All subjects · Chemistry · WCH11 (Unit 1)

Concentration, dilution and parts per million

Concentration tells you how much solute is in a given volume of solution. You need it in mol/dm3 and g/dm3, and for very dilute mixtures in parts per million.

Two units

Convert between them with the molar mass: g/dm3 = mol/dm3 x M.

Dilution

Adding water does not change the number of moles of solute. So c1V1 = c2V2. Making 250 cm3 from 25.0 cm3 is a tenfold dilution: the concentration falls to one tenth. Use a pipette for the measured volume and a volumetric flask for the final volume.

Parts per million

For tiny amounts, such as pollutants in air or ions in water, use parts per million (ppm): ppm = (mass of solute / total mass) x 106. For gases, volumes are used the same way: 0.04% of the air is 400 ppm.

Worked example

What is the concentration in g/dm3 of 0.100 mol/dm3 sodium hydroxide? (Na = 23.0, O = 16.0, H = 1.0)

  1. M(NaOH) = 40.0 g/mol
  2. 0.100 x 40.0

Answer: 4.00 g/dm3

Key idea: c = n/V; g/dm3 = mol/dm3 x M; c1V1 = c2V2; ppm = (part / whole) x 106.

Check yourself

  1. 0.0250 mol of solute is dissolved to make 500 cm3 of solution. Find the concentration.
    Show answer

    0.0500 mol/dm3. c = 0.0250 / 0.500 = 0.0500 mol/dm3.

  2. A solution of sulfuric acid is 0.150 mol/dm3. Find its concentration in g/dm3. (H = 1.0, S = 32.1, O = 16.0)
    Show answer

    14.7 g/dm3. M(H2SO4) = 98.1; 0.150 x 98.1 = 14.7 g/dm3.

  3. 25.0 cm3 of 2.00 mol/dm3 HCl is diluted to 250 cm3. Find the new concentration.
    Show answer

    0.200 mol/dm3. c2 = c1V1 / V2 = 2.00 x 25.0 / 250 = 0.200 mol/dm3.

  4. A 2.00 kg water sample contains 0.0060 g of lead ions. Find the concentration in ppm.
    Show answer

    3.0 ppm. 0.0060 / 2000 x 106 = 3.0 ppm.

  5. Carbon dioxide makes up 0.042% of air by volume. What is this in ppm?
    Show answer

    420 ppm. 0.042 / 100 x 106 = 420 ppm.

  6. Which apparatus should be used to make up exactly 250.0 cm3 of a diluted solution?
    • A volumetric flask
    • A beaker
    • A measuring cylinder
    • A conical flask
    Show answer

    A volumetric flask. A volumetric flask is calibrated to contain one precise volume.

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Last updated 7 November 2026. Spotted a mistake? Tell us.