A-Level Titration Calculations: Formula and Worked Example

A-level titration calculations use the measured volumes and known concentration of solutions to find an unknown concentration or amount of substance. Enter the titration volumes, the known solution’s concentration, and the balanced-equation mole ratio to calculate the unknown concentration and amount of solute.

Formula

At the equivalence point, the reacting substances are present in the mole ratio given by the balanced chemical equation. If the known substance has coefficient a_k and the unknown has coefficient a_u, then n_u = n_k × a_u / a_k. Since n = cV, the unknown concentration is c_u = [c_k × (V_k/1000) × (a_u/a_k)] / (V_u/1000). The division by 1000 converts each volume from mL to L.

• c_k is the known solution concentration in mol/L.
• V_k is the known solution volume used in the reaction, in mL.
• V_u is the unknown solution volume that reacted, in mL.
• a_k and a_u are the balanced-equation coefficients for the known and unknown substances. They are positive whole numbers.
• n_u is the amount of unknown solute in the reacting volume, in mol; c_u is its concentration, in mol/L.

For a 1:1 reaction, both coefficients are 1, so the expression reduces to c_u = c_kV_k/V_u when both volumes use the same unit. The coefficients cannot be guessed from the acid and base labels: use the balanced equation for the actual reaction.

Worked Example

Using the defaults, suppose a 25.00 mL sample of unknown solution reacts with 25.00 mL of a 0.1000 mol/L known solution. The equation is assumed to have a 1:1 mole ratio.

1. Convert the known volume: 25.00 mL / 1000 = 0.02500 L.
2. Find the known amount: n_k = 0.1000 mol/L × 0.02500 L = 0.002500 mol.
3. Apply the coefficient ratio: n_u = 0.002500 mol × 1 / 1 = 0.002500 mol.
4. Convert the unknown volume: 25.00 mL / 1000 = 0.02500 L.
5. Calculate concentration: c_u = 0.002500 mol / 0.02500 L = 0.1000 mol/L.

The calculator therefore returns an unknown concentration of 0.1000 mol/L and 0.002500 mol of unknown solute in the titre.

Assumptions

• The reaction equation is balanced, and the stated coefficients describe the reacting species.
• The recorded volumes are the volumes at the equivalence point, and the known concentration is accurate.
• Solutions are treated as sufficiently dilute for the usual concentration calculation; the method uses molar concentration and stoichiometry, not activity corrections.
• The measured unknown volume is the aliquot that reacted, not the total volume of a stock solution unless that whole volume was titrated.

What Titration Calculations Tell You

A titration determines how much of one solution reacts with a measured amount of another. In the usual school calculation, one solution has a known concentration and is delivered from a burette into a measured sample of the unknown solution. The volume needed to reach the endpoint is used as an estimate of the equivalence-point volume, where the reactants have combined in the stoichiometric ratio.

The calculation itself is not limited to acid–base titrations. The same mole-ratio method applies to suitable redox and other solution reactions. What changes is the balanced equation and how the endpoint is detected. For an acid–base titration, an indicator may show a colour change near the endpoint; a good indicator is selected so its transition range lies close to the steep pH change around equivalence.

How to Set Up the Calculation

Keep the chemical equation and the volume data together rather than relying on a memorised shortcut. A reliable sequence is:

1. Write and balance the reaction equation, including the correct formulas.
2. Identify which reactant has known concentration and which concentration is sought.
3. Use the titre: the volume delivered from the burette, calculated as final reading minus initial reading. Use consistent units and convert mL to L when calculating moles.
4. Calculate moles of the known reactant with n = cV.
5. Use the equation coefficients to convert known moles into moles of the unknown.
6. Divide the unknown moles by the volume of the unknown aliquot in litres to obtain mol/L.

As a non-1:1 example, the balanced reaction H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O has a 1:2 mole ratio for sulfuric acid to sodium hydroxide. If sodium hydroxide is known and sulfuric acid is unknown, use a_k = 2 and a_u = 1. Treating this as 1:1 would give twice the correct acid amount.

Reading Titration Data and Improving Accuracy

In practical work, a rough titration can help locate the endpoint region, followed by more careful runs. Use concordant titres—close repeat results according to the tolerance specified by the course or method—and calculate a mean from the suitable accurate titres, not automatically from every reading including a rough result. Read a burette at eye level and record its scale to the precision requested. The titre is the change in burette reading, not the final reading alone.

• Use the actual concentration supplied or standardised for the known solution; do not assume a bottle label is the experimental value.
• Keep track of which volume belongs to the burette and which is the pipetted aliquot. Swapping them changes the answer.
• Do not round intermediate mole values aggressively. Keep guard digits and round the final result to a precision justified by the measurements.
• Check units: mol/L multiplied by L gives mol. A volume left in mL without conversion introduces a factor-of-1000 error.
• Check whether the question asks for concentration, moles in the aliquot, or total moles in a larger sample. These are different quantities.

A titre is an experimental estimate, not an exact equivalence volume. Endpoint overshoot, imprecise readings, incomplete mixing, or an unsuitable indicator can affect the result. Repeating measurements can reduce random variation, but it does not fix a consistently biased method or an incorrectly balanced equation.

Frequently Asked Questions

What is the formula for titration calculations?
First calculate known moles with n = cV, using volume in litres. Then apply the balanced-equation ratio to find unknown moles and divide by the unknown solution volume in litres: c_u = [c_kV_k(a_u/a_k)]/V_u.

Do I have to convert mL to L?
Yes, if concentration is in mol/L and you calculate moles using n = cV. Convert each volume by dividing mL by 1000. In a simplified ratio for concentration, volumes can cancel if both are in the same unit, but using litres throughout helps prevent mistakes.

How do I know the mole ratio?
Balance the chemical equation, then read the coefficients of the two reacting substances. Those coefficients give their mole ratio. Subscripts within a chemical formula are not the reaction coefficients.

What is the difference between endpoint and equivalence point?
The equivalence point is the stoichiometric point defined by the reaction equation. The endpoint is the observed signal, such as an indicator colour change. The aim is to choose a method whose endpoint is close to equivalence.

Should I include the rough titre in the mean?
Usually the rough run is used to estimate where the endpoint lies, while the mean is calculated from the accurate concordant titres. Follow the instructions for the specific question or practical, since required criteria can vary.

Why might my calculated concentration be wrong?
Common causes include a wrong or unbalanced equation, using the wrong aliquot volume, a burette-reading subtraction error, an endpoint overshoot, or a missing mL-to-L conversion. Check the units and coefficient ratio before changing the arithmetic.

For any bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

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in vk | Known solution volume | mL | 25.00 | 0
in ck | Known solution concentration | mol/L | 0.1000 | 0
in vu | Unknown solution volume | mL | 25.00 | 0
in ak | Known substance coefficient | - | 1 | 1
in au | Unknown substance coefficient | - | 1 | 1
out cu | Unknown solution concentration | mol/L | (ck * (vk / 1000) / ak) * au / (vu / 1000) | 4
out nu | Moles of unknown solute in titre | mol | ck * (vk / 1000) * au / ak | 6