Concentration

Concentration describes how much solute is present in a given volume of solution.

A solution containing a large amount of solute in a particular volume is more concentrated. A solution containing a smaller amount of solute in the same volume is more dilute.

For example:

• 5 g of salt dissolved to make 100 mL of solution
• 20 g of salt dissolved to make 100 mL of solution

The second solution is more concentrated because it contains more solute in the same volume of solution.

What Does Concentration Tell Us?

Concentration allows us to compare solutions quantitatively.

It answers the question:

How much solute is present in a certain volume of solution?

Consider two salt solutions:

Solution A

10 g salt in 500 mL solution

Solution B

10 g salt in 100 mL solution

Both contain the same mass of salt, but Solution B contains that salt in a much smaller volume.

Therefore:

Solution B is more concentrated.

The important idea is that concentration depends on both the amount of solute and the volume of solution.

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Concentrated and Dilute Solutions

A concentrated solution contains relatively more solute in a given volume.

A dilute solution contains relatively less solute in a given volume.

These terms are useful for general comparisons, but they do not tell us the exact concentration.

For example:

Solution A is more concentrated than Solution B.

is a qualitative comparison.

But:

Solution A has a concentration of 25 g/L.

is a quantitative measurement.

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Calculating Concentration

A common way of expressing concentration is:

concentration = mass of solute / volume of solution

Using symbols:

c = m/V

where:

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

A common unit is:

g/L

meaning:

grams of solute per litre of solution

For example:

20 g/L

means there are:

20 g of solute in every 1 L of solution

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Understanding g/L

The unit g/L is a ratio.

Suppose a solution has a concentration of:

50 g/L

This means:

1 L solution contains 50 g solute

Therefore:

2 L solution contains 100 g solute

and:

0.5 L solution contains 25 g solute

The concentration remains the same because the ratio of solute to solution remains the same.

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Worked Example: Basic Concentration

A student dissolves 20 g of salt to make 2.0 L of solution.

Calculate the concentration.

Use:

c = m/V

Substitute:

c = 20 g / 2.0 L

c = 10 g/L

Answer

Concentration = 10 g/L

This means every litre of solution contains 10 g of salt.

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Worked Example: Smaller Volume

A solution contains:

15 g sugar

in:

0.50 L solution

Calculate the concentration.

c = m/V

c = 15 / 0.50

c = 30 g/L

Answer

Concentration = 30 g/L

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Converting Millilitres to Litres

A common source of mistakes is using millilitres when the required unit is g/L.

Remember:

1000 mL = 1 L

Therefore:

500 mL = 0.500 L

250 mL = 0.250 L

100 mL = 0.100 L

50 mL = 0.050 L

To convert:

mL → L

divide by:

1000

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Worked Example: Converting Volume

A solution contains:

8.0 g salt

in:

200 mL solution

Calculate the concentration in g/L.

First convert the volume:

200 mL = 0.200 L

Then:

c = m/V

c = 8.0 / 0.200

c = 40 g/L

Answer

Concentration = 40 g/L

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Worked Example: Very Small Volume

A medicine contains:

1.5 g

of dissolved substance in:

50 mL

of solution.

Convert:

50 mL = 0.050 L

Calculate:

c = 1.5 / 0.050

c = 30 g/L

Answer

Concentration = 30 g/L

This illustrates why small volumes can still have relatively high concentrations.

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Comparing Concentrations

Consider:

Solution A

10 g solute in 1 L solution

Solution B

20 g solute in 1 L solution

Solution B contains twice as much solute in the same volume.

Therefore:

B is twice as concentrated as A.

Their concentrations are:

A:

10 / 1 = 10 g/L

B:

20 / 1 = 20 g/L

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Comparing Different Volumes

Comparisons become more interesting when the volumes are different.

Solution A

10 g solute in 200 mL solution

Solution B

20 g solute in 500 mL solution

We cannot simply say B is more concentrated because it contains more solute.

We must calculate the concentration.

Solution A

200 mL = 0.200 L

c = 10 / 0.200

= 50 g/L

Solution B

500 mL = 0.500 L

c = 20 / 0.500

= 40 g/L

Therefore:

Solution A is more concentrated.

