How this instrument works
Percent-by-mass concentration (% w/w) states how many grams of solute sit in every 100 grams of solution — a label convention common on concentrated acid and base bottles. Molarity (mol/L) states how many moles of solute sit in every litre of solution — the unit stoichiometry calculations actually run on. The two describe the same solution but in incompatible units, and converting between them requires one more piece of information neither number carries on its own: the solution's density, which links a mass of solution to the volume it occupies.
The conversion works in two stages folded into one formula. Density turns the percent-by-mass figure into a mass of solute per litre of solution: multiplying percent-by-mass by density and by 10 gives grams of solute per litre (the factor of 10 arises from converting 100 g of solution, the percent basis, up to the 1,000 mL in a litre, scaled by density in g/mL). Dividing that grams-per-litre figure by the solute's molar mass then converts a mass quantity into a mole quantity — molarity itself.
This conversion matters most for concentrated commercial reagents like concentrated hydrochloric acid or sulfuric acid, which manufacturers label by percent-by-mass and specific gravity rather than by molarity. A chemist diluting stock acid to a target molarity for a titration or synthesis needs the molar concentration of the concentrated stock first, and that number isn't printed on the label directly — it has to be computed from the percentage, the density, and the compound's molar mass, exactly as this instrument does.
- Enter the solution's percent-by-mass concentration into Concentration (% w/w), as printed on the reagent label.
- Enter the solution's density in grams per millilitre into Solution density (g/mL) — also usually printed on the label or found in a reagent reference table.
- Enter the solute's molar mass in grams per mole into Molar mass (g/mol), computed from its molecular formula.
- Read Molarity (mol/L) directly beneath the three fields — it recalculates the instant any of them changes.
- Molar mass (g/mol) must be greater than zero — the instrument has nothing to divide against otherwise.
Worked example — concentrated hydrochloric acid, 37% w/w
Enter 37 into Concentration (% w/w), 1.19 into Solution density (g/mL), and 36.46 into Molar mass (g/mol) — the standard reagent-grade figures for concentrated hydrochloric acid and HCl's molar mass. Molarity reads 12.076247943 mol/L.
That works out from (37 x 10 x 1.19) / 36.46 = 440.3 / 36.46 = 12.076 mol/L, matching the well-known 'concentrated HCl is about 12 M' figure quoted throughout general chemistry references and reagent catalogs. A chemist needing a specific molar amount of HCl for a reaction can now use this 12.076 M figure directly in a dilution calculation, something the bottle's 37% label alone could not provide.
Questions
Why do I need density to convert percent concentration to molarity?
Because percent-by-mass tells you a mass ratio (grams of solute per 100 g of solution), while molarity needs a volume basis (moles per litre of solution). Density is the bridge between mass and volume for that specific solution — without it, there's no way to know how much solution volume a given mass actually occupies, and the conversion can't be done at all.
Where does the factor of 10 in the formula come from?
It rescales two things at once: percent-by-mass is defined per 100 g of solution, and density is defined per millilitre, but molarity needs a per-litre (1,000 mL) basis. Multiplying by 10 converts the 100 g basis up to the 1,000 mL/L basis consistently, so the arithmetic doesn't require separately tracking a factor of 1,000 for volume and a factor of 1/100 for percent — they combine into one constant of 10.
Why is concentrated hydrochloric acid's molarity often quoted as '12 M'?
Because that's what this exact conversion gives for the commercially standard concentrated HCl solution: 37% w/w at a density of 1.19 g/mL and HCl's molar mass of 36.46 g/mol works out to 12.076 mol/L, which rounds to the widely quoted 12 M or sometimes 12.1 M figure seen in reagent catalogs and general chemistry textbooks.
Does this formula work for any solute, not just acids?
Yes — the relationship between percent-by-mass, density and molarity is general and applies to any solute dissolved in any solvent, as long as you have accurate values for all three inputs. Concentrated acids and bases are the most common use case because they're routinely sold and labelled by percent-by-mass, but the same conversion works for sugar solutions, salt brines, or any other percent-labelled mixture.
What if the density I have is in a different unit, like kg/L?
Convert it to g/mL first, since the formula expects that specific unit — conveniently, kg/L and g/mL are numerically identical (1 kg/L = 1 g/mL), so a density quoted as 1.19 kg/L can be entered directly as 1.19 g/mL without any arithmetic. Densities given in other units, like lb/gal, need to be converted before entry or the result will be wrong by whatever factor separates the units.