v/v vs w/v vs w/w

Three percent notations, three different things. Confusing them is the most common dilution mistake on the lab bench and on the cleaner's trolley.

§ 1Definitions

  • % v/v · ml of solute per 100 ml of total solution. Both volumes. 70 % v/v ethanol = 70 ml ethanol topped up to 100 ml.
  • % w/v · g of solute per 100 ml of total solution. 0.9 % w/v NaCl = 9 g per litre.
  • % w/w · g of solute per 100 g of total solution. 98 % w/w sulphuric acid is the lab concentrated grade.

IUPAC defines volume fraction φ separately from mass fraction w; the notations diverge as soon as densities differ from 1 g/ml.[6]

§ 2Conversion

  • w/v → w/w divide by total solution density. 1 % w/v NaCl in water (density ≈ 1.005 g/ml) = 0.995 % w/w.
  • w/v → v/v needs solute density. 1 % w/v glycerol = 1 g per 100 ml; glycerol density 1.26 g/ml; so 0.79 ml per 100 ml = 0.79 % v/v.
  • % to mg/ml · multiply % w/v by 10. 0.9 % w/v = 9 mg/ml.

§ 3Which to use

  • Liquid-in-liquid → v/v. Ethanol, methanol, surfactant dilutions.
  • Solid-in-liquid → w/v. NaCl saline, agar, buffer salts.
  • Concentrated reagent label → w/w. Acids, hydrogen peroxide, hypochlorite often quoted w/w on SDS.

§ 4Related