Even though A contains less total solute, that solute is packed into a smaller volume.

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Concentration at the Particle Level

Imagine equal volumes of two solutions.

In the dilute solution, there are relatively few solute particles among the solvent particles.

In the concentrated solution, there are many more solute particles within the same volume.

The solute particles are still distributed throughout the solution.

The difference is the number of solute particles per unit volume.

This particle model helps explain why concentrated solutions may behave differently from dilute solutions.

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Increasing Concentration by Adding Solute

Suppose we have:

10 g solute in 1 L solution

Concentration:

10 g/L

If more solute is dissolved while the volume remains approximately the same, the concentration increases.

For example:

20 g solute in 1 L solution

has a concentration of:

20 g/L

More solute in the same volume means a greater concentration.

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Decreasing Concentration by Adding Solvent

Suppose we begin with:

20 g solute in 1 L solution

Concentration:

20 g/L

If solvent is added until the total volume becomes:

2 L

the amount of solute remains:

20 g

New concentration:

c = 20 / 2

= 10 g/L

The solution has become more dilute.

This process is called dilution.

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What Happens During Dilution?

During dilution:

• solvent is added
• total solution volume increases
• amount of solute stays the same
• concentration decreases

This is an important point:

Dilution does not remove solute.

It spreads the same amount of solute through a larger volume.

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Increasing Concentration by Removing Solvent

Suppose a salt solution contains:

20 g salt in 1 L solution

If water evaporates, the amount of water decreases while the salt remains.

If the solution volume decreases to:

0.5 L

then:

c = 20 / 0.5

= 40 g/L

The concentration has increased.

Evaporation can therefore make a solution more concentrated.

What Happens if Solute Is Removed?

Suppose some solute is removed while the volume remains approximately unchanged.

The amount of solute decreases.

Therefore:

concentration decreases

This is less common as a simple laboratory process because dissolved solute cannot usually just be picked out of a solution, but it can sometimes be removed using chemical or separation processes.

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Rearranging the Concentration Equation

The main equation is:

c = m/V

We can rearrange this to find mass or volume.

Finding Mass

m = cV

Finding Volume

V = m/c

So the three useful forms are:

c = m/V

m = cV

V = m/c

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Worked Example: Finding Mass

A solution has a concentration of:

25 g/L

and a volume of:

2.0 L

How much solute does it contain?

Use:

m = cV

m = 25 × 2.0

m = 50 g

Answer

Mass of solute = 50 g

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Worked Example: Finding Mass in a Smaller Volume

A solution has a concentration of:

40 g/L

What mass of solute is present in:

250 mL

of solution?

First convert:

250 mL = 0.250 L

Then:

m = cV

m = 40 × 0.250

m = 10 g

Answer

Mass of solute = 10 g

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Worked Example: Finding Volume

A solution contains:

30 g solute

and has a concentration of:

15 g/L

Find the volume.

Use:

V = m/c

V = 30 / 15

V = 2.0 L

Answer

Volume = 2.0 L

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Worked Example: Finding Volume in Millilitres

A solution contains:

12 g solute

at a concentration of:

48 g/L

Find the volume.

V = m/c

V = 12 / 48

V = 0.250 L

Convert:

0.250 L = 250 mL

Answer

Volume = 250 mL

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A Useful Equation Triangle

Students sometimes remember the relationship as:

m = c × V

Then rearrange as needed:

c = m ÷ V

V = m ÷ c

Rather than memorizing three unrelated equations, remember that mass equals concentration multiplied by volume.

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Comparing Solutions Using Calculations

Consider three solutions:

Solutions A and C have the same concentration even though C contains more total solute.

Solution B is twice as concentrated as A and C.

This shows why concentration is more useful than simply comparing the total amount of solute.

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Same Concentration, Different Amounts

Consider:

Solution A

10 g solute in 0.5 L

c = 10 / 0.5 = 20 g/L

Solution B

40 g solute in 2.0 L

c = 40 / 2.0 = 20 g/L

Both solutions have:

20 g/L

Therefore, they have the same concentration.

Solution B simply contains a larger total amount of solution.

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Concentration and Colour

For some coloured solutions, concentration affects colour intensity.

A more concentrated solution may appear darker because there are more coloured particles in a given volume.

A more dilute solution may appear lighter.

However, colour should not normally be used as an exact measurement of concentration without proper equipment and calibration.

Different substances produce different colours, and some solutions are colourless.

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Concentration in Everyday Life

Concentration is important far beyond the chemistry laboratory.

Examples include:

• medicines
• cleaning products
• sports drinks
• swimming pools
• fertilizers
• food and beverages
• environmental testing
• water treatment
• industrial chemicals

Instructions often specify concentrations because having too much or too little of a substance can affect how well a product works.

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Concentration in Medicines

Medicines often contain specific concentrations of active ingredients.

For example, a liquid medicine might contain a certain mass of active ingredient per volume of liquid.

The concentration helps determine how much active substance is delivered in a particular dose.

This is why accurate concentration measurements are important in pharmaceutical chemistry.

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Concentration in the Environment

Scientists measure concentrations of substances in:

• rivers
• lakes
• oceans
• drinking water
• soil water
• wastewater

They may measure substances such as:

• nitrate ions
• phosphate ions
• dissolved metals
• salts
• pollutants

Concentration provides more useful information than simply stating that a substance is present.

For example, detecting a pollutant does not tell us whether its concentration is very low or potentially significant.

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Concentration in Biology

Living organisms depend on carefully controlled concentrations.

Cells contain solutions of:

• ions
• sugars
• proteins
• other dissolved substances

Differences in concentration are important in processes such as:

• diffusion
• osmosis
• transport across membranes

A concentration gradient exists when the concentration of a substance differs between two regions.

Particles tend to diffuse from regions of higher concentration toward regions of lower concentration.

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Concentration and Reaction Rate

Concentration can also affect the rate of chemical reactions.

In many reactions, increasing the concentration of reactants increases the number of reacting particles in a given volume.

This can lead to more frequent successful collisions.

As a result, the reaction may occur faster.

This relationship becomes important when studying collision theory and rates of reaction.

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Mass Concentration vs. Molar Concentration

In these notes, we have mainly used mass concentration:

c = m/V

with units such as:

g/L

At more advanced levels of chemistry, concentration is often expressed using moles rather than grams.

For example:

mol/L

or:

mol dm⁻³

This is called molar concentration.

The underlying idea remains the same:

amount of solute per unit volume of solution

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Litres and Cubic Decimetres

In chemistry:

1 L = 1 dm³

Therefore:

g/L

and:

g/dm³

represent equivalent concentration units.

For example:

25 g/L = 25 g/dm³

Similarly:

mol/L = mol/dm³

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Concentration vs. Solubility

These terms should not be confused.

Concentration describes how much solute is currently present in a given volume of solution.

Solubility describes the maximum amount of a substance that can dissolve under particular conditions.

For example, a solution might have a relatively low concentration even though much more solute could still dissolve.

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Concentration vs. Saturation

A concentrated solution contains a relatively large amount of solute.

A saturated solution contains approximately the maximum amount of solute that can dissolve under the given conditions.

A solution can therefore be:

• dilute and unsaturated
• concentrated and unsaturated
• saturated

Concentrated does not automatically mean saturated.

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Worked Example: Evaporation

A solution contains:

12 g salt

in:

300 mL solution

Initial concentration:

300 mL = 0.300 L

c = 12 / 0.300

= 40 g/L

Water evaporates until the solution volume is:

150 mL

Assume no salt is lost.

Convert:

150 mL = 0.150 L

New concentration:

c = 12 / 0.150

= 80 g/L

Answer

The concentration increases from:

40 g/L → 80 g/L

Halving the volume while keeping the solute mass constant doubles the concentration.

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Worked Example: Dilution

A solution contains:

15 g sugar

in:

250 mL solution

Initial concentration:

250 mL = 0.250 L

c = 15 / 0.250

= 60 g/L

Water is added until the total volume becomes:

750 mL

The amount of sugar remains:

15 g

New volume:

750 mL = 0.750 L

New concentration:

c = 15 / 0.750

= 20 g/L

Answer

The concentration decreases:

60 g/L → 20 g/L

The solution becomes more dilute.

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Worked Example: Comparing Three Solutions

Consider:

Solution A

12 g solute in 200 mL

Solution B

18 g solute in 300 mL

Solution C

20 g solute in 250 mL

Calculate each concentration.

Solution A

200 mL = 0.200 L

c = 12 / 0.200 = 60 g/L

Solution B

300 mL = 0.300 L

c = 18 / 0.300 = 60 g/L

Solution C

250 mL = 0.250 L

c = 20 / 0.250 = 80 g/L

Therefore:

A and B have the same concentration.

C is the most concentrated.

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Predicting Changes in Concentration

It is useful to predict the result before calculating.

Add Solute

If the volume stays approximately constant:

concentration increases

Add Solvent

If the amount of solute stays constant:

concentration decreases

Remove Solvent

If the solute remains:

concentration increases

Remove Solute

If the volume remains approximately constant:

concentration decreases

Double Solute and Double Volume

concentration stays the same

because the ratio remains unchanged.

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Proportional Reasoning

Suppose a solution contains:

10 g/L

If the concentration stays constant:

Doubling the volume of the same solution doubles the amount of solute present.

But the concentration remains unchanged.

This distinction between amount and concentration is extremely important.

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Common Mistakes

Using Solvent Volume Instead of Solution Volume

The concentration equation normally uses the final volume of the solution:

c = mass of solute / volume of solution

For example, dissolving a solute in 100 mL of water does not necessarily produce exactly 100 mL of solution.

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Forgetting to Convert mL to L

If concentration is required in g/L, the volume must be in litres.

Incorrect:

c = 10 / 200

Correct:

200 mL = 0.200 L

then:

c = 10 / 0.200 = 50 g/L

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Assuming More Solute Always Means More Concentrated

Not necessarily.

Compare:

20 g in 2 L = 10 g/L

and:

10 g in 0.5 L = 20 g/L

The solution containing less total solute is actually more concentrated.

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Assuming Larger Volume Means More Dilute

Not necessarily.

A large volume can have exactly the same concentration as a small volume.

For example:

5 g in 0.5 L = 10 g/L

20 g in 2.0 L = 10 g/L

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Thinking Dilution Removes Solute

Adding solvent decreases concentration but does not remove solute.

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Confusing Concentration and Solubility

Concentration tells us how much solute is present.

Solubility tells us how much could dissolve under particular conditions.

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Confusing Concentrated and Saturated

A concentrated solution may still be able to dissolve additional solute.

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Forgetting Units

A concentration answer should include units.

For example:

25 g/L

not simply:

25

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Key Terms

Concentration — The amount of solute present in a given volume of solution.

Mass concentration — Concentration expressed using the mass of solute per unit volume of solution.

Solute — The substance dissolved in a solution.

Solvent — The substance that dissolves the solute.

Solution — A homogeneous mixture containing a solute dissolved in a solvent.

Concentrated solution — A solution containing a relatively large amount of solute per unit volume.

Dilute solution — A solution containing a relatively small amount of solute per unit volume.

Dilution — The process of decreasing concentration by adding solvent.

Volume — The amount of space occupied by a substance or solution.

g/L — Grams per litre, a common unit of mass concentration.

g/dm³ — Grams per cubic decimetre; equivalent to g/L.

Molar concentration — The amount of solute in moles per unit volume of solution.

Concentration gradient — A difference in concentration between two regions.

Solubility — The maximum amount of a substance that can dissolve under specified conditions.

Saturated solution — A solution containing approximately the maximum amount of dissolved solute possible under particular conditions.

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Key Takeaways

• Concentration describes the amount of solute in a given volume of solution.
• A concentrated solution contains relatively more solute per unit volume.
• A dilute solution contains relatively less solute per unit volume.
• Mass concentration can be calculated using:

c = m/V

• Mass can be calculated using:

m = cV

• Volume can be calculated using:

V = m/c

• A common concentration unit is g/L.
• Always convert mL to L when calculating concentration in g/L.
• Adding solute generally increases concentration.
• Adding solvent decreases concentration.
• Removing solvent increases concentration.
• Dilution does not remove solute.
• Two solutions can contain different total amounts of solute but have the same concentration.
• A solution with more total solute is not necessarily more concentrated.
• Concentration describes a ratio between amount of solute and volume.
• Concentration and solubility are different concepts.
• Concentrated and saturated are not synonyms.
• Concentration is important in chemistry, biology, medicine, environmental science, and industry.

The central relationship is:

CONCENTRATION = MASS OF SOLUTE ÷ VOLUME OF SOLUTION

or:

c = m/V

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Check Your Understanding

Understanding Concentration

1. Define concentration.

2. Explain the difference between a concentrated and dilute solution.

3. What does a concentration of 20 g/L mean?

4. Explain why concentration depends on both the amount of solute and the volume of solution.

5. Describe a concentrated solution using the particle model.

6. Describe a dilute solution using the particle model.

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Calculating Concentration

Use:

c = m/V

7. Calculate the concentration of 10 g solute in 2.0 L solution.

8. Calculate the concentration of 25 g solute in 0.50 L solution.

9. Calculate the concentration of 12 g solute in 0.30 L solution.

10. Calculate the concentration of 40 g solute in 2.5 L solution.

11. A solution contains 5 g solute in 250 mL. Calculate the concentration in g/L.

12. A solution contains 18 g solute in 300 mL. Calculate the concentration in g/L.

13. A solution contains 2.5 g solute in 50 mL. Calculate the concentration in g/L.

14. A solution contains 24 g solute in 800 mL. Calculate the concentration in g/L.

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Finding Mass

Use:

m = cV

15. A 2.0 L solution has a concentration of 15 g/L. Calculate the mass of solute.

16. A 0.50 L solution has a concentration of 40 g/L. Calculate the mass of solute.

17. How much solute is present in 250 mL of a 60 g/L solution?

18. How much solute is present in 750 mL of a 32 g/L solution?

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Finding Volume

Use:

V = m/c

19. A solution contains 20 g solute at a concentration of 10 g/L. Calculate its volume.

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

21. A solution contains 12 g solute at 48 g/L. Calculate its volume in litres and millilitres.

22. A solution contains 5 g solute at 20 g/L. Calculate its volume in millilitres.

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Comparing Solutions

23. Solution A contains 10 g solute in 200 mL. Solution B contains 20 g in 500 mL. Which is more concentrated? Show your calculations.

24. Solution A contains 15 g in 300 mL. Solution B contains 25 g in 500 mL. Compare their concentrations.

25. Solution A contains 8 g in 100 mL. Solution B contains 30 g in 500 mL. Which is more concentrated?

26. Explain why the solution containing the greatest mass of solute is not necessarily the most concentrated.

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Changes in Concentration

27. What happens to concentration when more solute is added while volume remains approximately constant?

28. What happens when solvent is added but the amount of solute remains unchanged?

29. Explain what happens to concentration when solvent evaporates.

30. A solution contains 20 g solute in 500 mL. Water is added until the volume reaches 1.0 L. Calculate the initial and final concentrations.

31. A solution contains 10 g salt in 500 mL. Water evaporates until the volume is 250 mL. Calculate the initial and final concentrations.

32. A solution contains 15 g solute in 300 mL. It is diluted to 900 mL. Calculate the new concentration.

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Analysis and Application

33. Two solutions both have a concentration of 25 g/L. One has a volume of 100 mL and the other has a volume of 2 L. Do they contain the same mass of solute? Explain.

34. A student claims that a 1 L solution must be more dilute than a 100 mL solution because it contains more liquid. Explain why this reasoning is incorrect.

35. A student calculates the concentration of 10 g solute in 200 mL as 0.05 g/L. Identify the likely mistake and calculate the correct answer.

36. Explain why adding water to a solution decreases its concentration even though the amount of solute does not change.

37. Explain the difference between concentration and solubility.

38. Explain why a concentrated solution is not necessarily saturated.

39. Give two examples of situations outside the chemistry laboratory where concentration is important.

40. A student prepares a solution containing 12 g solute in 200 mL. They then add water until the volume reaches 600 mL. Describe what happens at the particle level and calculate the concentration before and after dilution.