Calculate molarity from moles of solute and total solution volume.
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Molarity is the standard measure of solution concentration in chemistry laboratories worldwide. Whether you are preparing a buffer for biochemistry, making a standard solution for a titration, or diluting a stock acid for a school experiment, understanding molarity is essential. This guide covers the molarity formula, how to calculate moles and molar mass, the dilution equation, differences between molarity and related concentration units, and practical guidance for working in US and UK laboratory settings.
Molarity (symbol M) is defined as the number of moles of solute dissolved per litre of solution:
M = n ÷ V
Where:
Example: 0.5 mol of NaCl dissolved in 250 mL (0.250 L) of solution:
M = 0.5 ÷ 0.250 = 2.0 mol/L (2.0 M)
Molarity is temperature-dependent because volume changes with temperature while mass does not.
A mole (mol) is the SI base unit for amount of substance. One mole contains exactly 6.022 × 10²³ particles (Avogadro's number). The molar mass of a substance (g/mol) equals its atomic or molecular mass in grams — obtained by summing the atomic masses of all atoms in the formula from the periodic table.
n (moles) = mass (g) ÷ molar mass (g/mol)
| Substance | Formula | Molar Mass (g/mol) | Calculation |
|---|---|---|---|
| Sodium chloride | NaCl | 58.44 | Na(22.99) + Cl(35.45) |
| Hydrochloric acid | HCl | 36.46 | H(1.01) + Cl(35.45) |
| Sodium hydroxide | NaOH | 40.00 | Na(23) + O(16) + H(1) |
| Glucose | C₆H₁₂O₆ | 180.16 | 6(12.01)+12(1.008)+6(16.00) |
| Sulphuric acid | H₂SO₄ | 98.08 | 2(1.01)+32.07+4(16.00) |
| Copper(II) sulphate | CuSO₄ | 159.61 | Cu(63.55)+S(32.07)+4O(64) |
| Ethanol | C₂H₅OH | 46.07 | 2(12.01)+6(1.008)+16.00 |
This procedure is the same in US and UK labs. The key difference is that US labs often use the term "DI water" (deionised) while UK labs say "distilled water" or "Type 2 water." Both NIST (US) and UKAS-accredited UK labs follow similar volumetric preparation protocols.
When diluting a concentrated stock solution to a lower concentration:
M₁V₁ = M₂V₂
Where:
V₁ = (M₂ × V₂) ÷ M₁ = (0.1 × 250) ÷ 10 = 25 ÷ 10 = 2.5 mL of 10 M HCl
Add 2.5 mL of concentrated HCl to approximately 200 mL of water in a volumetric flask, then make up to 250 mL with water. Always add acid to water, never water to concentrated acid.
| Concentration Measure | Symbol | Definition | Temperature dependent? |
|---|---|---|---|
| Molarity | M or c | mol solute per litre of solution | Yes (volume changes with temperature) |
| Molality | m | mol solute per kilogram of solvent | No (mass does not change) |
| Normality | N | equivalents per litre | Yes |
| % w/v | %w/v | grams solute per 100 mL solution | Slightly (volume) |
| % w/w | %w/w | grams solute per 100 g solution | No |
| ppm (parts per million) | ppm | mg per litre (for dilute aqueous solutions) | Slightly |
Standard concentrations used in both US and UK teaching and research labs:
Titration is a technique for determining the concentration of an unknown solution (the analyte) by reacting it with a solution of known concentration (the titrant). The molarity of the analyte is calculated from the stoichiometry of the reaction and the volumes used:
n(titrant) = M(titrant) × V(titrant)
n(analyte) = n(titrant) × stoichiometric ratio
M(analyte) = n(analyte) ÷ V(analyte)
Example: 25.0 mL of NaOH titrated with 0.100 M HCl, requiring 23.5 mL HCl to reach the endpoint (1:1 stoichiometry):
When diluting concentrated acids (hydrochloric, sulphuric, nitric) or bases (sodium hydroxide), proper safety procedure is essential:
In UK schools and colleges, CLEAPSS (Consortium of Local Education Authorities for the Provision of Science Services) provides guidance on safe concentrations and procedures. In the US, NSTA (National Science Teaching Association) and local district guidelines govern school lab safety.
Molarity (M) = moles of solute (n) ÷ volume of solution in litres (V). So M = n/V. Rearranged: n = M × V (to find moles), and V = n/M (to find volume needed). All three forms are used in lab calculations.
Calculate mass needed: 1.0 mol × 58.44 g/mol = 58.44 g of NaCl. Weigh out 58.44 g. Dissolve in approximately 800 mL of distilled water. Transfer to a 1-litre volumetric flask and make up to the 1-litre mark with distilled water. Mix thoroughly. This gives exactly 1.0 M NaCl.
The dilution formula is M₁V₁ = M₂V₂. M₁ and V₁ are the concentration and volume of the original (more concentrated) solution; M₂ and V₂ are the concentration and volume of the diluted solution. Always add acid to water when diluting corrosive solutions.
Molarity (M) = moles of solute per litre of solution. Molality (m) = moles of solute per kilogram of solvent. Molarity is temperature-dependent (volume changes with temperature). Molality is temperature-independent (mass does not change), making it preferred for thermodynamic calculations and properties like boiling point elevation and freezing point depression.
Add the atomic masses of all atoms in the formula from a periodic table. For NaOH: Na = 22.99, O = 16.00, H = 1.008. Total = 22.99 + 16.00 + 1.008 = 40.00 g/mol. For H₂SO₄: 2(1.008) + 32.07 + 4(16.00) = 2.016 + 32.07 + 64.00 = 98.09 g/mol.
CLEAPSS provides hazard sheets for chemicals used in UK schools, specifying safe concentrations for student use. For example, CLEAPSS guidance limits HCl to no more than 2 M for student use without special precautions. NaOH should not exceed 0.5 M for general student handling. Concentrated acids (the neat commercial product, typically 10–18 M) require fume hood use and teacher-only handling in schools.
Normality (N) = equivalents per litre, where an equivalent depends on the reaction type. For acids, one equivalent equals one mole of H⁺ ions. For 1 M H₂SO₄, normality = 2 N (because H₂SO₄ provides 2 H⁺). Normality is an older unit still used in some industrial and clinical lab settings in both the US and UK, but IUPAC recommends using molarity and stoichiometric factors instead.
Step 1: n = M × V = 0.5 mol/L × 0.100 L = 0.05 mol. Step 2: mass = n × molar mass = 0.05 mol × 36.46 g/mol = 1.823 g of HCl. In practice, commercial concentrated HCl is approximately 12 M, so you would dilute a small volume of the concentrated acid rather than dissolving pure HCl gas.
Disclaimer: All chemical procedures described are for educational purposes. Always follow institutional safety protocols, wear appropriate PPE, and consult material safety data sheets (MSDS/SDS) before working with any chemical. UK users should follow COSHH regulations and CLEAPSS guidance; US users should follow OSHA laboratory standards and institutional chemical hygiene plans.