Concentration of Solutions

This lesson covers the concentration of solutions as required by the AQA GCSE Chemistry specification (4.3.3). You need to be able to calculate concentration in g/dm3, convert between cm3 and dm3, and (at Higher Tier) work with concentration in mol/dm3. Understanding concentration is essential for titration calculations and for many practical chemistry applications.

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What Is Concentration?

The concentration of a solution tells you how much solute is dissolved in a given volume of solvent (or solution). A solution with a lot of solute dissolved is described as concentrated; one with very little solute is described as dilute.

Term	Definition
Solute	The substance that dissolves (e.g. salt, sugar, acid)
Solvent	The liquid the solute dissolves in (usually water)
Solution	The mixture formed when a solute dissolves in a solvent
Concentration	The amount of solute per unit volume of solution

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Units of Volume

In chemistry, volumes are measured in cm3 (cubic centimetres) or dm3 (cubic decimetres, also known as litres).

1 dm3 = 1000 cm3 = 1 litre

To convert:

• cm3 to dm3: divide by 1000
• dm3 to cm3: multiply by 1000

Volume in cm3	Volume in dm3
100 cm3	0.1 dm3
250 cm3	0.25 dm3
500 cm3	0.5 dm3
1000 cm3	1.0 dm3
25 cm3	0.025 dm3

Exam Tip: The most common mistake in concentration calculations is forgetting to convert cm3 to dm3. If the volume is given in cm3, divide by 1000 before using it in the concentration formula. Always check your units before calculating.

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Concentration in g/dm3

The concentration in grams per cubic decimetre (g/dm3) tells you the mass of solute dissolved in 1 dm3 of solution.

Concentration (g/dm3) = mass of solute (g) / volume of solution (dm3)

This can be rearranged:

• mass = concentration x volume
• volume = mass / concentration

Worked Example 1

A solution contains 20 g of sodium chloride dissolved in 500 cm3 of water. Calculate the concentration in g/dm3.

Step 1: Convert volume to dm3: 500 / 1000 = 0.5 dm3

Step 2: concentration = mass / volume = 20 / 0.5 = 40 g/dm3

Worked Example 2

What mass of glucose is dissolved in 250 cm3 of a 10 g/dm3 solution?

Step 1: Convert volume: 250 / 1000 = 0.25 dm3

Step 2: mass = concentration x volume = 10 x 0.25 = 2.5 g

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Concentration Calculation Steps

graph TD
    A["Identify: mass, volume, concentration"] --> B{"Volume in dm3?"}
    B -->|"No"| C["Convert cm3 to dm3: divide by 1000"]
    B -->|"Yes"| D["Use the formula directly"]
    C --> D
    D --> E["concentration = mass / volume"]
    D --> F["mass = concentration x volume"]
    D --> G["volume = mass / concentration"]

    style A fill:#3498db,color:#fff
    style B fill:#e67e22,color:#fff
    style C fill:#e74c3c,color:#fff
    style D fill:#27ae60,color:#fff
    style E fill:#9b59b6,color:#fff
    style F fill:#9b59b6,color:#fff
    style G fill:#9b59b6,color:#fff

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Concentration in mol/dm3 [H]

At Higher Tier, you also need to work with concentration in moles per cubic decimetre (mol/dm3).

Concentration (mol/dm3) = moles of solute / volume of solution (dm3)

This can be rearranged:

• moles = concentration x volume
• volume = moles / concentration

Worked Example 3 [H]

What is the concentration in mol/dm3 of a solution containing 0.2 mol of HCl in 500 cm3?

Step 1: Convert volume: 500 / 1000 = 0.5 dm3

Step 2: concentration = moles / volume = 0.2 / 0.5 = 0.4 mol/dm3

Worked Example 4 [H]

How many moles of NaOH are in 250 cm3 of a 2.0 mol/dm3 solution?

Step 1: Convert volume: 250 / 1000 = 0.25 dm3

Step 2: moles = concentration x volume = 2.0 x 0.25 = 0.5 mol

Exam Tip: There are two types of concentration at Higher Tier: g/dm3 and mol/dm3. Make sure you read the question carefully to determine which one is being asked for. The formulas look similar but use different quantities (mass vs moles).

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Converting Between g/dm3 and mol/dm3 [H]

To convert between the two concentration units, you need the Mr of the solute:

Concentration in g/dm3 = concentration in mol/dm3 x Mr

Concentration in mol/dm3 = concentration in g/dm3 / Mr

Worked Example 5 [H]

Convert 4.0 g/dm3 NaOH solution to mol/dm3.

• Mr of NaOH = 23 + 16 + 1 = 40
• concentration in mol/dm3 = 4.0 / 40 = 0.1 mol/dm3

Worked Example 6 [H]

A solution of H2SO4 has a concentration of 0.5 mol/dm3. What is this in g/dm3?

• Mr of H2SO4 = (2 x 1) + 32 + (4 x 16) = 98
• concentration in g/dm3 = 0.5 x 98 = 49 g/dm3

Exam Tip: To convert g/dm3 to mol/dm3, divide by Mr. To convert mol/dm3 to g/dm3, multiply by Mr. Think of it as: grams are "bigger" than moles, so you multiply moles by Mr to get grams.

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Dilution

When you add more water to a solution, the concentration decreases but the amount of solute stays the same.

amount of solute before dilution = amount of solute after dilution

In terms of mass: mass = concentration (g/dm3) x volume (dm3)

In terms of moles [H]: moles = concentration (mol/dm3) x volume (dm3)

Worked Example 7

100 cm3 of a 50 g/dm3 NaCl solution is diluted to 500 cm3. What is the new concentration?

Step 1: mass of NaCl = 50 x (100/1000) = 5 g

Step 2: New concentration = 5 / (500/1000) = 5 / 0.5 = 10 g/dm3

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Summary Table of Key Formulae

Formula	Used For	Units
concentration = mass / volume	Finding concentration in g/dm3	g/dm3
mass = concentration x volume	Finding mass of solute	g
concentration = moles / volume [H]	Finding concentration in mol/dm3	mol/dm3
moles = concentration x volume [H]	Finding moles of solute	mol
g/dm3 = mol/dm3 x Mr [H]	Converting mol/dm3 to g/dm3	g/dm3
mol/dm3 = g/dm3 / Mr [H]	Converting g/dm3 to mol/dm3	mol/dm3

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Additional Worked Examples