Concentration of Solutions

This lesson covers how to express and calculate the concentration of solutions as required by the Edexcel GCSE Combined Science specification (1SC0). You will learn to work in both g/dm³ (Foundation and Higher) and mol/dm³ (Higher tier only), and to convert between units.

---

What Is Concentration?

Concentration tells you how much solute is dissolved in a given volume of solution.

• A concentrated solution has a large amount of solute in a given volume.
• A dilute solution has a small amount of solute in a given volume.

---

Concentration in g/dm³

This is the simplest way to express concentration and is used at both Foundation and Higher tier.

$\text{concentration (g/dm}^3) = \frac{\text{mass of solute (g)}}{\text{volume of solution (dm}^3)}$concentration (g/dm3)=volume of solution (dm3)mass of solute (g)​

The Triangle

graph TD
    A["<b>mass (g)</b>"] --- B["<b>concentration<br/>(g/dm³)</b>"]
    A --- C["<b>volume<br/>(dm³)</b>"]
    B --- C
    style A fill:#f59e0b,color:#000,stroke:#d97706
    style B fill:#3b82f6,color:#fff,stroke:#2563eb
    style C fill:#3b82f6,color:#fff,stroke:#2563eb

To Find	Formula
Concentration	$c = \dfrac{m}{V}$c=Vm​
Mass	$m = c \times V$m=c×V
Volume	$V = \dfrac{m}{c}$V=cm​

Converting cm³ to dm³

1 dm³ = 1000 cm³

To convert cm³ to dm³: divide by 1000.

$250 \text{ cm}^3 = \frac{250}{1000} = 0.25 \text{ dm}^3$250 cm3=1000250​=0.25 dm3

Exam Tip: The most common mistake in concentration questions is forgetting to convert cm³ to dm³. Always check your volume units before substituting.

---

Worked Examples — g/dm³

Example 1

Question: 5.0 g of sodium chloride is dissolved in 250 cm³ of water. Calculate the concentration in g/dm³.

Step 1: Convert volume: $250 \text{ cm}^3 = 0.25 \text{ dm}^3$250 cm3=0.25 dm3

Step 2: Calculate concentration: $c = \frac{m}{V} = \frac{5.0}{0.25} = 20 \text{ g/dm}^3$c=Vm​=0.255.0​=20 g/dm3

Example 2

Question: What mass of potassium hydroxide is needed to make 500 cm³ of a 10 g/dm³ solution?

Step 1: Convert volume: $500 \text{ cm}^3 = 0.5 \text{ dm}^3$500 cm3=0.5 dm3

Step 2: Calculate mass: $m = c \times V = 10 \times 0.5 = 5.0 \text{ g}$m=c×V=10×0.5=5.0 g

Example 3

Question: What volume of solution is needed to dissolve 8.0 g of solute to make a 40 g/dm³ solution?

$V = \frac{m}{c} = \frac{8.0}{40} = 0.2 \text{ dm}^3 = 200 \text{ cm}^3$V=cm​=408.0​=0.2 dm3=200 cm3

---

Concentration in mol/dm³ (Higher Tier)

At Higher tier, concentration can also be expressed in moles per cubic decimetre (mol/dm³), sometimes written as M (molar).

$\text{concentration (mol/dm}^3) = \frac{\text{moles of solute}}{\text{volume of solution (dm}^3)}$concentration (mol/dm3)=volume of solution (dm3)moles of solute​

The Triangle

graph TD
    A["<b>moles (mol)</b>"] --- B["<b>concentration<br/>(mol/dm³)</b>"]
    A --- C["<b>volume<br/>(dm³)</b>"]
    B --- C
    style A fill:#f59e0b,color:#000,stroke:#d97706
    style B fill:#10b981,color:#fff,stroke:#059669
    style C fill:#10b981,color:#fff,stroke:#059669

To Find	Formula
Concentration (mol/dm³)	$c = \dfrac{n}{V}$c=Vn​
Moles	$n = c \times V$n=c×V
Volume	$V = \dfrac{n}{c}$V=cn​

---

Worked Examples — mol/dm³ (Higher Tier)

Example 4

Question: 0.5 mol of HCl is dissolved in 250 cm³ of solution. What is the concentration in mol/dm³?

