C4.4 Expressing Concentrations

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: concentration in g/dm³, making up a solution, converting units of volume and mass, and how mass and volume affect concentration. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• Calculate the mass concentration of a solution in g/dm³ and rearrange the equation to find a mass or a volume
• Convert volumes between cm³, dm³ and m³, and masses between mg, g, kg and tonnes
• Describe how to make up a solution of known concentration in a volumetric flask
• (Higher tier) explain how the mass of solute and the volume of solution affect the concentration

Key words

• Solute: The substance that dissolves (for example, salt).
• Solvent: The liquid that the solute dissolves in (for example, water).
• Solution: The mixture formed when a solute dissolves in a solvent.
• Concentration: The mass of solute in each dm³ of solution, in g/dm³.
• dm³ (cubic decimetre): A volume equal to 1000 cm³, the same as 1 litre.
• Dilute / concentrated: A dilute solution has a small mass of solute in each dm³; a concentrated one has a large mass of solute in each dm³.

Mass concentration in g/dm³

The concentration of a solution tells you how much solute is dissolved in each cubic decimetre (dm³) of solution. A deeper-coloured solution of copper sulfate, for example, has more grams of solute in every dm³.

concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)

rearranged: mass (g) = concentration × volume (dm³); volume (dm³) = mass ÷ concentration

Volumes in the lab are usually measured in cm³. There are 1000 cm³ in 1 dm³, so divide cm³ by 1000 to get dm³. For example, 150 cm³ = 150 ÷ 1000 = 0.150 dm³.

Worked example: 7.5 g of sodium chloride dissolved to make 150 cm³ of solution

volume = 150 ÷ 1000 = 0.150 dm³
concentration = 7.5 ÷ 0.150 = 50 g/dm³

Answer: 50 g/dm³

Worked example: mass of solute in 300 cm³ of a 30 g/dm³ solution

volume = 300 ÷ 1000 = 0.300 dm³
mass = concentration × volume = 30 × 0.300 = 9.0 g

Answer: 9.0 g

Making up a solution of known concentration

To make an accurate solution, chemists use a volumetric flask. It is designed to hold one exact volume when filled to its graduation mark.

• Weigh the solute accurately into a beaker and dissolve it in a little distilled water.
• Pour the solution into the volumetric flask through a funnel. Rinse the beaker and funnel with distilled water and add the rinsings, so no solute is left behind.
• Add distilled water until the bottom of the meniscus is on the graduation mark (add the last drops with a dropping pipette, reading at eye level).
• Stopper the flask and turn it upside down several times so the solution is evenly mixed.

Worked example: what to weigh out

A technician needs 250 cm³ of a 20 g/dm³ solution of potassium nitrate.
mass = 20 × 0.250 = 5.0 g

Answer: weigh 5.0 g, then make up to the mark in a 250 cm³ flask

What changes the concentration? (Higher tier)

• More solute in the same volume → more concentrated (A → B). Concentration is proportional to the mass of solute.
• Less solution (smaller volume) with the same solute → more concentrated (A → C). Halving the volume doubles the concentration.
• Adding water (diluting) spreads the same solute through a bigger volume → less concentrated.

Worked example: diluting a solution

50 cm³ of a 60 g/dm³ solution is made up to 200 cm³ with water.
mass of solute = 60 × 0.050 = 3.0 g (this does not change)
new concentration = 3.0 ÷ 0.200 = 15 g/dm³

Answer: 15 g/dm³ (volume × 4, so concentration ÷ 4)

Key fact: When you dilute a solution, the mass of solute stays the same. Only the volume changes.

Converting units

Concentration calculations need the mass in grams and the volume in dm³. Each step between neighbouring units in the chart (drawn in the printable lesson notes) is a factor of 1000. Think logically: going to a smaller unit gives a bigger number.

Worked example: unit conversions

35 cm³ = 35 ÷ 1000 = 0.035 dm³
0.6 m³ = 0.6 × 1000 = 600 dm³
450 mg = 450 ÷ 1000 = 0.450 g
2.5 tonnes = 2.5 × 1000 × 1000 = 2 500 000 g (2.5 × 10⁶ g)

Answer: always check the units before you calculate

Worked example: a concentration from milligrams

A water sample contains 600 mg of dissolved salts in 250 cm³.
mass = 600 ÷ 1000 = 0.600 g; volume = 0.250 dm³
concentration = 0.600 ÷ 0.250 = 2.4 g/dm³

Answer: 2.4 g/dm³

Exam tip: If the volume is in cm³, divide by 1000 before you use it in the concentration equation. Show the conversion as a separate line of working – it often earns a mark.

Common mistakes

• Using cm³ in the equation. 7.5 g in 150 cm³ is not 0.05 g/dm³ – convert to 0.150 dm³ first.
• Multiplying by 1000 when converting cm³ to dm³. A dm³ is bigger, so the number gets smaller.
• Thinking dilution changes the mass of solute. Adding water changes the volume only.
• Forgetting that 1 tonne = 1 000 000 g: there are two steps of 1000 between tonnes and grams.

Revision questions

Try these, then check your answers below each one.

Question 1. 12 g of salt is dissolved to make 0.40 dm³ of solution. Calculate the concentration in g/dm³.

Answer: 30 g/dm³

Working: 12 ÷ 0.40 = 30 g/dm³.

Question 2. 3.0 g of copper sulfate is dissolved to make 150 cm³ of solution. Calculate the concentration in g/dm³.

Answer: 20 g/dm³

Working: 150 cm³ = 0.150 dm³; 3.0 ÷ 0.150 = 20 g/dm³.

Question 3. How many cm³ are there in 1 dm³? (Choose from: 10, 100, 1000, 1 000 000.)

Answer: 1000

Working: 1 dm³ = 10 cm × 10 cm × 10 cm = 1000 cm³.

Related lessons

• Previous lesson: C4.2–3 Equations and Calculations and From Masses to Balanced Equations
• Next lesson: C5.1 The Reactivity Series
• In this chapter: C4.1 Relative Masses and Moles

Continue in the full course

This lesson is section C4.4 (AGCSC2103) of our free GCSE Combined Science course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Combined Science course.