Concentration mol/dm³: definition and core relationship

Quantitative chemistry • Concentration of solutions

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Effect on number of moles when molar mass increases for the same mass

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The number of moles decreases because n = m / M and a larger M divides the same mass into fewer moles.

Key concepts

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Definition of concentration (mol/dm³)

Concentration in mol/dm³ equals the amount of substance (in moles) dissolved in one cubic decimetre of solution. The symbol c commonly represents concentration and the unit mol dm⁻³ (often written mol/dm³) describes moles per cubic decimetre. Concentration measures how many particles (moles) are present in a specified volume of solution.

Core mathematical relationship

The primary formula connects moles, volume and concentration: c = n / V where c is concentration (mol/dm³), n is amount of substance (mol) and V is volume (dm³). Cause → effect: when the amount of substance increases at constant volume, concentration increases; when volume increases at constant amount, concentration decreases. The formula provides the direct proportionalities required for calculations.

Link with mass of solute

Mass converts to amount in moles using the molar mass (molecular or formula mass): n = m / M where m is mass in grams and M is molar mass in g mol⁻¹. Combining with c = n / V yields c = m / (M × V). Cause → effect: a larger solute mass at fixed molar mass and fixed final volume causes a larger concentration; a larger molar mass for the same mass of substance causes a smaller concentration because fewer moles form from the same mass.

Units and conversions

Volume must be in cubic decimetres (dm³) for c to be in mol dm⁻³. Common laboratory volumes are measured in cm³ (mL); conversion uses 1000 cm³ = 1 dm³ so V(dm³) = V(cm³) ÷ 1000. Molar mass units must be g mol⁻¹ and mass in g so that n is in mol. Careful unit conversion prevents factor-of-1000 errors.

Key notes

Important points to keep in mind

Concentration c = n / V with V in dm³ yields c in mol dm⁻³.

Convert mass to moles using n = m / M with M in g mol⁻¹.

Convert cm³ (mL) to dm³ by dividing by 1000 before using V in the core equation.

Use the final solution volume; adding solute can change volume slightly.

Express final answers to a reasonable number of significant figures based on input measurements.