Key Takeaways
- There are only 5 steps to any titration calculation. Convert volume to dm3, find moles of the known, apply the ratio, convert the unknown volume, then calculate concentration. Follow this process and you will always get the method marks.
- Concordant titres must be averaged correctly. Only average titre values within 0.10 cm3 of each other. Always ignore the rough titre.
- The cm3 to dm3 conversion is worth a mark on its own. Examiners specifically look for "divide by 1000" in your working. Forget this step and you lose an easy mark.
- AQA GCSE papers often ask for answers in g/dm3. If the question says "mass concentration", multiply your mol/dm3 answer by the Mr.
Contents
Titration calculations are one of the most frequently examined quantitative topics in both GCSE and IB Chemistry. They appear in AQA Required Practical 1, in Edexcel Core Practical, and across multiple IB exam papers every year. The good news is that every titration calculation follows the same fixed method, and once you learn it, you can apply it to any question.
This guide walks you through the complete method, from processing raw titre data to calculating concentration in both mol/dm3 and g/dm3. It includes three fully worked examples, covers dilutions and back-titrations, and links directly to our free Titration Calculator so you can check your working instantly.
What is a Titration?
A titration is a practical technique used to find the concentration of an unknown solution. You do this by reacting it with a solution of known concentration until the reaction is complete. The point at which this happens is called the end point, and it is detected using an indicator that changes colour.
In a typical acid-base titration:
- The known solution (usually an acid) is placed in the burette.
- The unknown solution (usually an alkali) is placed in the conical flask using a pipette.
- The known solution is added slowly until the indicator changes colour.
- The titre is the volume of known solution used, read from the burette.
The experiment is repeated several times to obtain concordant results.
How to Find the Concordant Average
Exam questions rarely give you a single volume. Instead, they present a results table with a rough titre and two or three trial titres. You need to identify the concordant values and calculate their average. This is the volume you use in your calculation.
The concordant titre rule
- Ignore the rough titre entirely. It is only used to get an approximate value for subsequent trials.
- Identify concordant values. These are titre values within 0.10 cm3 of each other.
- Average only the concordant values. Do not include the rough or any anomalous results.
Worked Example: Finding the concordant average
A student records the following titration results:
Rough: 25.10 cm3 | Trial 1: 24.50 cm3 | Trial 2: 24.45 cm3 | Trial 3: 24.55 cm3
Our Titration Calculator includes a built-in concordant titre averager. Click "Calculate average from raw titres" next to the volume input and it will do this step for you.
The 5-Step Method
Every standard titration calculation, regardless of the exam board, follows these five steps. Memorise them and you will always score at least 4 out of 5 method marks.
The method (memorise this)
- Convert the volume of the known solution from cm3 to dm3. Divide by 1000. This step is worth 1 mark on its own.
- Calculate the moles of the known solution. Use n = C × V (where V is in dm3).
- Use the molar ratio from the balanced equation to find the moles of the unknown substance. If the ratio is 1:1, the moles are the same. If it is 1:2 (like H2SO4 + 2NaOH), multiply accordingly.
- Convert the volume of the unknown solution from cm3 to dm3.
- Calculate the concentration of the unknown. Use C = n / V.
That is the entire method. The maths is straightforward. What costs students marks is forgetting the unit conversions or misreading the molar ratio.
Three Worked Examples
Example 1: HCl + NaOH (1:1 ratio)
Worked Example 1: Finding the concentration of NaOH
25.00 cm3 of NaOH solution is titrated with 0.100 mol/dm3 HCl. The mean titre is 24.50 cm3. The balanced equation is: HCl + NaOH → NaCl + H2O. Calculate the concentration of NaOH.
Example 2: H2SO4 + NaOH (1:2 ratio - the diprotic acid trap)
Worked Example 2: Using a 1:2 molar ratio
25.00 cm3 of NaOH is titrated with 0.200 mol/dm3 H2SO4. The mean titre is 12.50 cm3. The equation is: H2SO4 + 2NaOH → Na2SO4 + 2H2O. Find the concentration of NaOH.
Example 3: Finding concentration in g/dm3
Worked Example 3: Converting to g/dm3 (AQA-style)
From Example 1, the concentration of NaOH is 0.0980 mol/dm3. The Mr of NaOH is 40. Express this as a mass concentration in g/dm3.
