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The concentration of a solution can be measured in g dm^-3 or in mol dm^-3. It is more useful to know the concentration of a reactant in mol dm^-3 as the amount of reactant in a given volume can be calculated.

Concentration using moles

The concentration of a solution can be calculated using:

• the amount of dissolvedsolute in moles (mol)
• the volume of solution (or solvent) in cubic decimetres (dm³)

The units for concentration can also be shown as mol dm³ or M (for 'molar'), but these mean the same as mol dm³.

Worked example

0.5 mol of sodium hydroxide is dissolved in 2 dm³ of water. Calculate the concentration of the sodium hydroxide solution formed.

Concentration = 0.25 mol dm^-3

Volume units

Volumes used in concentration calculations must be in dm³, not in cm³. It is useful to know that 1 dm³ = 1,000 cm³. This means:

• divide by 1,000 to convert from cm³ to dm³
• multiply by 1,000 to convert from dm³ to cm³

For example, 250 cm³ is 0.25 dm³ (250 ÷ 1000). It is often easiest to convert from cm³ to dm³ before continuing with a concentration calculation.

Converting between units

The relative formula mass, M_r, of the solute is used to convert between mol dm^-3 and g dm^-3:

• to convert from mol dm^-3 to g dm^-3, multiply by the M_r
• to convert from g dm^-3 to mol dm^-3, divide by the M_r

Worked example

Calculate the concentration of 0.1 mol dm^-3 sodium hydroxide solution in g dm^-3. (M_r of NaOH = 40)

Concentration = 0.1 × 40

= 4 g dm^-3