TAHA Engineering Toolsby TAHA Knowledge Lab

Chemical Engineering

Chemical Concentration Converter

Convert a concentration between molarity, g/L, mg/L, % w/v, % w/w, ppm, ppb, molality and mole fraction.

Inputs

A container of solution split into a small solute part and a larger solvent part, with three labels: per volume, per mass, per solvent, joined by M and rho.solutesolventsolution: volume V, density ρper volume: c = n ÷ V, β = m ÷ Vper mass: w = m ÷ mass of solutionper solvent: b = n ÷ mass of solvent, xlinked by M (solute) and ρ
The same solution can be described per volume of solution (mol/L, g/L, % w/v), per mass of solution (% w/w, ppm) or per amount of solvent (molality, mole fraction). Molar mass M and density ρ link the three. Diagram not to scale.

1000 kg/m³ (1 g/mL) is water. Concentrated solutions are denser; use measured or published data for your solution.

18.015 g/mol for water. Needed only for the mole fraction.

Result

Molar concentration
1.83265mol/L
Molar concentration
1,832.65mmol/L
Mass concentration
107.1g/L
Mass concentration
107,100mg/L
Mass per volume
10.71% w/v
Mass percent
10% w/w
Parts per million by mass
100,000ppm (mg/kg)
Parts per billion by mass
100,000,000ppb (µg/kg)
Molality
1.90129mol/kg solvent
Mole fraction of solute
0.0331173
Mass fraction of solute
0.1
Working
Mass fraction w = 0.1 (from % w/w (mass percent)) c = w × ρ ÷ M = 0.1 × 1,071 g/L ÷ 58.44 g/mol = 1.83265 mol/L b = 1000 w ÷ [M (1 − w)] = 1.90129 mol/kg x = (w/M) ÷ [w/M + (1 − w)/Ms] = 0.0331173

This is 10 % w/w = 1.83265 mol/L = 107.1 g/L (molality 1.90129 mol/kg solvent).

  • ppm here is by mass (mg per kg of solution). It equals mg/L only for dilute solutions with a density close to 1 kg/L.

Educational estimate — check the assumptions below.

About this calculator

Concentrations are written in many units: per volume of solution (mol/L, g/L, mg/L, % w/v), per mass of solution (% w/w, ppm, ppb), or per amount of solvent (molality, mole fraction). Converting between the groups needs the solute’s molar mass and, between volume and mass units, the solution’s density.

Enter one value in its unit; every other unit is shown. The calculation goes through the mass fraction w of the solute. This is a calculation tool only, not chemical handling advice.

Formula

c = w ρ ÷ M    β = w ρ    % w/v = β ÷ 10    ppm = 10⁶ w

b = 1000 w ÷ [M (1 − w)]    x = (w/M) ÷ [w/M + (1 − w)/Ms] = b ÷ (b + 1000/Ms)

w = mass fraction of solute, ρ = solution density (g/L), M = solute molar mass (g/mol), Ms = solvent molar mass (g/mol), c = molar concentration (mol/L), β = mass concentration (g/L), b = molality (mol/kg of solvent), x = mole fraction. From molality: w = (bM/1000) ÷ (1 + bM/1000).

Worked example

  • 10% w/w sodium chloride (M 58.44 g/mol), density 1071 kg/m³ (example value): c = 0.10 × 1071 ÷ 58.44 = 1.8326 mol/L; β = 107.1 g/L (10.71% w/v); b = 1000 × 0.10 ÷ (58.44 × 0.90) = 1.9013 mol/kg; x = 0.033117; 100 000 ppm by mass.
  • 1.000 mmol/L glucose (M 180.16 g/mol), density 1000 kg/m³: 180.16 mg/L = 180.16 ppm by mass; b = 1.00018 mmol/kg; x = 1.8018 × 10⁻⁵.
  • 2.000 mol/kg sodium chloride → w = 0.104649 (10.4649% w/w), which converts back to exactly 2.000 mol/kg.

Assumptions and limitations

  • One solute in one solvent. The density is that of the solution, at the temperature of use; it is entered by you, not looked up.
  • ppm and ppb are by mass. They equal mg/L and µg/L only when the solution density is about 1 kg/L.
  • Normality is not included, because it depends on the reaction the solution is used for.
  • A calculation tool only, not chemical handling advice.

References

  • IUPAC, Quantities, Units and Symbols in Physical Chemistry (Green Book): amount concentration, mass concentration, mass fraction, molality, amount fraction.