How to use the molarity calculator
- Choose what to calculate: molarity, the mass of solute, the volume of solution, or a dilution.
- Enter the molar mass of the solute in g/mol. It is the sum of the atomic weights in its formula; the molecular weight calculator works it out from a formula such as NaCl or CuSO4·5H2O.
- Enter the known values: the mass of solute (g, mg or kg), the molarity (M, mM or µM) and the volume of solution (mL, L or µL).
- For a dilution, choose which of C₁, V₁, C₂ and V₂ to solve for, and enter the other three.
- Read the answer, the moles of solute, the mass concentration and the working.
How molarity is calculated
Molarity is the amount of solute, in moles, per liter of finished solution. IUPAC calls it amount concentration, with the unit mol/L (also written mol/dm³ or M):
The dilution equation holds because adding solvent doesn't change the number of moles: the moles taken from the stock (C₁ × V₁) end up in the final solution (C₂ × V₂). Both sides only need to use the same units.
Worked example
The defaults are 10 g of sodium chloride (NaCl, 58.44 g/mol) made up to 250 mL of solution:
- Moles: 10 ÷ 58.44 = 0.17112 mol
- Volume in liters: 250 mL = 0.250 L
- Molarity: 0.17112 ÷ 0.250 = 0.6845 M (684.5 mM)
- Mass concentration: 10 g ÷ 0.25 L = 40 g/L, or 4% w/v
To make 250 mL of 0.5 M NaCl instead, weigh out 0.5 × 0.250 × 58.44 = 7.305 g. Dissolving the original 10 g to reach 0.5 M needs 0.17112 ÷ 0.5 = 0.3422 L, or 342.2 mL.
The dilution mode starts with a 1 M stock and a target of 500 mL at 0.1 M: V₁ = 0.1 × 500 ÷ 1 = 50 mL of stock, topped up with 450 mL of water. That is a 10-fold dilution.
Molar masses of common solutes
| Compound | Formula | Molar mass (g/mol) |
|---|---|---|
| Sodium chloride | NaCl | 58.44 |
| Sodium hydroxide | NaOH | 40.00 |
| Hydrochloric acid | HCl | 36.46 |
| Potassium chloride | KCl | 74.55 |
| Calcium chloride | CaCl₂ | 110.98 |
| Sodium bicarbonate | NaHCO₃ | 84.01 |
| Sulfuric acid | H₂SO₄ | 98.07 |
| Glucose | C₆H₁₂O₆ | 180.16 |
| Sucrose | C₁₂H₂₂O₁₁ | 342.30 |
Values use the IUPAC abridged standard atomic weights. For hydrated salts, use the hydrate's molar mass: copper sulfate pentahydrate is 249.68 g/mol, not the 159.60 of anhydrous CuSO₄.
Molarity vs. molality and other mistakes
Molarity uses the volume of the solution. Dissolve 7.305 g of salt in water and fill a volumetric flask to the 250 mL mark; adding the salt to 250 mL of water gives slightly more than 250 mL and a slightly lower molarity. Molality (mol/kg) uses the mass of solvent instead and doesn't change with temperature, so it is preferred for precise work over a temperature range. Other common slips are entering milliliters as liters, a factor of 1,000, and forgetting the water in a hydrate. Always add acid to water, never the reverse, and follow your lab's safety rules for concentrated stocks.
Frequently asked questions
What does 1 M mean?
A 1 M (one molar) solution has one mole of solute in every liter of solution. For sodium chloride that is 58.44 g made up to 1 L. A 1 mM solution is a thousand times weaker.
How do I make a solution of a given molarity?
Multiply molarity × volume in liters × molar mass to get the grams to weigh out. For 500 mL of 0.2 M glucose: 0.2 × 0.5 × 180.16 = 18.02 g. Dissolve it in less water, then top up to the 500 mL mark.
How do I use C1V1 = C2V2?
Enter three of the four values and solve for the fourth. To dilute a 2 M stock to 100 mL of 0.5 M, V₁ = 0.5 × 100 ÷ 2 = 25 mL of stock, plus 75 mL of solvent. Keep C₁ and C₂ in the same units, and V₁ and V₂ in the same units.
Does temperature change molarity?
Slightly. Liquids expand as they warm, so the same moles occupy more volume and the molarity falls a little. For most lab work near room temperature the effect is under 1%, but precise work notes the temperature or uses molality.
Related calculators
- Molecular Weight Calculator — Molar mass of any chemical formula, with brackets and hydrates, and the mass percent of each element.
- Density Calculator — Solve ρ = m ÷ V for density, mass or volume in metric or US units, with common material densities.
- Mass Calculator — Mass from density and volume, or from a weight and the gravity where it was measured, in any unit.
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