Step 1: Convert volume: $250 \text{ cm}^3 = 0.25 \text{ dm}^3$250 cm3=0.25 dm3

Step 2: Calculate concentration: $c = \frac{n}{V} = \frac{0.5}{0.25} = 2.0 \text{ mol/dm}^3$c=Vn​=0.250.5​=2.0 mol/dm3

Example 5

Question: How many moles of NaOH are in 100 cm³ of 0.5 mol/dm³ solution?

$n = c \times V = 0.5 \times 0.1 = 0.05 \text{ mol}$n=c×V=0.5×0.1=0.05 mol

Example 6

Question: What volume of 2.0 mol/dm³ $\text{H}_2\text{SO}_4$H2​SO4​ contains 0.4 mol?

$V = \frac{n}{c} = \frac{0.4}{2.0} = 0.2 \text{ dm}^3 = 200 \text{ cm}^3$V=cn​=2.00.4​=0.2 dm3=200 cm3

Exam Tip: When working with mol/dm³, you must know the moles of solute. If given mass, convert to moles first using $n = m / M_r$n=m/Mr​.

---

Converting Between g/dm³ and mol/dm³ (Higher Tier)

$\text{concentration (g/dm}^3) = \text{concentration (mol/dm}^3) \times M_r$concentration (g/dm3)=concentration (mol/dm3)×Mr​

$\text{concentration (mol/dm}^3) = \frac{\text{concentration (g/dm}^3)}{M_r}$concentration (mol/dm3)=Mr​concentration (g/dm3)​

Worked Example

Question: A sodium hydroxide solution has a concentration of 4.0 g/dm³. What is this in mol/dm³? ($M_r$Mr​ of NaOH = 40)

$c = \frac{4.0}{40} = 0.1 \text{ mol/dm}^3$c=404.0​=0.1 mol/dm3

Worked Example

Question: A hydrochloric acid solution has a concentration of 0.5 mol/dm³. What is this in g/dm³? ($M_r$Mr​ of HCl = 36.5)

$c = 0.5 \times 36.5 = 18.25 \text{ g/dm}^3$c=0.5×36.5=18.25 g/dm3

---

Dilution

When you add more water (solvent) to a solution:

• The number of moles of solute stays the same.
• The volume increases.
• The concentration decreases.

This relationship is expressed as:

$c_1 V_1 = c_2 V_2$c1​V1​=c2​V2​

Where $c_1$c1​ and $V_1$V1​ are the initial concentration and volume, and $c_2$c2​ and $V_2$V2​ are the final concentration and volume.

Worked Example

Question: 50 cm³ of 2.0 mol/dm³ HCl is diluted to 200 cm³. What is the new concentration?

$c_2 = \frac{c_1 V_1}{V_2} = \frac{2.0 \times 50}{200} = 0.5 \text{ mol/dm}^3$c2​=V2​c1​V1​​=2002.0×50​=0.5 mol/dm3

Exam Tip: Dilution questions often trip students up. Remember: adding water does NOT change the number of moles — it just spreads them out over a bigger volume.

---

Common Mistakes to Avoid

Mistake	Correction
Forgetting to convert cm³ to dm³	Divide by 1000 every time
Confusing g/dm³ with mol/dm³	Check the units requested in the question
Using mass when mol/dm³ is needed	Convert mass to moles first: $n = m / M_r$n=m/Mr​
Mixing up solute and solution	Concentration = solute ÷ total solution volume

---

Summary

• Concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³).
• Concentration (mol/dm³) = moles of solute ÷ volume of solution (dm³) — Higher tier only.
• Convert between units: $c$c (g/dm³) = $c$c (mol/dm³) × $M_r$Mr​.
• Always convert cm³ to dm³ by dividing by 1000.
• Dilution: $c_1 V_1 = c_2 V_2$c1​V1​=c2​V2​ — moles stay the same when water is added.

---

Extended Worked Examples

The single biggest source of error in concentration questions is mixing up cm³ and dm³. Always convert volumes to dm³ (divide cm³ by 1000) before you plug in numbers. Every answer below shows the unit conversion explicitly.

Example 7 — Preparing a Standard Solution

Question: A student needs 250 cm³ of a 0.100 mol/dm³ sodium carbonate solution for a titration. What mass of $\text{Na}_2\text{CO}_3$Na2​CO3​ should be weighed out?

Step 1 — convert volume to dm³: 250 cm³ = 0.250 dm³.

Step 2 — moles needed: $n = c \times V = 0.100 \times 0.250 = 0.0250 \text{ mol}$n=c×V=0.100×0.250=0.0250 mol.