Moles in Solutions (Concentration)

This lesson covers how to calculate concentration and relate it to moles, mass and volume. These calculations are essential for GCSE Chemistry and are required by the Edexcel specification (1CH0). Concentration in mol/dm³ is a Higher tier topic.

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

Concentration can be expressed in two ways:

1. g/dm³ (grams per cubic decimetre) — Foundation and Higher
2. mol/dm³ (moles per cubic decimetre) — Higher only

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Volume Conversions

Before doing concentration calculations, you must be confident converting between units of volume:

Unit	Abbreviation	Relationship
Cubic centimetre	cm³	1 dm³ = 1000 cm³
Cubic decimetre	dm³	1 dm³ = 1 litre
Litre	L	1 L = 1000 mL = 1000 cm³

To convert cm³ to dm³: divide by 1000

To convert dm³ to cm³: multiply by 1000

Exam Tip: A very common mistake is forgetting to convert cm³ to dm³. If the question gives volume in cm³, you must divide by 1000 before using it in a concentration formula (unless the formula is already set up for cm³).

flowchart TD
    Top["moles (mol)<br/>—— or ——<br/>mass (g)"]
    Top --> Eq["concentration = moles ÷ volume<br/>concentration = mass ÷ volume"]
    Eq --> L["volume = moles ÷ concentration<br/>volume = mass ÷ concentration"]
    Eq --> R["moles = concentration × volume<br/>mass = concentration × volume"]
    R --> Note["Volume must be in dm³<br/>(divide cm³ by 1000)"]
    L --> Note

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Concentration in g/dm³

The formula for concentration in grams per cubic decimetre is:

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

This can be rearranged:

• mass = concentration × volume
• volume = mass ÷ concentration

Worked Example 1

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

Solution:

1. Convert volume: 250 cm³ ÷ 1000 = 0.25 dm³
2. concentration = mass ÷ volume = 5.0 ÷ 0.25 = 20 g/dm³

Worked Example 2

Question: A solution of potassium nitrate has a concentration of 40 g/dm³. What mass of solute is in 500 cm³ of solution?

Solution:

1. Convert volume: 500 cm³ ÷ 1000 = 0.5 dm³
2. mass = concentration × volume = 40 × 0.5 = 20 g

Worked Example 3

Question: What volume of a 10 g/dm³ solution contains 2.5 g of solute?

Solution:

1. volume = mass ÷ concentration = 2.5 ÷ 10 = 0.25 dm³
2. Convert to cm³ if needed: 0.25 × 1000 = 250 cm³

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Concentration in mol/dm³ (Higher)

The formula for concentration in moles per cubic decimetre is:

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

This can be rearranged:

• moles = concentration × volume
• volume = moles ÷ concentration

Worked Example 4 (Higher)

Question: 0.1 mol of hydrochloric acid is dissolved in 500 cm³ of solution. Calculate the concentration in mol/dm³.

Solution:

1. Convert volume: 500 cm³ ÷ 1000 = 0.5 dm³
2. concentration = moles ÷ volume = 0.1 ÷ 0.5 = 0.2 mol/dm³

Worked Example 5 (Higher)

Question: How many moles of NaOH are in 250 cm³ of a 2.0 mol/dm³ solution?

Solution:

1. Convert volume: 250 cm³ ÷ 1000 = 0.25 dm³
2. moles = concentration × volume = 2.0 × 0.25 = 0.5 mol

Worked Example 6 (Higher)

Question: What volume of 0.5 mol/dm³ sulfuric acid contains 0.05 mol of H₂SO₄?

Solution:

1. volume = moles ÷ concentration = 0.05 ÷ 0.5 = 0.1 dm³
2. Convert to cm³: 0.1 × 1000 = 100 cm³

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

To convert between the two concentration units, use Mr:

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

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

Worked Example 7 (Higher)

Question: A solution of sodium hydroxide (NaOH) has a concentration of 4.0 g/dm³. Convert this to mol/dm³.

Solution:

1. Mr of NaOH = 23 + 16 + 1 = 40
2. concentration (mol/dm³) = 4.0 ÷ 40 = 0.1 mol/dm³

Worked Example 8 (Higher)

Question: A solution of HCl has a concentration of 0.5 mol/dm³. Express this in g/dm³.

Solution:

1. Mr of HCl = 1 + 35.5 = 36.5
2. concentration (g/dm³) = 0.5 × 36.5 = 18.25 g/dm³

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Combining Concentration with Reacting Masses (Higher)

In more challenging questions, you may need to combine concentration calculations with reacting mass calculations.

Worked Example 9 (Higher)

Question: 25 cm³ of 0.1 mol/dm³ sodium hydroxide reacts with hydrochloric acid. Calculate the mass of sodium chloride produced.

NaOH + HCl → NaCl + H₂O

Solution:

1. Convert volume: 25 cm³ ÷ 1000 = 0.025 dm³
2. moles of NaOH = concentration × volume = 0.1 × 0.025 = 0.0025 mol
3. From the equation, 1 mol NaOH produces 1 mol NaCl
4. moles of NaCl = 0.0025 mol
5. Mr of NaCl = 23 + 35.5 = 58.5
6. mass of NaCl = 0.0025 × 58.5 = 0.146 g

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Summary of Formulae

Quantity	Formula
Concentration (g/dm³)	mass (g) ÷ volume (dm³)
Mass (g)	concentration (g/dm³) × volume (dm³)
Volume (dm³)	mass (g) ÷ concentration (g/dm³)
Concentration (mol/dm³) (Higher)	moles ÷ volume (dm³)
Moles (Higher)	concentration (mol/dm³) × volume (dm³)
Convert g/dm³ → mol/dm³ (Higher)	g/dm³ ÷ Mr
Convert mol/dm³ → g/dm³ (Higher)	mol/dm³ × Mr

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Common Mistakes

1. Forgetting to convert cm³ to dm³ — Always divide by 1000 when the volume is given in cm³.
2. Confusing g/dm³ and mol/dm³ — g/dm³ uses mass; mol/dm³ uses moles.
3. Using the wrong formula — Use the formula triangle to help rearrange.
4. Rounding too early — Keep full calculator values until the final answer.

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Summary