Chemistry · Stock solutions
Concentrated stock dilution calculator.
Enter the percent (w/w) and density from the label. Get the stock molarity and the volume to dilute for a target solution.
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Molarity of a concentrated stock
Reagent bottles list a mass percent (w/w) and a density. Grams of solute per litre of stock = density (g/mL) x 1000 x percent / 100. Divide by the molar mass to get the stock molarity, then use C1V1 = C2V2 to find how much stock to dilute.
Worked example (how to make 1 M HCl from concentrated acid). OpenStax gives a laboratory HCl that is 37.2% HCl by mass with a density of 1.19 g/mL. That is 1.19 x 1000 x 0.372 = 442.7 g HCl per litre, and with a molar mass of 36.458 g/mol the stock is 12.14 M. For 1 L of 1 M HCl: V1 = 1 x 1000 / 12.14 = 82.4 mL of stock. For 250 mL of 0.5 M, take 10.3 mL.
Read the percent and density off your own bottle or SDS: they vary between suppliers and lots, and density changes with temperature. Always add the concentrated acid slowly to water, never water to the acid, work in a fume hood with eye and skin protection, then fill to the mark. A solution made this way is approximate; standardise it if you need an exact concentration.
Frequently asked questions
How do I make 1 M HCl from 37% hydrochloric acid?
A 37.2% w/w stock at 1.19 g/mL is about 12.14 M, so about 82.4 mL of stock per litre of final solution. Add the acid to water in a volumetric flask and fill to the mark. Check your own bottle label for its percent and density.
How do I find molarity from percent and density?
Molarity = density (g/mL) x 1000 x (percent / 100) / molar mass (g/mol).
Should I add acid to water or water to acid?
Add the acid to the water, slowly and with mixing, because diluting concentrated acid releases heat. Follow your SDS and lab procedure.
Why is the diluent volume only approximate?
Volumes of liquids are not exactly additive, so the stock and water volumes do not always add to the final volume. Fill to the mark instead.
Sources
Checked
- OpenStax Chemistry 2e, 3.4 Other Units for Solution Concentrations (mass percent, ppm, ppb, 37.2% HCl example)
- OpenStax Chemistry 2e, 3.3 Molarity
- CIAAW: Abridged Standard Atomic Weights 2024 (molar masses)
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Lab safety and scope
This is arithmetic, not professional advice. Check every result against your own procedure, the safety data sheet (SDS) for each chemical, and your lab supervisor or instructor before you prepare, mix or dispose of anything. Verify values on the reagent bottle, since purity and hydration state change the real molar mass.