➗ cm3 to dm3
Divide by 1000.
250 cm3 ÷ 1000 = 0.25 dm3
50 cm3 ÷ 1000 = 0.050 dm3
Moles » Concentration of Solutions
What you'll learn this session
Study time: 30 minutes
AQA spec: 4.3.2.5
- What the concentration of a solution means
- How to measure concentration in grams per dm3 (g/dm3)
- How to convert cm3 to dm3
- How to calculate the mass of solute in a solution, and work back the other way
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Unlock This CourseWhat is concentration?
More squash in the same water means a stronger drink: concentration is mass of solute per dm³ of solution
Many chemical reactions take place in solutions. Remember, a solution is made when a solute dissolves in a solvent, such as water.
Think about making a glass of squash. A small splash of squash in a big glass of water tastes weak. A lot of squash in a small amount of water tastes strong. The difference is how much squash there is in each bit of the drink. Chemists call this the concentration.
The concentration of a solution tells you how much solute is dissolved in a certain volume of the solution. It can be measured as a mass per given volume of solution. At GCSE, the unit we use for this is grams per dm3, written g/dm3.
So a sugar solution with a concentration of 50 g/dm3 has 50 g of sugar dissolved in every 1 dm3 of solution.
Key terms:
- Concentration: the mass of solute dissolved in a given volume of solution, for example in g/dm3.
- Cubic decimetre (dm3): a unit of volume. 1 dm3 = 1000 cm3 = 1 litre.
Converting cm3 to dm3
In the lab, you usually measure volumes in cm3, for example with a measuring cylinder. But concentration in g/dm3 needs the volume in dm3. So you often need to convert first.
✖ dm3 to cm3
Multiply by 1000.
0.4 dm3 × 1000 = 400 cm3
2 dm3 × 1000 = 2000 cm3
A quick check: a volume in dm3 should always be a smaller number than the same volume in cm3, because a dm3 is a much bigger unit.
The concentration equation
To work out concentration in g/dm3, use this equation:
Equation
concentration (g/dm3) = mass of solute (g) ÷ volume of solution (dm3)
You can change the subject of the equation to find the other two quantities:
⚖ Find concentration
concentration = mass ÷ volume
⚙ Find mass
mass = concentration × volume
⚗ Find volume
volume = mass ÷ concentration
Note that the volume is the volume of the whole solution, not just the water you started with.
Worked example 1: finding concentration
25 g of glucose is dissolved in water to make 0.50 dm3 of solution. Calculate the concentration in g/dm3.
concentration = 25 ÷ 0.50 = 50 g/dm3
Worked example 2: converting the volume first
4.0 g of potassium nitrate is dissolved in water to make 250 cm3 of solution. Calculate the concentration in g/dm3.
Step 1: volume = 250 ÷ 1000 = 0.250 dm3
Step 2: concentration = 4.0 ÷ 0.250 = 16 g/dm3
Calculating the mass of solute
Blue copper sulfate dissolving: concentration × volume in dm³ tells you how many grams are in the flask
You must be able to calculate the mass of solute in a given volume of a solution when you know its concentration. Multiply the concentration by the volume in dm3.
Worked example 3: finding the mass
A bottle contains sodium hydroxide solution with a concentration of 30 g/dm3. What mass of sodium hydroxide is in 200 cm3 of this solution?
Step 1: volume = 200 ÷ 1000 = 0.200 dm3
Step 2: mass = 30 × 0.200 = 6.0 g
Worked example 4: finding the volume
A magnesium sulfate solution has a concentration of 40 g/dm3. What volume of this solution contains 10 g of magnesium sulfate? Give your answer in cm3.
Step 1: volume = 10 ÷ 40 = 0.25 dm3
Step 2: 0.25 × 1000 = 250 cm3
A good sense check: if the volume is less than 1 dm3, the mass of solute must be less than the number in the concentration. In example 3, 200 cm3 is a fifth of a dm3, so it holds a fifth of 30 g, which is 6 g.
Higher tier only
How mass and volume affect concentration
You need to explain how the mass of solute and the volume of solution are related to the concentration. Look at the equation: concentration = mass ÷ volume.
- More solute, same volume: the concentration goes up. Concentration is directly proportional to the mass of solute. Double the mass and the concentration doubles.
- Same solute, bigger volume: the concentration goes down. Concentration is inversely proportional to the volume. Double the volume and the concentration halves.
- Adding water to a solution: the mass of solute stays the same, but the volume increases. So the solution becomes less concentrated.
- Pouring some solution out: the concentration of the part you pour out is the same. It holds less solute, but it also has a smaller volume, so the ratio of mass to volume does not change.
For example, 20 g of solute in 500 cm3 of solution has a concentration of 20 ÷ 0.500 = 40 g/dm3. If water is added to make the volume 1000 cm3, there is still 20 g of solute, so the concentration becomes 20 ÷ 1.000 = 20 g/dm3. The volume doubled, so the concentration halved.
Common mistakes
Forgetting to convert cm3 to dm3. 4.0 g in 250 cm3 is not 4.0 ÷ 250 = 0.016 g/dm3. That answer is 1000 times too small.
Converting the wrong way. Students multiply by 1000 instead of dividing. Ask yourself if the number should get smaller (cm3 to dm3) or bigger (dm3 to cm3).
Dividing the wrong way round. Concentration is mass ÷ volume, not volume ÷ mass. Checking the unit helps: g/dm3 means grams divided by dm3.
Missing or wrong units. Always write g/dm3 after a concentration and g after a mass.
Exam-style question
A student dissolves 12.5 g of magnesium sulfate in water. They make the solution up to a total volume of 250 cm3.
(a) Calculate the concentration of the solution in g/dm3. [2 marks]
(b) Calculate the mass of magnesium sulfate in 40 cm3 of this solution. [2 marks]
(c) (Higher tier only) The student adds water to the solution until the total volume is 500 cm3. Explain what happens to the concentration. [2 marks]
Model answer
(a) volume = 250 ÷ 1000 = 0.250 dm3 (1 mark). concentration = 12.5 ÷ 0.250 = 50 g/dm3 (1 mark).
(b) volume = 40 ÷ 1000 = 0.040 dm3 (1 mark). mass = 50 × 0.040 = 2.0 g (1 mark).
(c) The mass of magnesium sulfate stays the same, but the volume of solution doubles (1 mark). So the concentration halves, to 25 g/dm3 (1 mark).
Exam tip
Before you put any volume into the equation, look at the unit. If it is in cm3, divide by 1000 first. Show this step in your working, because it can earn you a mark even if your final answer is wrong.