Molarity vs Molality vs Normality

The three definitions

• Molarity (M): moles of solute per liter of solution.
• Molality (m or mol/kg): moles of solute per kilogram of solvent.
• Normality (N): equivalents of solute per liter of solution, which is molarity × the equivalents per mole.

A worked example

Dissolve 4.9 g of sulfuric acid, H₂SO₄ (98.08 g/mol), which is 0.050 mol.

• Made up to 500 mL of solution: 0.050 ÷ 0.500 L = 0.10 M.
• Sulfuric acid gives 2 H⁺ per molecule, so the same solution is 0.10 × 2 = 0.20 N.
• Dissolved in 500 g of water instead: 0.050 ÷ 0.500 kg = 0.10 mol/kg.

When to use each

Molarity is the everyday unit in the lab: you make up a volumetric flask to the mark and pipette volumes. Its drawback is that volume changes with temperature, so molarity does too.

Molality uses masses, which do not change with temperature. It is the unit for colligative properties such as freezing point depression and boiling point elevation, and for work over a range of temperatures. For dilute water solutions, molarity and molality are almost equal, because a liter of such a solution holds about a kilogram of water.

Normality depends on the reaction, which is why IUPAC no longer recommends it, but it is still common in titrations. One equivalent is the amount that gives or takes one mole of H⁺ (or OH⁻, or electrons in a redox reaction): HCl and NaOH have 1 per mole, H₂SO₄ 2 and H₃PO₄ up to 3.

Percent concentrations

Percent solutions are a fourth common way to state concentration: % w/v is grams per 100 mL of solution, % v/v is milliliters per 100 mL, and % w/w is grams per 100 g.

Calculators

The Molality and Normality Calculator works out both from a formula and masses. The Molarity Calculator solves for mass, volume or molarity, and the Percent Solution Calculator handles w/v, v/v and w/w.