Concentration and titration calculations (Higher)

Q: In a titration, what are the specific functions of a pipette and a burette?

A pipette measures a fixed, accurate volume of one solution into a flask, while a burette adds the second solution drop by drop to find the exact neutralisation point.

Q: What are the four steps of the "M-R-M-C" method for titration calculations?

1. Write the balanced equation. 2. Calculate M oles of the known. 3. Use the R atio. 4. Calculate the M oles of the unknown and then the final C oncentration.

Chemistry (1CH0) · Pearson Edexcel GCSE (9-1) · 4 min read · Updated: 7 Sept 2026

Welcome to Concentration and Titration Calculations!

Hello! If you’ve made it to this chapter, you’re diving into the "Higher Tier" heart of Chemistry. While these calculations might look intimidating at first, they follow a very logical pattern. Think of it like a recipe: once you know the ratios and the steps, you can solve any problem. In this section, we will learn how to measure the "strength" of solutions and use a technique called titration to find unknown concentrations with pinpoint accuracy.

1. The Basics: What is Concentration?

In Chemistry, concentration tells us how much of a substance (the solute) is dissolved in a certain volume of liquid (the solvent). You might already know how to calculate this in grams per decimetre cubed (\(g/dm^{3}\)), but for Higher Tier, we use moles.

The Crucial Volume Conversion

Before you do any math, you must remember that chemistry volumes are almost always measured in decimetres cubed (\(dm^{3}\)), but lab equipment like pipettes and burettes measures in centimetres cubed (\(cm^{3}\)).

The Rule: To turn \(cm^{3}\) into \(dm^{3}\), you must divide by 1000.

\(1000 cm^{3} = 1 dm^{3}\)

\(25.0 cm^{3} = 0.025 dm^{3}\)

Quick Review: Always check your units! If you see \(cm^{3}\) in a calculation question, divide it by 1000 before you start.

2. Calculating Concentration in \(mol/dm^{3}\)

At the Higher Tier level, we measure concentration using moles per decimetre cubed (\(mol/dm^{3}\)). This is often called "molarity."

The Formula:

\(Concentration \ (mol/dm^{3}) = \frac{Number \ of \ moles}{Volume \ (dm^{3})}\)

You can also rearrange this to find the number of moles:

\(Moles = Concentration \times Volume\)

Converting between \(g/dm^{3}\) and \(mol/dm^{3}\)

Sometimes a question will ask you to convert between the two types of concentration. To do this, you need the relative formula mass (\(M_{r}\)) of the substance.

To go from moles to grams: Multiply by the \(M_{r}\).
To go from grams to moles: Divide by the \(M_{r}\).

\(Concentration \ (g/dm^{3}) = Concentration \ (mol/dm^{3}) \times M_{r}\)

Example: If you have \(0.5 mol/dm^{3}\) of \(NaOH\) (\(M_{r} = 40\)), the concentration in \(g/dm^{3}\) is \(0.5 \times 40 = 20 g/dm^{3}\).

3. Titration: The Experimental Side

Titration is a method used to find the exact concentration of an acid or an alkali. You will have performed this in Core Practical 5.9C.

In a typical titration:

A pipette is used to measure a fixed volume of one solution (usually the alkali) into a conical flask.
A burette is used to add the other solution (usually the acid) drop by drop.
An indicator (like phenolphthalein or methyl orange) tells you exactly when the reaction has neutralised (the end-point).

4. How to Solve Titration Calculations

Don't worry if these seem tricky; just follow these four consistent steps every time. We call this the "M-R-M-C" method.

The Problem: \(25.0 cm^{3}\) of \(0.10 mol/dm^{3}\) \(NaOH\) reacted exactly with \(20.0 cm^{3}\) of \(HCl\). What is the concentration of the \(HCl\)?

Step 1: Write the balanced equation

Identify the ratio of the reactants.

