Concentrated Acid Molarity Calculator (HCl, H₂SO₄, HNO₃ Stock Solutions)
Molarity of a concentrated acid or other stock solution from its percentage and density, and how much of it to measure out to make a dilute solution.
Results
What this tool does
A bottle label gives the percentage by mass and the density, not the molarity, and the molarity follows from them: 1 L weighs 1000 × ρ grams, of which the percentage is solute, divided by its molar mass. A 37 % hydrochloric acid at 1.19 g/mL works out at about 12 mol/L. Volumes of acid and water are not exactly additive, so measure the acid and make up to the mark with water rather than adding a calculated volume of water. Always add the acid slowly to the water, never the other way round.
Formula
M = 10 × (% by mass) × ρ(g/mL) ÷ M_molar · V_stock = M_final × V_final ÷ M_stock · molality = 1000 × % ÷ (M_molar × (100 − %))
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pc | Strength of the concentrated solution (% by mass) | % |
rh | Density of the concentrated solution | g/mL |
mw | Molar mass of the solute | g/mol |
v2 | Volume you want to make | mL |
c2 | Molarity you want | mol/L |
MS | Molarity of the concentrated solution | mol/L |
VS | Concentrated solution to measure out | mL |
VW | Water to make up to the mark (approx.) | mL |
GL | Solute in the concentrated solution | g/L |
ML | Molality of the concentrated solution | mol/kg |
Worked example
- Strength of the concentrated solution (% by mass)37 %
- Density of the concentrated solution1.19 g/mL
- Molar mass of the solute36.46 g/mol
- Volume you want to make1000 mL
- Molarity you want1 mol/L
- Molarity of the concentrated solution12.08 mol/L
- Concentrated solution to measure out82.81 mL
- Water to make up to the mark (approx.)917.2 mL
- Solute in the concentrated solution440 g/L
- Molality of the concentrated solution16.11 mol/kg
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.