Concentrated Acid Molarity Calculator (from % and density)

Understanding the concentrated acid molarity calculator — concept and principle

Concentrated acids and bases are sold by mass percentage and density, for example "hydrochloric acid 37%, d = 1.18", not by molarity. To make a 1 M working solution you first need the molarity of the bottle. This calculator converts a common reagent's percentage and density into molarity and then tells you how many millilitres of the concentrate to dilute to your target concentration and volume.

How it is calculated

• Stock molarity M_st = (% × ρ × 10) ÷ M, where % is the mass percentage, ρ the density in g/mL and M the molar mass in g/mol.
• Stock volume = C_t × V_t ÷ M_st, the usual C₁V₁ = C₂V₂ rearranged, with C_t the target molarity and V_t the target volume in mL.

The principle

Take one litre of the concentrate. It weighs ρ × 1000 g. Of that, the fraction %/100 is the acid itself, so the acid mass is ρ × 1000 × %/100 = % × ρ × 10 grams. Dividing by the molar mass converts grams to moles, and since we started with one litre, the result is mol/L. The dilution step then just conserves moles of acid.

Worked example

Defaults: HCl 37%, ρ = 1.18 g/mL, M = 36.46 g/mol; target 1 M, 1000 mL.

1. Mass of HCl in 1 L: 37 × 1.18 × 10 = 436.6 g.
2. Stock molarity: 436.6 ÷ 36.46 = 11.97476687 M.
3. Stock volume: 1 × 1000 ÷ 11.97476687 = 83.50893266 mL.

How to read the result

Measure about 83.5 mL of 37% HCl and add it slowly to roughly 800 mL of water, then make up to 1000 mL after cooling. The built-in reagents give approximately: H₂SO₄ 98% about 18.4 M, HNO₃ 70% about 15.7 M, glacial acetic acid about 17.4 M, ammonia 28% about 14.8 M (as NH₃), H₃PO₄ 85% about 14.6 M and H₂O₂ 30% about 9.8 M. Check the certificate on your own bottle, because grades differ.

Common mistakes

• Adding water to concentrated acid, which can boil and splash violently.
• Using the nominal percentage when the label gives a range such as 36–38%.
• Forgetting that the result for sulfuric acid is molarity, not normality (18.4 M is about 36.8 N).
• Making up to volume while the solution is still hot.

Frequently asked questions

What is the molarity of 37% hydrochloric acid?

About 12 M (11.97 M with density 1.18 g/mL).

Why is the acetic acid density 1.049 in the calculation?

Glacial acetic acid has a density of about 1.049 g/mL at 25 °C; the menu rounds it to 1.05.

Can I use this for my own percentage and density?

The formula is general; just apply M = % × ρ × 10 ÷ molar mass with your label values.

Sources: Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman · Haynes, W. M. (ed.), CRC Handbook of Chemistry and Physics, CRC Press