In chemistry, concentration describes how much solute is dissolved in a given amount of solution or solvent. Mastering the different ways to express concentration is essential for laboratory work, pharmaceutical calculations, industrial processes and school chemistry. This guide explains the most important concentration measures with clear formulas and worked examples.
Why Concentration Matters
The same substance can have completely different effects at different concentrations. Ethanol at 5% (v/v) is beer; at 70% it is a disinfectant. Hydrogen peroxide at 3% is a topical antiseptic; at 30% it is a dangerous oxidiser. Getting concentration calculations right is critical in medicine, food science, environmental monitoring and research.
Molar Concentration (Molarity)
Molarity is the most widely used concentration unit in chemistry. It expresses the number of moles of solute per litre of solution.
Formula: c = n / V
Where: c = molarity (mol/L, written M), n = moles of solute (mol), V = volume of solution (L)
Worked Example
How do you prepare 500 mL of a 0.1 M sodium chloride (NaCl) solution?
Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol
n = c × V = 0.1 mol/L × 0.5 L = 0.05 mol
mass = n × M = 0.05 × 58.5 = 2.925 g of NaCl dissolved in water and made up to 500 mL.
Mass Percentage Concentration
Mass percentage (% m/m) expresses grams of solute per 100 grams of solution. This is commonly used for acids, bases and commercial solutions.
Formula: w% = (m_solute / m_solution) × 100%
Worked Example
Commercial hydrochloric acid contains 36.5 g of HCl in 100 g of solution. Its mass percentage is therefore 36.5%. To find molarity given density 1.18 g/mL:
Mass of HCl per litre = 1.18 g/mL × 1000 mL × 0.365 = 430.7 g/L
Moles per litre = 430.7 / 36.5 = 11.8 M
Volume Percentage (% v/v)
Used for liquid mixtures, especially solutions of one liquid in another. Expresses millilitres of solute per 100 mL of solution.
Formula: %(v/v) = (V_solute / V_solution) × 100%
Vodka labelled 40% (v/v) contains 40 mL of ethanol in every 100 mL of product.
Molality
Molality expresses moles of solute per kilogram of solvent (not solution). It is temperature-independent because it is based on mass, not volume — making it preferred for calculations involving boiling point elevation and freezing point depression.
Formula: m = n / m_solvent(kg)
Worked Example
Calculate the molality of a solution made by dissolving 20 g of glucose (C6H12O6, molar mass 180 g/mol) in 250 g of water.
n = 20 / 180 = 0.111 mol
m_solvent = 0.250 kg
Molality = 0.111 / 0.250 = 0.444 mol/kg
Mole Fraction
The mole fraction of a component is the ratio of its moles to the total moles in the mixture. Used in thermodynamics and gas law calculations.
X_A = n_A / (n_A + n_B + ...)
Parts Per Million (ppm) and Parts Per Billion (ppb)
Used for very dilute solutions — drinking water standards, environmental pollutants, trace element analysis.
- 1 ppm = 1 mg of solute per 1 kg of solution (for dilute aqueous solutions ≈ 1 mg/L)
- 1 ppb = 1 μg per kg of solution
For example, the EU drinking water limit for lead is 10 μg/L = 10 ppb.
Converting Between Concentration Units
To convert molarity to mass percentage, you need the molar mass of the solute and the density of the solution:
w% = (c × M_solute) / (10 × ρ)
Where c is molarity in mol/L, M_solute is molar mass in g/mol, and ρ is density in g/mL.
Common Mistakes to Avoid
- Confusing mass of solution with mass of solvent when calculating percentages
- Forgetting to convert mL to L or g to kg before substituting into formulas
- Using volume percentage for solutions where mixing causes volume contraction (e.g., ethanol + water)
- Confusing molarity and molality — they are numerically similar for dilute aqueous solutions but differ for concentrated ones
Use the chemistry calculators at Liczbnik.pl to instantly convert between molarity, mass percentage, molality and other concentration units for your specific solute and solution.