Solution Concentration Calculator
Calculate solution concentrations using different units: molarity, molality, mole fraction, ppm, or ppb.
The six units this calculator handles
| Unit | Symbol | Definition |
|---|---|---|
| Molarity | M | mol solute / L solution |
| Molality | m | mol solute / kg solvent |
| Mole fraction | X | mol component / total mol |
| Mass percent | wt% | (g solute / g solution) × 100 |
| Parts per million | ppm | mg solute / kg solution |
| Parts per billion | ppb | μg solute / kg solution |
Each came out of a different practical need. Molarity is the bench unit — it makes titration math trivial. Molality is what colligative property equations use because it does not drift with temperature. Mole fraction is the thermodynamic unit. Mass percent is what pharmacy and industrial formulation labels report. ppm and ppb are what environmental and trace analysis use because they keep small numbers readable.
What conversions need
Most cross-unit conversions need two extra inputs. The molar mass of the solute is required any time the conversion crosses between mole-based units (M, m, X) and mass-based units (wt%, ppm, ppb). The density of the solution is required whenever the conversion crosses between volume-based units (M) and mass-based units (everything else) — without density you cannot get from “per liter of solution” to “per kilogram of solvent” or “per gram of solution.”
For dilute aqueous solutions you can approximate density as 1.00 g/mL; for anything concentrated, look up the actual value or measure it.
Worked examples
Molarity to molality. 1.00 M NaCl, density 1.04 g/mL, M(NaCl) = 58.44 g/mol. 1 L = 1040 g total. Mass of NaCl = 58.44 g. Mass of water = 1040 − 58.44 = 981.6 g = 0.9816 kg. Molality = 1.00 / 0.9816 = 1.019 m.
Mass percent to molarity. 10.0% (w/w) H₂SO₄, density 1.07 g/mL, M = 98.08 g/mol. 1 L = 1070 g. Mass of H₂SO₄ = 0.100 × 1070 = 107.0 g. Moles = 107.0 / 98.08 = 1.091 mol → 1.091 M.
Molarity to ppm. 0.0010 M Pb(NO₃)₂, reporting ppm of Pb. M(Pb) = 207.2 g/mol. Dilute, so density ≈ 1.00 g/mL. Mass of Pb per liter = 0.0010 × 207.2 = 0.2072 g = 207.2 mg. 207 ppm Pb.
Mole fraction to molality. X(ethanol) = 0.020 in water. For every 0.020 mol ethanol there are 0.980 mol water. Mass of water = 0.980 × 18.015 = 17.65 g = 0.01765 kg. Molality = 0.020 / 0.01765 = 1.13 m.
When each unit fits
Molarity is the bench unit for titrations and reaction stoichiometry in solution. Molality shows up in colligative property calculations — boiling point elevation, freezing point depression — because mass doesn’t drift with temperature the way volume does. Mole fraction is the unit for Raoult’s law and vapor-liquid equilibrium, where you need to count particles rather than mass or volume. Mass percent is the labeling convention for pharmaceutical formulations and industrial chemistry. ppm and ppb dominate environmental monitoring, drinking water standards, and any trace-contaminant work where the numbers would otherwise sit at 10⁻⁵ or smaller in molarity.