What Is Concentration?

A solution forms when a substance called the solute dissolves in another substance called the solvent.

For example, when salt dissolves in water:

• Salt is the solute.
• Water is the solvent.
• Salt water is the solution.

Concentration tells us how much solute is present in a particular volume of solution.

A solution containing a large amount of solute in a given volume is more concentrated than one containing less solute in the same volume.

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Dilute and Concentrated Solutions

A dilute solution contains a relatively small amount of solute compared with the amount of solution.

A concentrated solution contains a relatively large amount of solute.

For example:

Solution A contains 2 g of salt in 100 cm³ of solution.

Solution B contains 10 g of salt in 100 cm³ of solution.

Solution B is more concentrated because it contains more solute in the same volume.

However, simply comparing the mass of solute is not always enough. We must also consider the volume of the solution.

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Calculating Concentration

When concentration is measured using mass and volume, we use:

concentration = mass of solute ÷ volume of solution

In symbols:

c = m ÷ V

where:

• c = concentration
• m = mass of solute
• V = volume of solution

A common unit is:

g/dm³

This means grams of solute per cubic decimeter of solution.

Another possible unit is:

g/cm³

Always check the units given in the question.

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Understanding g/dm³

Suppose a solution has a concentration of:

20 g/dm³

This means that every:

1 dm³ of solution

contains:

20 g of solute

Since:

1 dm³ = 1000 cm³

a concentration of 20 g/dm³ also means that 1000 cm³ of the solution contains 20 g of solute.

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Worked Example: Calculating Concentration

A student dissolves 15 g of salt to make 0.5 dm³ of solution.

Use:

concentration = mass ÷ volume

Substitute:

concentration = 15 ÷ 0.5

Therefore:

concentration = 30 g/dm³

The solution contains 30 g of salt per dm³ of solution.

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Converting Volume Units

Many concentration questions give volume in cm³, but require concentration in g/dm³.

Remember:

1000 cm³ = 1 dm³

Therefore:

cm³ → dm³: divide by 1000

and:

dm³ → cm³: multiply by 1000

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Worked Example: Converting cm³ to dm³

Convert 250 cm³ to dm³.

250 ÷ 1000 = 0.250 dm³

Therefore:

250 cm³ = 0.250 dm³

This conversion should usually be completed before calculating a concentration in g/dm³.

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Worked Example: Concentration with Unit Conversion

A solution contains 8 g of sugar in 200 cm³ of solution.

First convert the volume:

200 cm³ ÷ 1000 = 0.200 dm³

Now calculate:

concentration = 8 ÷ 0.200

concentration = 40 g/dm³

Therefore, the concentration is:

40 g/dm³

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A Reliable Problem-Solving Method

For concentration calculations:

Step 1: Identify the mass of solute.

Step 2: Identify the volume of solution.

Step 3: Check the units.

Step 4: Convert the volume if necessary.

Step 5: Use concentration = mass ÷ volume.

Step 6: Substitute the values.

Step 7: Calculate.

Step 8: Include the correct unit.

This method helps prevent many common mistakes.

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Rearranging the Concentration Equation

The concentration equation can also be used to calculate mass or volume.

Starting with:

concentration = mass ÷ volume

we can rearrange it.

To calculate mass:

mass = concentration × volume

To calculate volume:

volume = mass ÷ concentration

So we have three useful relationships:

concentration = mass ÷ volume

mass = concentration × volume

volume = mass ÷ concentration

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Worked Example: Calculating Mass

A solution has a concentration of 25 g/dm³ and a volume of 2 dm³.

Use:

mass = concentration × volume

Substitute:

mass = 25 × 2

Therefore:

mass = 50 g

There are 50 g of solute in the solution.

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Worked Example: Calculating Mass in a Smaller Volume

A solution has a concentration of 60 g/dm³.

What mass of solute is present in 250 cm³?

First convert the volume:

250 cm³ = 0.250 dm³

Now use:

mass = concentration × volume

mass = 60 × 0.250

mass = 15 g

Therefore, 250 cm³ of the solution contains:

15 g of solute

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Worked Example: Calculating Volume

A solution contains 12 g of solute and has a concentration of 30 g/dm³.

Use:

volume = mass ÷ concentration

Substitute:

volume = 12 ÷ 30

volume = 0.4 dm³

Therefore:

volume = 0.4 dm³

or:

400 cm³

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Choosing the Correct Equation

Before calculating, ask:

What am I trying to find?

If you need concentration:

concentration = mass ÷ volume

If you need mass:

mass = concentration × volume

If you need volume:

volume = mass ÷ concentration

Writing the equation before substituting numbers makes calculations easier to check.

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Comparing Concentrations

Two solutions cannot always be compared simply by looking at the mass of solute.

Consider:

Solution A

10 g of salt in 100 cm³

Solution B

15 g of salt in 300 cm³

Solution B contains more salt overall, but that does not necessarily mean it is more concentrated.

We need to calculate both concentrations.

