Molarity Calculator
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Molarity = 0.1 M (0.1 mol in 1 L)
How to use the molarity calculator
- Molarity: enter the mass (or moles) of solute and the final volume of the solution. Give the solute as a chemical formula or type its molar mass.
- Mass to weigh: enter the concentration you want, the volume to make and the solute. The answer is the mass to dissolve.
- Dilution: choose the unknown, enter the other three values, and pick units. Both concentrations share one unit and both volumes share one unit.
Molarity formulas
n = m ÷ M
m = c × V × M
C₁ × V₁ = C₂ × V₂
Molarity (c) is the amount of solute in moles (n) per liter of solution (V), written mol/L or M. The amount comes from the mass of solute (m, in grams) divided by its molar mass (M, in g/mol), so the mass needed for a solution is c × V × M. For a dilution, the moles of solute don't change when you add solvent, so the stock concentration times the stock volume (C₁V₁) equals the final concentration times the final volume (C₂V₂). That relation works in any units, as long as both sides use the same ones.
Worked examples
- Molarity: 5.844 g of sodium chloride (58.44 g/mol) is 0.1 mol. Dissolved and made up to 500 mL, it gives 0.2 M.
- Mass to weigh: 250 mL of 0.1 M copper(II) sulfate needs 0.1 × 0.25 × 249.677 = 6.242 g of the blue pentahydrate, CuSO₄·5H₂O. Using the anhydrous molar mass instead would give only 3.99 g, and the solution would be too weak.
- Dilution: to make 100 mL of 0.5 M from a 2 M stock, V₁ = 0.5 × 100 ÷ 2 = 25 mL of stock, made up with 75 mL of water, a 4-fold dilution.
Mass of common reagents for standard solutions
Calculated with the calculator's engine and IUPAC atomic weights. Weigh the solid, dissolve it, then make up to the stated volume.
| Reagent | Formula | g/mol | 1 M, 1 L | 0.1 M, 1 L | 10 mM, 100 mL |
|---|---|---|---|---|---|
| Sodium chloride | NaCl | 58.44 | 58.44 g | 5.844 g | 58.4 mg |
| Potassium chloride | KCl | 74.548 | 74.55 g | 7.455 g | 74.5 mg |
| Sodium hydroxide | NaOH | 39.997 | 40 g | 4 g | 40 mg |
| Sodium bicarbonate | NaHCO₃ | 84.006 | 84.01 g | 8.401 g | 84 mg |
| Calcium chloride dihydrate | CaCl₂·2H₂O | 147.008 | 147.01 g | 14.701 g | 147 mg |
| Magnesium sulfate heptahydrate | MgSO₄·7H₂O | 246.466 | 246.47 g | 24.647 g | 246.5 mg |
| Tris base | C₄H₁₁NO₃ | 121.136 | 121.14 g | 12.114 g | 121.1 mg |
| Glucose | C₆H₁₂O₆ | 180.156 | 180.16 g | 18.016 g | 180.2 mg |
| Copper(II) sulfate pentahydrate | CuSO₄·5H₂O | 249.677 | 249.68 g | 24.968 g | 249.7 mg |
Molarity, molality and percent
Molarity is per liter of solution, so it changes slightly with temperature as the liquid expands. Molality (mol per kilogram of solvent) does not, which is why it is used for freezing-point and boiling-point work. Percent concentrations (w/v, w/w or v/v) express the same idea by mass or volume; the dilution mode handles % and mg/mL directly because C₁V₁ = C₂V₂ only needs matching units.
Tips for making solutions
- Make up to volume, don't add a fixed volume of water. Dissolving a solid changes the volume, so fill a volumetric flask to the mark after the solid dissolves.
- Check the label for water of crystallization. CaCl₂·2H₂O and anhydrous CaCl₂ need different masses for the same molarity.
- Add acid to water, never water to concentrated acid, and wear eye protection when handling corrosive reagents such as sodium hydroxide.
- Serial dilutions are more accurate than one very large dilution: two 1:10 steps measure better than a single 1:100.
The molecular weight calculator shows the full molar mass breakdown of any formula, and the density calculator converts between mass and volume of liquids.
Frequently asked questions
How do you calculate molarity?
Divide the moles of solute by the liters of solution: M = n ÷ V. If you know the mass, first divide it by the molar mass. 5.844 g of NaCl (58.44 g/mol) is 0.1 mol; made up to 500 mL, that is 0.2 M.
How many grams do I need to make a solution?
Multiply the molarity by the volume in liters and the molar mass: m = c × V × M. For 250 mL of 0.1 M copper(II) sulfate pentahydrate (249.677 g/mol), weigh 0.1 × 0.25 × 249.677 = 6.242 g.
How do I use C1V1 = C2V2 for a dilution?
Rearrange for the unknown. To make 100 mL of 0.5 M from a 2 M stock, V₁ = C₂ × V₂ ÷ C₁ = 0.5 × 100 ÷ 2 = 25 mL of stock, brought up to 100 mL with 75 mL of solvent.
What is the difference between molarity and molality?
Molarity is moles of solute per liter of solution and changes slightly with temperature. Molality is moles per kilogram of solvent and does not. For dilute water solutions near room temperature the two numbers are close.
What does 1 M mean?
One mole of solute per liter of solution. A 1 M sodium hydroxide solution contains 39.997 g of NaOH in each liter of the final solution, and 1 mM is a thousandth of that, about 0.040 g per liter.