\(NaOH + HCl \rightarrow NaCl + H_{2}O\)

The ratio is 1:1.

Step 2: Calculate Moles of the "Known" solution

The "known" is the one where you have both the volume and the concentration (\(NaOH\)).

\(Volume \ in \ dm^{3} = 25.0 / 1000 = 0.025 dm^{3}\)

\(Moles = Conc \times Vol = 0.10 \times 0.025 = 0.0025 \ moles \ of \ NaOH\)

Step 3: Use the Reacting Ratio

Look at your balanced equation. If 1 mole of \(NaOH\) reacts with 1 mole of \(HCl\), then \(0.0025\) moles of \(NaOH\) must react with \(0.0025\) moles of \(HCl\).

Moles of \(HCl = 0.0025\)

Step 4: Calculate the unknown Concentration

Now use the volume of the \(HCl\) (\(20.0 cm^{3}\)) and the moles you just found.

\(Volume \ of \ HCl \ in \ dm^{3} = 20.0 / 1000 = 0.020 dm^{3}\)

\(Concentration = \frac{Moles}{Volume} = \frac{0.0025}{0.020} = 0.125 \ mol/dm^{3}\)

Key Takeaway: Always find the moles of what you know first, use the ratio to find the moles of the unknown, then calculate the concentration.

5. Common Mistakes to Avoid

Unit Errors: Forgetting to divide \(cm^{3}\) by 1000. Always do this first!
Ratio Confusion: If the equation is \(2NaOH + H_{2}SO_{4}\), the ratio is 2:1. You would need to divide or multiply the moles accordingly.
Decimal Places: Titration results are very precise. Keep your numbers in your calculator until the very end to avoid rounding errors.

Did you know? In industrial chemistry, getting these calculations wrong by even a tiny fraction could mean wasting thousands of pounds of chemicals or creating an unsafe product!

Quick Review Box

1. Moles = \(Concentration \ (mol/dm^{3}) \times Volume \ (dm^{3})\)
2. \(1 dm^{3} = 1000 cm^{3}\)
3. \(g/dm^{3} = mol/dm^{3} \times M_{r}\)
4. Titration finds the concentration of an unknown acid or alkali using a neutralisation reaction.

Note: This chapter focuses on solution concentrations. For calculations involving the volumes of gases or how much product a reaction makes, see the chapters on "Molar volume" and "Percentage yield".

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is the definition of concentration in a chemical solution?

Concentration measures the amount of a solute (in grams or moles) dissolved in a specific volume of solvent (usually 1 \(dm^{3}\)).

How do you convert a volume from \(cm^{3}\) to \(dm^{3}\)?

To convert \(cm^{3}\) to \(dm^{3}\), you must divide the value by 1000 (\(1 dm^{3} = 1000 cm^{3}\)).

What is the formula for calculating concentration in \(mol/dm^{3}\)?

\(Concentration \ (mol/dm^{3}) = \frac{Number \ of \ moles}{Volume \ (dm^{3})}\)

How do you convert a concentration from \(mol/dm^{3}\) to \(g/dm^{3}\)?

Multiply the concentration in \(mol/dm^{3}\) by the relative formula mass (\(M_{r}\)) of the substance.

What is the purpose of a titration experiment?

Titration is an experimental technique used to determine the exact concentration of an acid or an alkali by reacting it with a solution of known concentration.

In a titration, what are the specific functions of a pipette and a burette?

A pipette measures a fixed, accurate volume of one solution into a flask, while a burette adds the second solution drop by drop to find the exact neutralisation point.

What are the four steps of the "M-R-M-C" method for titration calculations?

1. Write the balanced equation. 2. Calculate Moles of the known. 3. Use the Ratio. 4. Calculate the Moles of the unknown and then the final Concentration.

Why is the balanced chemical equation essential for titration calculations?

It provides the reacting ratio, telling you how many moles of acid react with a specific number of moles of alkali.

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