Converting to g/dm3
AQA GCSE Chemistry papers frequently ask for answers in g/dm3 rather than mol/dm3. The conversion is straightforward:
Mass concentration (g/dm3) = Molar concentration (mol/dm3) × Mr
Our Titration Calculator has an optional Mr input field. If you fill it in, the tool automatically displays both the molar and mass concentrations in the result.
Dilution Calculations
Dilution questions use the formula C1V1 = C2V2, where C1 and V1 are the concentration and volume before dilution, and C2 and V2 are the values after dilution.
The principle is simple: the number of moles does not change during a dilution, only the concentration and volume change. This means moles before = moles after, which gives us C1V1 = C2V2.
Worked Example 4: Dilution
25.0 cm3 of 2.0 mol/dm3 HCl is diluted to 250.0 cm3. What is the new concentration?
Important: For C1V1 = C2V2, the volumes do not need to be in dm3 as long as both sides use the same unit. This is because the units cancel out.
Back-Titrations (IB and A-Level)
A back-titration is used when the substance being analysed cannot be titrated directly. This is common when finding the percentage purity of an impure sample, such as an antacid tablet.
The method works like this:
- Add a known excess of a reactant (e.g. HCl) to the impure sample.
- The pure substance in the sample reacts with some of the excess, but not all of it.
- Titrate the leftover excess with a second solution (e.g. NaOH) to find out how much remained unreacted.
- Subtract the leftover from the total to find the moles that actually reacted with the sample.
- Convert to mass and calculate percentage purity.
Worked Example 5: Back-titration for % purity
A 5.00 g impure sample of CaCO3 is dissolved in 50.0 cm3 of 1.00 mol/dm3 HCl (excess). The leftover HCl is titrated with 0.500 mol/dm3 NaOH, requiring 20.0 cm3. The ratio of HCl to NaOH is 1:1, and the ratio of CaCO3 to HCl is 1:2. Mr of CaCO3 = 100. Find the percentage purity.
Common Exam Mistakes
These are the errors that examiners report every year. All of them are avoidable.
Forgetting to convert cm3 to dm3
This is the single most common mistake in titration questions. Divide by 1000 and write it clearly. This step is worth 1 mark on its own in most mark schemes.
Including the rough titre in the average
The rough titre exists only to give the student an approximate endpoint. It must never be included in the concordant average. If you include it, your mean volume will be wrong and every subsequent calculation will be incorrect.
Using the wrong molar ratio
H2SO4 is diprotic, meaning it requires 2 moles of NaOH per mole of acid. Students who assume a 1:1 ratio for every titration will get the wrong answer. Always look at the balanced equation and count the coefficients.
Confusing mol/dm3 and g/dm3
If the question asks for concentration in g/dm3, you need an extra step: multiply the molar concentration by the Mr. If you give your answer in mol/dm3 when the question asks for g/dm3, you will lose marks even if your calculation is otherwise correct.
Frequently Asked Questions
How do you calculate concentration from titration results?
Calculate the moles of the known solution using n = C × V (with volume in dm3). Apply the molar ratio from the balanced equation to find the moles of the unknown substance. Then divide by the volume of the unknown solution (also in dm3) to find the concentration: C = n ÷ V.
What are concordant titres and how do you calculate them?
Concordant titres are titre values that are within 0.10 cm3 of each other. To find the concordant average, ignore the rough titre entirely, identify which of the remaining values are within 0.10 cm3 of each other, and calculate the mean of only those values.
How do you convert mol/dm3 to g/dm3?
Multiply the molar concentration by the molar mass (Mr) of the substance. For example, 0.1 mol/dm3 of NaOH has a molar mass of 40, so the mass concentration is 0.1 × 40 = 4.0 g/dm3. This conversion is frequently required by AQA GCSE papers.
What is a back-titration and when is it used?
A back-titration is used when the substance cannot be titrated directly. You add a known excess of reactant, let it react with the substance, then titrate the leftover excess to find out how much was consumed. This is commonly used to find the purity of impure samples like antacid tablets. Back-titrations appear in IB, A-Level, and occasionally in higher-tier GCSE papers.
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