How It Works
This converter works in 4 steps.
Enter the mass fraction
Type % w/w from the label or certificate.
Enter the solution density
Type ρ in g/mL, kg/L, or lb/US gal at the stated temperature.
Enter the molecular weight
Type the solute MW for the molarity result.
Read the results
The converter returns g/L, mg/mL, % w/v, and M.
The Formula
The formula multiplies mass fraction by density and by 1,000 mL/L.
ρ_solute (g/L) = (w / 100) × ρ_solution (g/mL) × 1,000M = ρ_solute / MW% w/v = (w / 100) × ρ_solution × 100- w:
- Mass fraction (% w/w)
- ρ_solution:
- Solution density (g/mL)
- MW:
- Solute molecular weight (g/mol)
96% w/w sulfuric acid with ρ = 1.84 g/mL holds 0.96 × 1.84 × 1,000 = 1,766 g/L H₂SO₄, which equals 18.0 M.
Conversion Table
The conversion table converts 6 common concentrated liquids from % w/w to g/L and M at about 20 °C.
| Liquid | Mass fraction | Density | Mass per volume | Molarity |
|---|---|---|---|---|
| Hydrochloric acid | 37% w/w | 1.19 g/mL | 440.3 g/L | 12.08 M |
| Sulfuric acid | 96% w/w | 1.84 g/mL | 1,766 g/L | 18.01 M |
| Nitric acid | 70% w/w | 1.42 g/mL | 994 g/L | 15.78 M |
| Sodium hydroxide | 50% w/w | 1.52 g/mL | 760 g/L | 19 M |
| Sodium chloride brine | 26% w/w | 1.197 g/mL | 311.2 g/L | 5.325 M |
| Sucrose syrup | 50% w/w | 1.23 g/mL | 614.8 g/L | 1.796 M |
What Is the Mass Fraction-to-Volume Concentration Converter?
The Mass Fraction-to-Volume Concentration Converter is a tool that converts mass fraction (% w/w) into mass per volume (g/L) or molarity (M) by including the solution density. The density turns grams of solution into milliliters of solution.
Concentrated reagents carry mass-percent labels, while recipes need volumes. Without density, % w/w cannot become g/L. For 37% w/w hydrochloric acid at 1.19 g/mL, 1 L of solution weighs 1,190 g and holds 440 g of HCl. The converter takes density at the stated temperature, usually 20 °C (68 °F).
Common Uses
There are 5 main uses of this converter.
Reagent molarity
Chemists find the molarity of concentrated acids and bases.
Process dosing
Engineers convert % w/w caustic into g/L for pump settings.
Safety data review
Users convert SDS concentration data to volume terms.
Bulk delivery checks
Plants check tanker deliveries stated in % w/w.
Recipe conversion
Formulators convert mass recipes to volume recipes.