per 100 g solution | No |
| ppm | Milligrams per litre, for dilute aqueous solutions | Slightly |
Molality is preferred for work involving temperature changes — freezing point depression and boiling point elevation — precisely because it is unaffected by thermal expansion.
Dilution
Adding solvent changes the volume but not the number of moles, which gives the most-used equation in a wet lab:
C1V1 = C2V2
To make 100 mL of 0.1 M from a 1 M stock: V1 = (0.1 × 100) ÷ 1 = 10 mL of stock, made up to 100 mL with solvent. Note that you add 90 mL of solvent, not 100.
Serial Dilution
Very large dilution factors are made in steps rather than one jump, because measuring 1 µL accurately is far harder than measuring 100 µL. A 1:10 dilution repeated five times gives 1:100,000 with far better precision than attempting it directly.
| Step | Dilution | Concentration from 1 M |
|---|---|---|
| 1 | 1:10 | 0.1 M |
| 2 | 1:100 | 0.01 M |
| 3 | 1:1,000 | 1 mM |
| 4 | 1:10,000 | 0.1 mM |
| 5 | 1:100,000 | 10 µM |
Common Laboratory Concentrations
| Solution | Typical concentration |
|---|---|
| Physiological saline | 0.15 M NaCl (0.9% w/v) |
| Concentrated hydrochloric acid | 12 M |
| Concentrated sulfuric acid | 18 M |
| Household vinegar | ~0.8 M acetic acid |
| Seawater | ~0.6 M NaCl |
| Standard titration base | 0.1 M NaOH |
Safety Note on Acids
When diluting concentrated acid, always add acid to water, never water to acid. The reaction is strongly exothermic, and water added to concentrated acid can boil instantly and spatter. The traditional mnemonic is "do as you oughta, add acid to water".
Frequently Asked Questions
How do I make 500 mL of 0.2 M NaOH?
moles = 0.2 × 0.5 = 0.1; mass = 0.1 × 40.00 = 4.00 g. Dissolve in about 300 mL of water, then make up to 500 mL.
What is the difference between molarity and molality?
Molarity uses litres of solution, molality uses kilograms of solvent. For dilute aqueous solutions near room temperature the two are nearly equal; they diverge for concentrated solutions and at other temperatures.
Why does the calculator warn about final volume?
Because dissolving a solute changes the volume. Concentration is defined per litre of finished solution, so the solution must be made up to the mark rather than having a measured volume of solvent added.
How do I convert ppm to molarity?
For dilute aqueous solutions, 1 ppm is about 1 mg/L. Divide by the molar mass and by 1,000 to get moles per litre.