Concentration of solutions

What you'll learn

What solute, solvent, solution and concentration mean.
How to use concentration in grams per cubic decimetre, g/dm³.
How to calculate the mass of solute in a known volume of solution.
How changing mass or volume affects concentration, especially for Higher Tier explanations.

Why concentration matters

Many chemical reactions happen in solutions, because dissolved particles can move around and collide with other particles. For example, copper sulfate can dissolve in water to make a blue copper sulfate solution.

To describe how “strong” a solution is, chemists use concentration.

Definition

Solutions

A solute is the substance that dissolves.
A solvent is the liquid that does the dissolving.
A solution is the mixture formed when a solute dissolves in a solvent.
Aqueous, written as (aq), means dissolved in water.

The same solute can make a more concentrated or less concentrated solution depending on how much solute is dissolved and what final volume the solution has.

Diagram comparing lower and higher concentration solutions using solute particles and solution volume

What concentration means

Concentration tells you the amount of solute in a certain volume of solution.

A more concentrated solution has more solute per unit volume. A more dilute solution has less solute per unit volume.

Definition

Concentration in g/dm³

In this topic, concentration is measured as mass of solute per volume of solution:

\frac{m}{V}

where $c$ is concentration in g/dm³, $m$ is mass of solute in g, and $V$ is volume of solution in dm³.

So, if you dissolve more solute in the same volume, the concentration increases. If you add more solvent so the final volume increases, the concentration decreases.

Key Idea

The big idea

Concentration is a ratio: it compares mass of solute with volume of solution.

The units: g/dm³ and cm³

At GCSE, concentration is often measured in grams per cubic decimetre, written as g/dm³.

A cubic decimetre is the same as a litre.

You also need to be confident converting between cm³ and dm³:

cm31\ \text{dm}^{3} = 1000\ \text{cm}^{3}

So:

cm31000V\ \text{in dm}^{3} = \frac{V\ \text{in cm}^{3}}{1000}

This matters because exam questions often give volumes in cm³, but concentration calculations usually need volume in dm³.

Example

Converting a volume

A student uses 250 cm³ of solution. Convert this volume into dm³.

Use the conversion from cm³ to dm³, so divide by 1000:
$\frac{250}{1000}$
Calculate the volume:
$0.250\ \text{dm}^{3}$
Check the size of the answer: 250 cm³ is less than 1000 cm³, so the answer should be less than 1 dm³.

Common Mistake

Forgetting to convert volume

If the concentration is in g/dm³, the volume must be in dm³ before you substitute into the formula. Do not put 250 cm³ straight into $\frac{m}{V}$ unless the units are designed for cm³.

Calculating concentration

If you know the mass of solute and the volume of solution, use:

\frac{m}{V}

The answer tells you how many grams of solute there are in 1 dm³ of solution.

Example

Calculating concentration

A student dissolves 6.0 g of sodium chloride in water and makes 200 cm³ of solution. Calculate the concentration in g/dm³.

Convert the volume into dm³ because the answer needs g/dm³:
$\frac{200}{1000} = 0.200\ \text{dm}^{3}$
Substitute into the concentration formula:
$\frac{m}{V} = \frac{6.0}{0.200}$
Calculate the concentration:
$30\ \text{g/dm}^{3}$

Calculating the mass of solute

The spec specifically expects you to calculate the mass of solute in a given volume of solution when the concentration is known.

Start with:

\frac{m}{V}

To find mass, rearrange the equation:

m = c V

This means:

mass of solute = concentration × volume of solution

Example

Calculating mass of solute

A solution has a concentration of 40 g/dm³. Calculate the mass of solute in 250 cm³ of solution.

Convert the volume into dm³:
$\frac{250}{1000} = 0.250\ \text{dm}^{3}$
Choose the rearranged equation because the question asks for mass:
$m = c V$
Substitute the values, including units:
$40\ \text{g/dm}^{3} \times 0.250\ \text{dm}^{3}$
Calculate the mass:
$10\ \text{g}$

Tip

Quick unit check

In $m = c V$ , the dm³ units cancel: g/dm³ × dm³ gives g. That tells you your answer is a mass.

Calculating volume

Sometimes you may need to find the volume of solution instead. Rearrange the formula to make volume the subject:

\frac{m}{c}

This gives the volume in dm³ if the mass is in g and concentration is in g/dm³.

Example

Calculating volume of solution

A solution has a concentration of 25 g/dm³. What volume of solution contains 5.0 g of solute?

Choose the rearranged equation for volume:
$\frac{m}{c}$
Substitute the known values:
$\frac{5.0}{25}$
Calculate the volume in dm³:
$0.20\ \text{dm}^{3}$
Convert to cm³ if a lab-style volume is more useful:
$cm30.20\ \text{dm}^{3} = 200\ \text{cm}^{3}$

Higher Tier: explaining the relationship

This part is Higher Tier only: you may need to explain how mass, volume and concentration are related.

