Solution strength

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.

% (w/v) = g solute / 100 mL solution  ·  % (w/w) = g / 100 g  ·  % (v/v) = mL / 100 mL
Type of percentage

Percent ↔ molarity with density

Use this for concentrated stock reagents sold by weight percent — acids, ammonia, hydrogen peroxide, formaldehyde.

molarity = (% w/w × 10 × density in g/mL) / MW
Concentrated reagent% w/wDensity g/mLMWMolarity
Hydrochloric acid371.1936.4612.1 M
Sulfuric acid981.8498.0818.4 M
Nitric acid701.4163.0115.7 M
Acetic acid (glacial)99.71.0560.0517.4 M
Phosphoric acid851.68598.0014.6 M
Ammonium hydroxide280.9035.057.2 M
Hydrogen peroxide301.1134.019.8 M
Formaldehyde (formalin)371.0930.0313.4 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.

1 ppm = 1 mg/L = 1 µg/mL (aqueous, ρ ≈ 1.00 g/mL)
UnitValue

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.

b = nsolute / msolvent (kg)  ·  ΔTf = Kf × b × i

Normality (N)

Molarity multiplied by the number of reactive equivalents per molecule.

N = M × z  ·  equivalent weight = MW / z
SpecieszReason
HCl, NaOH, HNO₃1one proton or hydroxide
H₂SO₄, Ca(OH)₂2two protons / hydroxides
H₃PO₄ (full titration)3three ionisable protons
CaCl₂2two charge equivalents per formula unit
KMnO₄ (acidic, → Mn²⁺)5five electrons transferred
K₂Cr₂O₇ (acidic, → Cr³⁺)6six electrons transferred
Na₂S₂O₃ (iodometry)1one 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

AnalyteMWmg/dL → mmol/LExample
Glucose180.16× 0.0555100 mg/dL = 5.55 mmol/L
Cholesterol386.65× 0.02586200 mg/dL = 5.17 mmol/L
Triglycerides885.4× 0.01129150 mg/dL = 1.69 mmol/L
Creatinine113.12× 88.4 (→ µmol/L)1.0 mg/dL = 88.4 µmol/L
Urea nitrogen (BUN)28.01× 0.35714 mg/dL = 5.0 mmol/L
Calcium40.08× 0.249510 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.

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