Solution prep from concentrated stock
Turn a bottle's density and assay into its molarity, then get the exact volume of concentrate to pipette for your target concentration — with every value overridable from your CoA.
The formula
C = 10 × ρ × w / MW
- C
- molarity of the concentrated stock, mol/L
- ρ
- density of the concentrate, g/mL
- w
- assay in % w/w — the ×10 reconciles the percent with the mL→L step
- MW
- molecular weight of the solute, g/mol
Worked example
Prepare 1 L of 1 M HCl from 37% concentrated stock
The bottle says 37% (w/w), density 1.19 g/mL. Stock molarity: C = 10 × 1.19 × 37 / 36.46 = 12.08 M — the number to sanity-check against the label, which for concentrated HCl reads ≈ 12 M.
Volume to pipette: V₁ = (1 mol/L × 1000 mL) / 12.076 mol/L = 82.8 mL — the calculator divides by the full-precision stock molarity, not the 12.08 shown above. Part-fill a 1 L volumetric flask with water, add the 82.8 mL of concentrate, let it cool, and make up to the mark.
Common pitfalls
The assay is % w/w, not % w/v
37% HCl means 37 g of HCl per 100 g of solution, not per 100 mL. The density is exactly what bridges weight to volume — skip it and every result is wrong by the density factor.
Nominal grade values are not your bottle's values
The table's densities and assays are typical numbers. Your certificate of analysis states the real ones for your lot — key them in; every field here is editable for exactly that reason.
Density changes with temperature
The typical values assume 20 °C. This calculator applies no temperature correction — if your lab runs warm or your CoA states a different reference temperature, use the CoA density.
Add acid to water, never water to acid
Diluting concentrated acids is exothermic — sulfuric acid violently so. Part-fill the flask with water first, add the concentrate slowly, let it cool before making up to the mark.