From the equation:

\frac{m}{V}

you can see two important relationships.

If the volume stays the same, concentration is directly proportional to the mass of solute. That means doubling the mass doubles the concentration.

If the mass of solute stays the same, concentration is inversely proportional to the volume of solution. That means doubling the volume halves the concentration.

Key Idea

Mass and volume relationships

Same volume: more mass of solute means higher concentration.
Same mass of solute: larger volume of solution means lower concentration.
Adding solvent without adding solute is called dilution.

Example

Explaining changes in concentration

A solution contains 20 g of solute in 0.500 dm³ of solution.

Calculate the original concentration:
$\frac{20}{0.500} = 40\ \text{g/dm}^{3}$
If the same 20 g of solute is made up to 1.000 dm³, compare the volume: the volume has doubled.
Because the mass is unchanged but the volume has doubled, the concentration halves:
new concentration = 20 g/dm³.
If instead the volume stayed at 0.500 dm³ but the mass increased to 40 g, the mass would double, so the concentration would double to 80 g/dm³.

Common Mistake

Using volume of solvent instead of volume of solution

Concentration uses the final volume of the solution, not just the volume of water added. In practical work, a solution is often made up to a final mark, such as 250 cm³.

Putting it together

For GCSE concentration calculations, your main job is to match the information in the question to the correct form of the equation.

If you need to find...	Use...
concentration	$\frac{m}{V}$
mass of solute	$m = c V$
volume of solution	$\frac{m}{c}$

Before calculating, always check the units. If the concentration is in g/dm³, the volume must be in dm³.

Exam technique

In the exam

Identify what the question is asking for: concentration, mass, or volume.
Convert cm³ to dm³ before using a concentration in g/dm³.
Write the equation, substitute values with units, then check that your final unit matches the quantity you calculated.

Self review

Check yourself

What is the difference between a solute, a solvent and a solution?
How many dm³ are there in 100 cm³?
If you keep the mass of solute the same but double the volume of solution, what happens to the concentration?

Concentration of solutions

What you'll learn

What solute, solvent, solution and concentration mean.
How to use concentration in grams per cubic decimetre, g/dm³.
How to calculate the mass of solute in a known volume of solution.
How changing mass or volume affects concentration, especially for Higher Tier explanations.

Why concentration matters

To describe how “strong” a solution is, chemists use concentration.

Definition

Solutions

A solute is the substance that dissolves.
A solvent is the liquid that does the dissolving.
A solution is the mixture formed when a solute dissolves in a solvent.
Aqueous, written as (aq), means dissolved in water.

The same solute can make a more concentrated or less concentrated solution depending on how much solute is dissolved and what final volume the solution has.

Diagram comparing lower and higher concentration solutions using solute particles and solution volume

What concentration means

Concentration tells you the amount of solute in a certain volume of solution.

A more concentrated solution has more solute per unit volume. A more dilute solution has less solute per unit volume.

Definition

Concentration in g/dm³

In this topic, concentration is measured as mass of solute per volume of solution:

\frac{m}{V}

where $c$ is concentration in g/dm³, $m$ is mass of solute in g, and $V$ is volume of solution in dm³.

So, if you dissolve more solute in the same volume, the concentration increases. If you add more solvent so the final volume increases, the concentration decreases.

Key Idea

The big idea

Concentration is a ratio: it compares mass of solute with volume of solution.

The units: g/dm³ and cm³

At GCSE, concentration is often measured in grams per cubic decimetre, written as g/dm³.

A cubic decimetre is the same as a litre.

You also need to be confident converting between cm³ and dm³:

cm31\ \text{dm}^{3} = 1000\ \text{cm}^{3}

So:

cm31000V\ \text{in dm}^{3} = \frac{V\ \text{in cm}^{3}}{1000}

This matters because exam questions often give volumes in cm³, but concentration calculations usually need volume in dm³.

Example

Converting a volume

A student uses 250 cm³ of solution. Convert this volume into dm³.

Use the conversion from cm³ to dm³, so divide by 1000:
$\frac{250}{1000}$
Calculate the volume:
$0.250\ \text{dm}^{3}$
Check the size of the answer: 250 cm³ is less than 1000 cm³, so the answer should be less than 1 dm³.

Common Mistake

Forgetting to convert volume

If the concentration is in g/dm³, the volume must be in dm³ before you substitute into the formula. Do not put 250 cm³ straight into $\frac{m}{V}$ unless the units are designed for cm³.

Calculating concentration

If you know the mass of solute and the volume of solution, use:

\frac{m}{V}

The answer tells you how many grams of solute there are in 1 dm³ of solution.

Example

Calculating concentration

A student dissolves 6.0 g of sodium chloride in water and makes 200 cm³ of solution. Calculate the concentration in g/dm³.

