Calculate molarity from mass, the mass to weigh for a target molarity, molality, and C₁V₁ = C₂V₂ dilutions, with normality and % w/v shown too. Each result shows the calculation, so you can record it in your reagent logbook.
Molarity vs molality
| Molarity (M) | Molality (m) | |
|---|---|---|
| Definition | Moles of solute per litre of solution | Moles of solute per kilogram of solvent |
| Units | mol/L | mol/kg |
| Temperature dependent? | Yes (volume changes with temperature) | No (based on mass) |
| Typical use | Reagents, buffers, mobile phases, volumetric solutions | Colligative properties, osmolality, physical chemistry |
Formulas
Moles = mass (g) ÷ molar mass (g/mol)
Molarity (mol/L) = moles ÷ volume of solution (L)
Molality (mol/kg) = moles ÷ mass of solvent (kg)
Mass to weigh (g) = molarity × volume (L) × molar mass
Dilution: C₁V₁ = C₂V₂
Normality (N) = molarity × number of equivalents per mole
Worked examples
1. Molarity of normal saline
9 g of NaCl (molar mass 58.44 g/mol) in 1 L of solution. Moles = 9 ÷ 58.44 = 0.154 mol. Molarity = 0.154 ÷ 1 = 0.154 M (154 mmol/L). This is 0.9% w/v sodium chloride.
2. Preparing 500 mL of 0.1 M NaOH
Mass = 0.1 mol/L × 0.5 L × 40.00 g/mol = 2.00 g. Dissolve and make up to 500 mL. For volumetric solutions, standardize against a primary standard (for example potassium hydrogen phthalate) and report the actual molarity.
3. 0.05 M potassium dihydrogen phosphate buffer for HPLC
KH₂PO₄ has a molar mass of 136.09 g/mol. Mass = 0.05 × 1 L × 136.09 = 6.80 g per litre. Adjust the pH as the method specifies before making up to volume.
4. Molality of a sodium chloride solution
5.85 g NaCl in 500 g of water. Moles = 5.85 ÷ 58.44 = 0.1001 mol. Molality = 0.1001 ÷ 0.500 kg = 0.200 mol/kg.
5. Diluting a stock solution
To make 100 mL of 0.05 M from a 1 M stock: V₁ = 0.05 × 100 ÷ 1 = 5 mL. Transfer 5 mL of stock to a 100 mL volumetric flask and make up to volume. The dilution factor is 20.
Normality and equivalents
Normality is still used for some titrants. It equals the molarity multiplied by the number of reacting equivalents per mole: 1 for HCl and NaOH, 2 for H₂SO₄ in full neutralization, and 5 for KMnO₄ in acid redox titrations. Modern pharmacopoeias mostly express volumetric solutions in molarity.
Practical tips
- Use the molar mass of the exact form you weigh, including water of crystallization (for example sodium dihydrogen phosphate dihydrate vs anhydrous).
- Correct for reagent purity or assay when accuracy matters.
- Make up to volume at the temperature the volumetric flask is calibrated for, usually 20 °C.
- For a fixed final volume, always dilute “to” the mark, not “with” a calculated volume of diluent, because volumes are not always additive.
- Record the reagent lot, the weight, the final volume and the expiry date on the solution label and in the logbook.
Frequently asked questions
What is the difference between molarity and molality?
Molarity is moles per litre of solution. Molality is moles per kilogram of solvent. Molality does not change with temperature, while molarity does.
How do I convert mg/mL to molarity?
Divide the concentration in g/L by the molar mass. For example, 5 mg/mL = 5 g/L. For a substance with a molar mass of 250 g/mol, that is 5 ÷ 250 = 0.02 M.
What does 1 M mean?
One mole of solute per litre of solution, for example 58.44 g of NaCl made up to 1 L.
Is mmol/L the same as mM?
Yes. 1 mM = 1 mmol/L = 0.001 mol/L.
Related tools and guides
- Density and specific gravity calculator
- Assay calculator
- Serial dilution guide and calculator
- Pharmaceutical Lab Toolkit: all calculators
References
- IUPAC Compendium of Chemical Terminology (the “Gold Book”): amount concentration and molality.
- USP, Ph. Eur. and IP: volumetric solutions and reagents sections.