Quantitative chemistry: concentration of solutions

What you'll learn

This guide covers everything you need to know about concentration of solutions for AQA GCSE Chemistry. You'll learn how to calculate concentration in both mass per volume (g/dm³) and amount per volume (mol/dm³), convert between units, and apply these calculations to solve practical chemistry problems. These skills are essential for both Paper 1 and Paper 2, particularly in quantitative chemistry questions worth 4-6 marks.

Key terms and definitions

Concentration — the amount of solute dissolved in a given volume of solution, measured in g/dm³ or mol/dm³

Solute — the substance that dissolves in a solvent to form a solution

Solvent — the liquid in which a solute dissolves (usually water in GCSE Chemistry)

Solution — the mixture formed when a solute dissolves in a solvent

dm³ — cubic decimetre, a unit of volume equal to 1 litre or 1000 cm³

Molar concentration — concentration expressed as moles of solute per cubic decimetre of solution (mol/dm³)

Mass concentration — concentration expressed as grams of solute per cubic decimetre of solution (g/dm³)

Dilution — the process of decreasing the concentration of a solution by adding more solvent

Core concepts

Understanding concentration units

Concentration tells you how much solute is present in a specific volume of solution. At GCSE level, you need to work with two types of concentration:

Mass concentration (g/dm³):

• Measures the mass of solute in grams dissolved in 1 dm³ of solution
• More straightforward for everyday contexts
• Commonly used when dealing with solutions where you don't need to consider moles

Molar concentration (mol/dm³):

• Measures the number of moles of solute dissolved in 1 dm³ of solution
• Essential for stoichiometric calculations and titrations
• Sometimes written as M (molarity), though the exam uses mol/dm³

The volume unit dm³ is crucial to understand:

• 1 dm³ = 1000 cm³ = 1 litre
• You'll often need to convert between cm³ and dm³
• To convert cm³ to dm³: divide by 1000
• To convert dm³ to cm³: multiply by 1000

Calculating mass concentration

The formula for mass concentration is:

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

This can be rearranged using the triangle method:

• Mass = concentration × volume
• Volume = mass / concentration

Key steps for calculations:

1. Identify the mass of solute in grams
2. Convert the volume to dm³ if given in cm³
3. Substitute values into the formula
4. Include units in your answer

Working with volumes in cm³:

When volume is given in cm³, you have two options:

• Convert to dm³ first, then calculate concentration in g/dm³
• Use the formula: concentration (g/dm³) = [mass (g) / volume (cm³)] × 1000

The second approach is useful but requires careful attention to units.

Calculating molar concentration

For molar concentration, you need to know the number of moles of solute:

Concentration (mol/dm³) = moles of solute (mol) / volume of solution (dm³)

Remember that: Moles = mass (g) / Mr (relative formula mass)

So the complete calculation often involves:

1. Calculate the Mr of the solute
2. Calculate the number of moles using mass and Mr
3. Convert volume to dm³
4. Calculate concentration using moles and volume

This type of question commonly appears as a multi-step problem worth 4-5 marks.

Converting between concentration types

You can convert between mass concentration and molar concentration if you know the Mr of the solute:

Concentration (g/dm³) = concentration (mol/dm³) × Mr

Concentration (mol/dm³) = concentration (g/dm³) / Mr

This is particularly useful when:

• Given concentration in one unit but need to use it in calculations requiring the other
• Checking your answer makes sense
• Solving problems involving titrations or reacting masses

Dilution calculations

When you dilute a solution by adding solvent, the amount of solute stays the same but the concentration decreases.

Key principle: The number of moles of solute before dilution = number of moles after dilution

This leads to the relationship: C₁V₁ = C₂V₂

Where:

• C₁ = initial concentration
• V₁ = initial volume
• C₂ = final concentration
• V₂ = final volume

Important points about dilution:

• Both concentrations must be in the same units
• Both volumes must be in the same units
• The final volume is larger than the initial volume
• The final concentration is lower than the initial concentration

Calculating volumes and masses from concentration

Given a concentration, you can work backwards to find:

To find mass of solute needed:

• Rearrange: mass (g) = concentration (g/dm³) × volume (dm³)
• Or: moles = concentration (mol/dm³) × volume (dm³), then mass = moles × Mr

To find volume of solution:

• Rearrange: volume (dm³) = mass (g) / concentration (g/dm³)
• Or: volume (dm³) = moles / concentration (mol/dm³)

These calculations are common in required practical contexts, such as:

• Preparing a solution of known concentration
• Calculating volumes needed for titrations
• Determining how much solute to dissolve

