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A solution forms when a solute dissolves in a solvent. The concentration of a solution is a measure of how 'crowded' the solute particles are. The more concentrated the solution, the more particles it contains in a given volume.

Calculating concentration

The concentration of a solution can be calculated using:

• the mass of dissolved solute in grams, g
• the volume of solution (or solvent) in cubic decimetres, dm³

The units for concentration can also be shown as g dm^-3, but this means the same as g/dm³.

Worked example

8 g of sodium hydroxide is dissolved in 2 dm³ of water. Calculate the concentration of the sodium hydroxide solution formed.

concentration = 4 g/dm³

Volume units

Apparatus used to measure volumes is usually marked in cm³ or ml. Although these are different units, they describe the same volume. For example, 250 ml = 250 cm³.

Volumes used in concentration calculations must be in dm³, not in cm³ or ml. It is useful to know that 1 dm³ = 1000 cm³. This means:

• divide by 1000 to convert from cm³ to dm³
• multiply by 1000 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.

Calculating the mass of solute

Rearranging the equation for concentration allows the mass of solute to be calculated:

mass of solute in g = concentration in g/dm³ × volume in dm³

Worked example

A solution of sodium chloride has a concentration of 10 g/dm³. What mass of sodium chloride is dissolved in 2 dm³ of the solution?

mass of solute in g = concentration in g/dm³ × volume in dm³

= 10 g/dm³ × 2 dm³

= 20 g

Higher tier

The concentration of a solution can be changed:

• concentration can be increased by dissolving more solute in a given volume of solution - this increases the mass of the solute
• concentration can be increased by allowing some of the solvent to evaporate - this decreases the volume of the solution