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Worked Example: Comparing Two Solutions

Solution A

Mass = 10 g

Volume = 100 cm³ = 0.100 dm³

concentration = 10 ÷ 0.100

concentration = 100 g/dm³

Solution B

Mass = 15 g

Volume = 300 cm³ = 0.300 dm³

concentration = 15 ÷ 0.300

concentration = 50 g/dm³

Therefore:

Solution A is twice as concentrated as Solution B.

Even though Solution B contains more solute overall, its larger volume makes it less concentrated.

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Concentration Is a Ratio

Concentration describes the relationship between:

amount of solute

and

volume of solution

This means that increasing both by the same factor does not change the concentration.

For example:

5 g in 100 cm³

and:

10 g in 200 cm³

have the same concentration.

For the first solution:

5 ÷ 0.100 = 50 g/dm³

For the second:

10 ÷ 0.200 = 50 g/dm³

Both have the same concentration.

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What Happens When More Solute Is Added?

Suppose the volume remains approximately constant.

If more solute is added:

• Mass of solute increases.
• Volume stays the same.
• Concentration increases.

For example:

5 g in 500 cm³ gives:

10 g/dm³

10 g in 500 cm³ gives:

20 g/dm³

Doubling the mass while keeping the volume constant doubles the concentration.

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What Happens When More Solvent Is Added?

Adding solvent increases the volume of the solution while the amount of solute remains the same.

Therefore, the concentration decreases.

This process is called dilution.

For example:

10 g of solute in 0.5 dm³:

concentration = 10 ÷ 0.5 = 20 g/dm³

If water is added until the volume becomes 1.0 dm³:

concentration = 10 ÷ 1.0 = 10 g/dm³

The mass of solute has not changed, but the concentration has decreased.

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Interpreting Concentration Values

A concentration value has physical meaning.

For example:

75 g/dm³

means:

75 g of solute is present per 1 dm³ of solution.

A larger concentration means more solute is present per unit volume.

For example:

Solution A = 20 g/dm³

Solution B = 80 g/dm³

Solution B contains four times as much solute per unit volume as Solution A.

Therefore, Solution B is four times as concentrated.

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Worked Example: Interpreting a Concentration

A sports drink contains sugar at a concentration of:

60 g/dm³

How much sugar is present in 500 cm³?

Convert:

500 cm³ = 0.500 dm³

Use:

mass = concentration × volume

mass = 60 × 0.500

mass = 30 g

Therefore, 500 cm³ of the drink contains:

30 g of sugar

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Concentration in Laboratory Chemistry

Scientists frequently need solutions with known concentrations.

Accurate concentrations are important in:

• Chemical reactions.
• Titrations.
• Medicine.
• Environmental testing.
• Food production.
• Biological experiments.
• Industrial chemistry.

If the concentration is incorrect, experimental results may also be incorrect.

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Preparing a Solution of Known Concentration

A solution of known mass concentration can be prepared by:

• Measuring the required mass of solute.
• Dissolving the solute in some solvent.
• Transferring the solution to an appropriate measuring container.
• Adding solvent until the required final volume is reached.
• Mixing thoroughly.

Notice that concentration calculations use the final volume of the solution, not simply the volume of solvent initially used.

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Worked Example: Preparing a Solution

A student wants to prepare:

500 cm³ of a 20 g/dm³ salt solution

First convert:

500 cm³ = 0.500 dm³

Use:

mass = concentration × volume

mass = 20 × 0.500

mass = 10 g

The student therefore needs:

10 g of salt

The final solution volume should be:

500 cm³

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Mass of Solute Versus Mass of Solution

Be careful to distinguish between:

mass of solute

and

mass of solution

The equation:

concentration = mass ÷ volume

uses the mass of the solute.

For example, if 10 g of salt is dissolved in water:

The value used for mass is:

10 g

not the combined mass of the water and salt.

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Volume of Solution Versus Volume of Solvent

Another important distinction is between:

volume of solvent

and

final volume of solution

Concentration is normally based on the final volume of the solution.

For example, a chemist may dissolve a substance in some water and then add more water until the final solution reaches exactly 250 cm³.

The volume used in the calculation is:

250 cm³

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Units Matter

Correct units are essential.

Common units include:

• g
• kg
• cm³
• dm³
• g/cm³
• g/dm³

If mass is given in milligrams:

1000 mg = 1 g

If volume is given in cm³:

1000 cm³ = 1 dm³

Always make the units compatible before calculating.

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Worked Example: Converting Mass and Volume

A solution contains 2500 mg of solute in 100 cm³.

Calculate the concentration in g/dm³.

Convert mass:

2500 mg = 2.5 g

Convert volume:

100 cm³ = 0.100 dm³

Calculate:

concentration = 2.5 ÷ 0.100

concentration = 25 g/dm³

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Multi-Step Problem

A student prepares 400 cm³ of solution containing 12 g of solute.

They then want to compare it with another solution having a concentration of 25 g/dm³.

First solution:

400 cm³ = 0.400 dm³

concentration = 12 ÷ 0.400

concentration = 30 g/dm³

Second solution:

25 g/dm³

Therefore:

The first solution is more concentrated.

This type of question combines unit conversion, calculation, and interpretation.

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Reverse Problem

A bottle contains 750 cm³ of a solution with a concentration of 40 g/dm³.