Worked examples

Example 1: Calculating mass concentration

Question: A student dissolves 15.0 g of sodium chloride in water to make 250 cm³ of solution. Calculate the concentration of the solution in g/dm³. (2 marks)

Solution:

Step 1: Convert volume to dm³

• 250 cm³ ÷ 1000 = 0.25 dm³ ✓

Step 2: Use the formula

• Concentration = mass ÷ volume
• Concentration = 15.0 ÷ 0.25
• Concentration = 60 g/dm³ ✓

Mark scheme points:

• Correct conversion of volume (1 mark)
• Correct calculation with unit (1 mark)

Example 2: Calculating molar concentration

Question: A solution contains 21.2 g of sodium carbonate (Na₂CO₃) dissolved in 400 cm³ of water. Calculate the molar concentration of the solution. (Ar: Na = 23, C = 12, O = 16) (4 marks)

Solution:

Step 1: Calculate Mr of Na₂CO₃

• Mr = (2 × 23) + 12 + (3 × 16)
• Mr = 46 + 12 + 48 = 106 ✓

Step 2: Calculate moles of Na₂CO₃

• Moles = mass ÷ Mr
• Moles = 21.2 ÷ 106
• Moles = 0.20 mol ✓

Step 3: Convert volume to dm³

• 400 cm³ ÷ 1000 = 0.4 dm³ ✓

Step 4: Calculate concentration

• Concentration = moles ÷ volume
• Concentration = 0.20 ÷ 0.4
• Concentration = 0.5 mol/dm³ ✓

Mark scheme points:

• Correct Mr calculation (1 mark)
• Correct moles calculation (1 mark)
• Correct volume conversion (1 mark)
• Correct final answer with unit (1 mark)

Example 3: Dilution calculation

Question: A student has 50 cm³ of hydrochloric acid with a concentration of 2.0 mol/dm³. They add water to make the total volume 200 cm³. Calculate the new concentration of the diluted acid. (3 marks)

Solution:

Step 1: Write down known values

• C₁ = 2.0 mol/dm³, V₁ = 50 cm³
• V₂ = 200 cm³, C₂ = ? ✓

Step 2: Apply C₁V₁ = C₂V₂

• 2.0 × 50 = C₂ × 200
• 100 = C₂ × 200 ✓

Step 3: Solve for C₂

• C₂ = 100 ÷ 200
• C₂ = 0.5 mol/dm³ ✓

Mark scheme points:

• Correct use of dilution relationship (1 mark)
• Correct working shown (1 mark)
• Correct answer with unit (1 mark)

Common mistakes and how to avoid them

• Forgetting to convert cm³ to dm³ — Always check the volume unit. If given in cm³, divide by 1000 to convert to dm³. Write this conversion step clearly in your working.

• Confusing mass and moles — When calculating molar concentration, you must convert mass to moles first using n = m/Mr. Don't put mass directly into the concentration formula.

• Mixing up concentration units — Read the question carefully. If asked for mol/dm³, don't give g/dm³. Check which unit is required and ensure your final answer matches.

• Incorrect Mr calculations — Take care when calculating relative formula mass, especially with brackets in formulae. For Ca(OH)₂, the Mr = 40 + 2(16 + 1) = 74, not 40 + 16 + 1.

• Not showing working — Multi-step calculations require clear working for method marks. Even if your final answer is wrong, you can gain marks for correct methods shown.

• Rounding too early — Keep full calculator values until the final step, then round to 2 or 3 significant figures as appropriate. Rounding intermediate values leads to rounding errors.

Exam technique for concentration of solutions

• Command word "Calculate" — You must show all working clearly. Write down the formula, substitute values, and give your answer with the correct unit. This typically earns 3-5 marks depending on the number of steps.

• Units are essential — The mark scheme always allocates marks for correct units. Always include g/dm³ or mol/dm³ in your final answer. Missing units often costs 1 mark.

• Use the data sheet — In Paper 2, you have access to the periodic table. Use the Ar values provided to calculate Mr accurately. Don't try to remember atomic masses.

• Check reasonableness — If your concentration is negative or extremely large (e.g., 10,000 mol/dm³), you've made an error. Typical GCSE concentrations range from 0.1 to 100 g/dm³ or 0.01 to 2 mol/dm³.

Quick revision summary

Concentration measures how much solute dissolves in a given volume. Calculate mass concentration using: concentration (g/dm³) = mass (g) / volume (dm³). For molar concentration: concentration (mol/dm³) = moles / volume (dm³). Always convert cm³ to dm³ by dividing by 1000. To find moles, use n = m/Mr. For dilutions, apply C₁V₁ = C₂V₂. Show all working, include correct units, and convert volumes carefully to score full marks.