Convert the volume into dm³ because the answer needs g/dm³:
$\frac{200}{1000} = 0.200\ \text{dm}^{3}$
Substitute into the concentration formula:
$\frac{m}{V} = \frac{6.0}{0.200}$
Calculate the concentration:
$30\ \text{g/dm}^{3}$

Calculating the mass of solute

The spec specifically expects you to calculate the mass of solute in a given volume of solution when the concentration is known.

Start with:

\frac{m}{V}

To find mass, rearrange the equation:

m = c V

This means:

mass of solute = concentration × volume of solution

Example

Calculating mass of solute

A solution has a concentration of 40 g/dm³. Calculate the mass of solute in 250 cm³ of solution.

Convert the volume into dm³:
$\frac{250}{1000} = 0.250\ \text{dm}^{3}$
Choose the rearranged equation because the question asks for mass:
$m = c V$
Substitute the values, including units:
$40\ \text{g/dm}^{3} \times 0.250\ \text{dm}^{3}$
Calculate the mass:
$10\ \text{g}$

Tip

Quick unit check

In $m = c V$ , the dm³ units cancel: g/dm³ × dm³ gives g. That tells you your answer is a mass.

Calculating volume

Sometimes you may need to find the volume of solution instead. Rearrange the formula to make volume the subject:

\frac{m}{c}

This gives the volume in dm³ if the mass is in g and concentration is in g/dm³.

Example

Calculating volume of solution

A solution has a concentration of 25 g/dm³. What volume of solution contains 5.0 g of solute?

Choose the rearranged equation for volume:
$\frac{m}{c}$
Substitute the known values:
$\frac{5.0}{25}$
Calculate the volume in dm³:
$0.20\ \text{dm}^{3}$
Convert to cm³ if a lab-style volume is more useful:
$cm30.20\ \text{dm}^{3} = 200\ \text{cm}^{3}$

Higher Tier: explaining the relationship

This part is Higher Tier only: you may need to explain how mass, volume and concentration are related.

From the equation:

\frac{m}{V}

you can see two important relationships.

If the volume stays the same, concentration is directly proportional to the mass of solute. That means doubling the mass doubles the concentration.

If the mass of solute stays the same, concentration is inversely proportional to the volume of solution. That means doubling the volume halves the concentration.

Key Idea

Mass and volume relationships

Same volume: more mass of solute means higher concentration.
Same mass of solute: larger volume of solution means lower concentration.
Adding solvent without adding solute is called dilution.

Example

Explaining changes in concentration

A solution contains 20 g of solute in 0.500 dm³ of solution.

Calculate the original concentration:
$\frac{20}{0.500} = 40\ \text{g/dm}^{3}$
If the same 20 g of solute is made up to 1.000 dm³, compare the volume: the volume has doubled.
Because the mass is unchanged but the volume has doubled, the concentration halves:
new concentration = 20 g/dm³.
If instead the volume stayed at 0.500 dm³ but the mass increased to 40 g, the mass would double, so the concentration would double to 80 g/dm³.

Common Mistake

Using volume of solvent instead of volume of solution

Concentration uses the final volume of the solution, not just the volume of water added. In practical work, a solution is often made up to a final mark, such as 250 cm³.

Putting it together

For GCSE concentration calculations, your main job is to match the information in the question to the correct form of the equation.

If you need to find...	Use...
concentration	$\frac{m}{V}$
mass of solute	$m = c V$
volume of solution	$\frac{m}{c}$

Before calculating, always check the units. If the concentration is in g/dm³, the volume must be in dm³.

Exam technique

In the exam

Identify what the question is asking for: concentration, mass, or volume.
Convert cm³ to dm³ before using a concentration in g/dm³.
Write the equation, substitute values with units, then check that your final unit matches the quantity you calculated.

Self review

Check yourself

What is the difference between a solute, a solvent and a solution?
How many dm³ are there in 100 cm³?
If you keep the mass of solute the same but double the volume of solution, what happens to the concentration?

Concentration of solutions

What you'll learn

Why concentration matters

What concentration means

The units: g/dm³ and cm³

Calculating concentration

Calculating the mass of solute

Calculating volume

Higher Tier: explaining the relationship

Putting it together

You've reached the end

Concentration of solutions

What you'll learn

Why concentration matters

What concentration means

The units: g/dm³ and cm³

Calculating concentration

Calculating the mass of solute

Calculating volume

Higher Tier: explaining the relationship

Putting it together

You've reached the end

Concentration of solutions

What you'll learn

Why concentration matters

What concentration means

The units: g/dm³ and cm³

Calculating concentration

Calculating the mass of solute

Calculating volume

Higher Tier: explaining the relationship

Putting it together

You've reached the end

Concentration of solutions Revision Guide

Concentration of solutions

What you'll learn

Why concentration matters

What concentration means

The units: g/dm³ and cm³

Calculating concentration

Calculating the mass of solute

Calculating volume

Higher Tier: explaining the relationship

Putting it together

You've reached the end

Concentration of solutions Revision Guide