How much solute does it contain?

Convert:

750 cm³ = 0.750 dm³

Use:

mass = concentration × volume

mass = 40 × 0.750

mass = 30 g

Therefore:

30 g of solute is present.

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Challenge Example

A student has two salt solutions.

Solution A

18 g of salt in 300 cm³

Solution B

25 g of salt in 500 cm³

Which is more concentrated?

Solution A

300 cm³ = 0.300 dm³

concentration = 18 ÷ 0.300

concentration = 60 g/dm³

Solution B

500 cm³ = 0.500 dm³

concentration = 25 ÷ 0.500

concentration = 50 g/dm³

Therefore:

Solution A is more concentrated.

The difference is:

60 - 50 = 10 g/dm³

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Reading Concentration Data

Suppose four solutions have the following concentrations:

The most dilute is:

Solution A

The most concentrated is:

Solution D

Solution D is:

75 ÷ 15 = 5

times as concentrated as Solution A.

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Concentration and Graphs

Concentration data can also be displayed graphically.

For example, if the volume remains constant and increasing amounts of solute are added, concentration increases directly with the mass of solute.

If the mass of solute remains constant while volume increases, concentration decreases.

Graphs can therefore help us identify relationships between mass, volume, and concentration.

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Real-World Applications

Concentration calculations are used in many areas.

Medicine

Medicines must contain carefully controlled quantities of active ingredients.

Food and Drink

Manufacturers control concentrations of ingredients such as sugar, salt, acids, and flavorings.

Environmental Science

Scientists measure concentrations of pollutants in water and soil.

Agriculture

Fertilizers and other agricultural chemicals may need to be prepared at particular concentrations.

Industry

Chemical manufacturing depends on accurate solution concentrations.

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Common Mistakes

Forgetting to Convert cm³ to dm³

If the answer is required in g/dm³:

divide cm³ by 1000 first.

Multiplying Instead of Dividing

To find concentration:

mass ÷ volume

not mass × volume.

Using the Mass of the Entire Solution

Use the mass of solute.

Using the Volume of Solvent

Use the final volume of solution unless the question explicitly states otherwise.

Forgetting Units

An answer of:

25

is incomplete.

Write:

25 g/dm³

Assuming More Solute Always Means Greater Concentration

Volume also matters.

20 g in 1 dm³ is less concentrated than 15 g in 0.5 dm³.

Confusing Concentration With Total Amount

A small volume of a concentrated solution can contain less total solute than a large volume of a dilute solution.

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Check Your Understanding

1. Define concentration.

2. What is the difference between a solute and a solvent?

3. Write the equation used to calculate mass concentration.

4. Convert 600 cm³ to dm³.

5. Convert 1.5 dm³ to cm³.

6. Calculate the concentration of 20 g of salt in 0.5 dm³ of solution.

7. Calculate the concentration of 12 g of sugar in 300 cm³ of solution.

8. A solution has a concentration of 50 g/dm³ and a volume of 2 dm³. Calculate the mass of solute.

9. A solution contains 15 g of solute at a concentration of 30 g/dm³. Calculate its volume.

10. Calculate the mass of solute in 250 cm³ of a 40 g/dm³ solution.

11. Which is more concentrated: 10 g in 100 cm³ or 30 g in 500 cm³?

12. Explain why adding water decreases the concentration of a solution.

13. A solution has a concentration of 80 g/dm³. Explain what this value means.

14. Why must units be checked before calculating concentration?

15. Explain the difference between the volume of solvent and the final volume of solution.

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Key Terms

• Solution – mixture formed when a solute dissolves in a solvent.
• Solute – substance dissolved in a solvent.
• Solvent – substance in which a solute dissolves.
• Concentration – amount of solute present per unit volume of solution.
• Dilute – containing a relatively small amount of solute per unit volume.
• Concentrated – containing a relatively large amount of solute per unit volume.
• Mass concentration – mass of solute per unit volume of solution.
• Dilution – reduction in concentration by adding solvent.
• g/dm³ – grams of solute per cubic decimeter of solution.
• cm³ – cubic centimeter, a unit of volume.
• dm³ – cubic decimeter, equal to 1000 cm³.

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Key Takeaways

• Concentration tells us how much solute is present in a particular volume of solution.
• A concentrated solution contains more solute per unit volume than a dilute solution.
• Concentration = mass ÷ volume.
• Mass = concentration × volume.
• Volume = mass ÷ concentration.
• A common concentration unit is g/dm³.
• 1000 cm³ = 1 dm³.
• Convert cm³ to dm³ by dividing by 1000.
• Always check that units are compatible before calculating.
• Concentration depends on both the amount of solute and the volume of solution.
• A solution containing more total solute is not necessarily more concentrated.
• Adding more solute generally increases concentration if volume remains constant.
• Adding solvent decreases concentration.
• Concentration values allow different solutions to be compared fairly.
• The mass used in a mass-concentration calculation is the mass of the solute.
• The volume used is the final volume of the solution.
• Concentration calculations are widely used in laboratory chemistry, medicine, environmental science, food production, and industry.