Percent solutions, ppm, molality and normality
The units that are not molar — percent by weight or volume, parts per million, moles per kilogram and equivalents — and how to move between them.
Make a percent solution
How much solute for a given final volume (or mass) at a given percentage.
Percent ↔ molarity with density
Use this for concentrated stock reagents sold by weight percent — acids, ammonia, hydrogen peroxide, formaldehyde.
| Concentrated reagent | % w/w | Density g/mL | MW | Molarity |
|---|---|---|---|---|
| Hydrochloric acid | 37 | 1.19 | 36.46 | 12.1 M |
| Sulfuric acid | 98 | 1.84 | 98.08 | 18.4 M |
| Nitric acid | 70 | 1.41 | 63.01 | 15.7 M |
| Acetic acid (glacial) | 99.7 | 1.05 | 60.05 | 17.4 M |
| Phosphoric acid | 85 | 1.685 | 98.00 | 14.6 M |
| Ammonium hydroxide | 28 | 0.90 | 35.05 | 7.2 M |
| Hydrogen peroxide | 30 | 1.11 | 34.01 | 9.8 M |
| Formaldehyde (formalin) | 37 | 1.09 | 30.03 | 13.4 M |
ppm, ppb, mg/dL and mass concentration
Type a value in any row and every other row updates. Density matters only if the solution is far from 1.00 g/mL.
| Unit | Value |
|---|
Molality (mol/kg)
Moles of solute per kilogram of solvent — not of solution. Independent of temperature, which is why it is used for colligative properties.
Normality (N)
Molarity multiplied by the number of reactive equivalents per molecule.
| Species | z | Reason |
|---|---|---|
| HCl, NaOH, HNO₃ | 1 | one proton or hydroxide |
| H₂SO₄, Ca(OH)₂ | 2 | two protons / hydroxides |
| H₃PO₄ (full titration) | 3 | three ionisable protons |
| CaCl₂ | 2 | two charge equivalents per formula unit |
| KMnO₄ (acidic, → Mn²⁺) | 5 | five electrons transferred |
| K₂Cr₂O₇ (acidic, → Cr³⁺) | 6 | six electrons transferred |
| Na₂S₂O₃ (iodometry) | 1 | one electron per thiosulfate |
Which unit should you use?
- % w/v is the default for aqueous lab stocks — 10 % SDS, 30 % acrylamide, 1 % agarose. It is strictly a mass/volume ratio, so “percent” is a convenient fiction.
- % w/w is how concentrated acids and organic reagents are sold, because their density varies. Always convert through density before using them in a molar calculation.
- % v/v is for liquid-in-liquid mixtures — ethanol, glycerol, Triton X-100 — but note that mixing 50 mL ethanol with 50 mL water gives about 96 mL, not 100.
- ppm/ppb dominate in environmental, trace-metal and water analysis.
- mg/dL survives in clinical chemistry (blood glucose, cholesterol) in the United States; most of the rest of the world reports mmol/L.
- Normality is largely legacy but still standard for titrants and ion-exchange capacity. IUPAC discourages it because z depends on the reaction, not the substance.
Common clinical conversions
| Analyte | MW | mg/dL → mmol/L | Example |
|---|---|---|---|
| Glucose | 180.16 | × 0.0555 | 100 mg/dL = 5.55 mmol/L |
| Cholesterol | 386.65 | × 0.02586 | 200 mg/dL = 5.17 mmol/L |
| Triglycerides | 885.4 | × 0.01129 | 150 mg/dL = 1.69 mmol/L |
| Creatinine | 113.12 | × 88.4 (→ µmol/L) | 1.0 mg/dL = 88.4 µmol/L |
| Urea nitrogen (BUN) | 28.01 | × 0.357 | 14 mg/dL = 5.0 mmol/L |
| Calcium | 40.08 | × 0.2495 | 10 mg/dL = 2.50 mmol/L |
Frequently asked questions
What does % w/v mean?
Grams of solute per 100 mL of solution. A 10% (w/v) SDS stock is 10 g SDS made up to 100 mL, which equals 100 g/L.
How do I convert ppm to mg/L?
For dilute aqueous solutions (density ≈ 1.00 g/mL), 1 ppm = 1 mg/L = 1 µg/mL. For solutions of appreciable density, divide by the density in g/mL to be exact.
What is normality and when is it used?
Normality (N) is molarity multiplied by the number of reactive equivalents per molecule — protons for acid/base, electrons for redox, charges for ion exchange. 1 M H₂SO₄ is 2 N in an acid–base titration.
How do I convert % w/w to molarity?
Multiply the mass percent by 10 and by the solution density in g/mL to get g/L, then divide by the molecular weight. Concentrated HCl at 37% w/w and 1.19 g/mL is 37 × 10 × 1.19 / 36.46 = 12.1 M.