Hong Life CalculatorsUnderstanding the concentration converter — concept and principle
The same solution can be labelled in many ways: mol/L on a lab protocol, % w/v on a reagent bottle, mg/L or ppm in a water report, normality in an old titration method. This converter starts from molarity and the solute's molar mass and expresses the concentration in all of these units at once, using the solution density for the mass-based ones.
How it is calculated
With c in mol/L, M in g/mol, eq the equivalents per mole and ρ the density in g/mL:
- g/L = c × M (identical to mg/mL).
- % w/v = c × M ÷ 10 (grams per 100 mL).
- ppm (mg/L) = c × M × 1000.
- Normality N = c × eq.
- % w/w = c × M ÷ (ρ × 1000) × 100, because one litre of solution weighs ρ × 1000 g.
- Molality b = c ÷ (ρ − c × M ÷ 1000) in mol/kg, where the denominator is the mass of solvent (kg) in one litre of solution.
The principle
Every unit describes the same amount of solute in a different reference: per litre of solution, per 100 mL, per gram of solution or per kilogram of solvent. Moving between per-volume and per-mass references needs the density. Normality counts reactive units instead of molecules: sulfuric acid can give 2 H⁺, so 1 mol of H₂SO₄ is 2 equivalents in an acid-base reaction.
Worked example
Defaults: c = 0.1 mol/L sulfuric acid, M = 98.079 g/mol, eq = 2, ρ = 1.0 g/mL.
- g/L: 0.1 × 98.079 = 9.8079 g/L (9.8079 mg/mL).
- % w/v: 9.8079 ÷ 10 = 0.98079%.
- ppm: 9.8079 × 1000 = 9,807.9 mg/L.
- Normality: 0.1 × 2 = 0.2 N.
- % w/w: 9.8079 ÷ 1000 × 100 = 0.98079%.
- Molality: solvent = 1.0 − 0.0098079 = 0.9901921 kg, so 0.1 ÷ 0.9901921 = 0.1009905048 mol/kg.
| Molar mass (g/mol) | g/L (= mg/mL) |
|---|---|
| 24.5 | 2.45197 |
| 49 | 4.90395 |
| 73.6 | 7.35592 |
| 98.1 | 9.8079 |
| 123 | 12.2599 |
| 147 | 14.7118 |
| 196 | 19.6158 |
How to read the result
For dilute aqueous solutions with density close to 1, % w/v and % w/w are almost equal and mg/L is practically ppm by mass. As the solution gets more concentrated, these pairs separate, and molality becomes noticeably larger than molarity. Use molality when temperature changes, since it does not depend on volume.
Common mistakes
- Treating mg/L as ppm for dense solutions or non-aqueous solvents, where they differ.
- Leaving the density at 1.0 for concentrated solutions; use a measured value.
- Using eq = 1 for polyprotic acids or redox reactions without checking the reaction.
- Mixing up % w/v (per volume) with % w/w (per mass).
Frequently asked questions
What is the equivalent number for HCl, H₂SO₄ and H₃PO₄?
In full neutralisation, 1, 2 and 3 respectively. Partial neutralisation uses fewer.
Is ppm the same as mg/kg?
Strictly yes; mg/L equals ppm only when one litre weighs about one kilogram.
Why is IUPAC discouraging normality?
Because its value depends on the reaction chosen, which makes it ambiguous; molarity with a stated reaction is clearer.
Sources: IUPAC Compendium of Chemical Terminology (Gold Book), "amount concentration", "molality" · Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman