Concentration of Solutions | Chemistry

📖 In-Depth Theory

What is Concentration?

The CONCENTRATION of a solution tells us how much solute is dissolved per unit volume of solution.

A CONCENTRATED solution has a LOT of solute dissolved in a given volume.

A DILUTE solution has a LITTLE solute dissolved in the same volume.

Concentration can be expressed in two ways at Foundation level:

1. In g/dm³ (grams per decimetre cubed):

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

2. In g/cm³ (grams per centimetre cubed) — less common:

Concentration (g/cm³) = mass of solute (g) ÷ volume of solution (cm³)

Note: 1 dm³ = 1000 cm³ = 1 litre

Calculating Concentration

FORMULA:

concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)

Rearranging:

mass (g) = concentration (g/dm³) × volume (dm³)

volume (dm³) = mass (g) ÷ concentration (g/dm³)

IMPORTANT: volume must be in dm³. If given in cm³, divide by 1000 first.

250 cm³ = 0.250 dm³

500 cm³ = 0.500 dm³

EXAMPLES:

1. 10 g of NaCl dissolved in 0.5 dm³ (500 cm³) of water.

Concentration = 10 ÷ 0.5 = 20 g/dm³

2. A solution has concentration 50 g/dm³. What mass is in 200 cm³?

Volume = 200 ÷ 1000 = 0.2 dm³

Mass = 50 × 0.2 = 10 g

3. 8 g of glucose gives a concentration of 16 g/dm³. What volume was used?

Volume = 8 ÷ 16 = 0.5 dm³ = 500 cm³

Dilution

DILUTION means adding more solvent (usually water) to reduce the concentration of a solution.

When you dilute a solution:

The AMOUNT of solute stays the SAME.

The VOLUME increases.

The CONCENTRATION decreases.

Dilution formula:

concentration₁ × volume₁ = concentration₂ × volume₂

Example:

100 cm³ of 40 g/dm³ solution is diluted to 400 cm³. What is the new concentration?

c₁V₁ = c₂V₂

40 × 0.1 = c₂ × 0.4

4 = c₂ × 0.4

c₂ = 4 ÷ 0.4 = 10 g/dm³

SERIAL DILUTION:

A technique where a solution is diluted by a fixed factor multiple times.

Useful for making a range of known concentrations.

Example: Start with 100 g/dm³ → dilute 1:10 → 10 g/dm³ → dilute 1:10 → 1 g/dm³.

⚠️ Common Mistake

Volume MUST be in dm³ when using the concentration formula. If given in cm³, divide by 1000 first. 250 cm³ = 0.250 dm³. Students frequently forget this conversion and get answers 1000 times too large or too small.

📐 Variables

cConcentration (c) is measured in g/dm³ (g/dm³)

mMass of solute (m) is measured in grams (g)

VVolume of solution (V) is measured in dm³ (dm³)

📐 Key Equations

concentration (g/dm³) = mass (g) ÷ volume (dm³)

mass (g) = concentration (g/dm³) × volume (dm³)

volume (dm³) = mass (g) ÷ concentration (g/dm³)

📌 Key Note

Concentration (g/dm³) = mass (g) ÷ volume (dm³). Convert cm³ to dm³: ÷ 1000. Concentrated = lots of solute per volume. Dilute = little solute per volume. Dilution: same mass, larger volume, lower concentration. c₁V₁ = c₂V₂.

🎯 Matching Activity — Concentration Calculations

Match each calculation to the correct answer. — drag the symbols on the right to match the component names on the left.

5 g NaCl in 0.5 dm³

Drop here

20 g/dm³, volume = 250 cm³ (0.25 dm³)

Drop here

8 g solute, concentration 40 g/dm³

Drop here

100 cm³ of 60 g/dm³ diluted to 300 cm³

Drop here

Mass = 20 × 0.25 = 5 g

Volume = 8 ÷ 40 = 0.2 dm³ = 200 cm³

Concentration = 10 g/dm³

New concentration = 20 g/dm³

⚽ FIFA Worked Examples

Concentration Calculation

15 g of sodium hydroxide (NaOH) is dissolved to make 500 cm³ of solution. Calculate the concentration in g/dm³.

F

concentration (g/dm³) = mass (g) ÷ volume (dm³)

I

volume = 500 cm³ ÷ 1000 = 0.5 dm³. Mass = 15 g

F

concentration = 15 ÷ 0.5

A

concentration = 30 g/dm³

🎯 Test Yourself

Question 1 of 2

1. 25 g of glucose is dissolved in 500 cm³ of water. What is the concentration in g/dm³?

2. A solution has a concentration of 80 g/dm³. What mass of solute is in 250 cm³ of this solution?

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🧪 Concentration of Solutions

What is Concentration?

Calculating Concentration

Dilution

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