Titration Calculations A Level: Formula and Example

A titration calculation uses the measured volume of a solution of known concentration to find an unknown concentration or amount, using the balanced reaction equation. Enter the titre volumes, known concentration, and reaction coefficients below to calculate the unknown concentration in mol/L and molar mass-normalised concentration in mol/L units.

Formula

The balanced equation determines the mole ratio. If the known reagent is A and the unknown is B, and the equation is n_AA + n_BB → products, then at the equivalence point:

c_B = (c_A × V_A / 1000) × n_B / (n_A × V_B / 1000)

• c_B is the unknown concentration in mol/L.
• c_A is the known concentration in mol/L.
• V_A is the titre volume of known solution in mL.
• V_B is the measured volume of unknown solution in mL.
• n_A and n_B are the balanced-equation coefficients, treated here as positive whole-number inputs.

Both volumes are converted from mL to L by dividing by 1000. Since both volumes share that conversion, it cancels when calculating concentration, but the calculator keeps it explicit. The second output gives moles of unknown substance in the sample, not its concentration.

Worked Example

For the default values, the known solution has concentration 0.1000 mol/L and the mean titre is 25.00 mL. The unknown sample volume is 25.00 mL, and both coefficients are 1.

1. Convert the titre: 25.00 mL / 1000 = 0.02500 L.
2. Find known-reagent moles: 0.1000 mol/L × 0.02500 L = 0.002500 mol.
3. Apply the 1:1 reaction ratio: unknown moles = 0.002500 mol × 1 / 1 = 0.002500 mol.
4. Convert the unknown volume: 25.00 mL / 1000 = 0.02500 L.
5. Calculate its concentration: 0.002500 mol / 0.02500 L = 0.1000 mol/L.

The calculator therefore reports 0.1000 mol/L for the unknown concentration and 0.002500 mol for the amount in the sample.

Assumptions

• The entered titre corresponds to the equivalence point, and the balanced reaction describes the relevant stoichiometry.
• The known concentration is accurate and expressed in mol/L; both stated volumes are measured solution volumes.
• The sample reacts according to the equation without significant side reactions or loss.
• This is study and lab-planning arithmetic, not a substitute for an experimental method or uncertainty analysis.

What A-Level Titration Calculations Mean

In a volumetric analysis, a solution with known concentration is added to a measured sample until the reactants have combined in the ratio specified by the chemical equation. The delivered volume is the titre. At the equivalence point, stoichiometric amounts have reacted; it does not necessarily mean equal volumes or equal concentrations. The endpoint is the observed indicator change or instrument signal used to identify that point, and should be as close as practical to the equivalence point.

At A level, questions commonly ask for an acid concentration, an alkali concentration, the amount of a substance in a sample, or a percentage purity. Each starts with the same chain: balance the equation, convert volume to dm³ or L, calculate moles from concentration times volume, use the mole ratio, then convert the result into the requested quantity. One litre equals one dm³, so mol/L and mol/dm³ have the same numerical value.

How to Set Up the Calculation

1. Write and balance the reaction. Use the coefficients from the balanced equation, not guessed ratios based on the formulas.
2. Identify the known solution and its titre. Use the delivered volume of that solution and its stated concentration.
3. Convert units consistently. For concentration in mol/L, express volume in L; divide mL by 1000.
4. Calculate known moles. Use n = cV, where n is moles, c is mol/L, and V is L.
5. Apply the reaction ratio. For A and B, n(B) = n(A) × coefficient(B) / coefficient(A).
6. Find the requested value. Divide unknown moles by the unknown sample volume in L for concentration. For mass, multiply moles by molar mass in g/mol.

For example, the balanced reaction HCl + NaOH → NaCl + H₂O has a 1:1 mole ratio. A different acid may donate more than one proton per molecule, so its ratio with hydroxide can differ. