What molarity means
Molarity (M) is the most common way to express the concentration of a solution in chemistry and biology labs: the number of moles of solute in one liter of solution. A 1 M solution of sodium chloride contains 58.44 g of NaCl per liter, because that is the mass of one mole. Working in moles rather than grams lets you compare solutions of different compounds on the same footing, since reactions happen molecule by molecule.
The formulas
- Moles n = mass ÷ molar mass
- Molarity M = n ÷ volume in liters
- Mass to weigh = molarity × volume (L) × molar mass
- Mass concentration (g/L) = mass ÷ volume
- Percent w/v = grams per 100 mL
Worked example: normal saline
Medical saline is 0.9% NaCl, or 9 g per liter.
- Moles: 9 g ÷ 58.44 g/mol = 0.154 mol.
- Molarity: 0.154 mol ÷ 1 L = 0.154 M, or 154 mM.
- Each NaCl gives one Na⁺ and one Cl⁻, so the solution holds about 308 mOsm/L, close to blood plasma.
Worked example: preparing a solution
You need 250 mL of 0.5 M NaCl.
- Mass = 0.5 mol/L × 0.250 L × 58.44 g/mol = 7.31 g.
- Dissolve it in about 200 mL of distilled water.
- Transfer to a 250 mL volumetric flask and fill to the mark.
Common lab solutions
| Solution | Molar mass (g/mol) | Mass for 1 L at 0.1 M |
|---|---|---|
| Sodium chloride, NaCl | 58.44 | 5.84 g |
| Potassium chloride, KCl | 74.55 | 7.46 g |
| Sodium hydroxide, NaOH | 40.00 | 4.00 g |
| Glucose | 180.16 | 18.02 g |
| Tris base | 121.14 | 12.11 g |
| Copper sulfate pentahydrate | 249.69 | 24.97 g |
Tips for accurate solutions
- Use the right molar mass. Hydrates include their water: CuSO4·5H2O weighs 249.69 g/mol, anhydrous CuSO4 only 159.61.
- Make up to volume, do not add solute to a full volume of water. The dissolved solid takes up some space.
- Units: 1 M = 1,000 mM = 1,000,000 µM. Biology buffers are often in mM, drug and hormone levels in µM or nM.
- Temperature matters slightly, because the volume of water changes with temperature. Volumetric glassware is calibrated at 20 °C.
- Dilute from a stock when you need small concentrations: weighing a few milligrams is less accurate than diluting a 1 M stock.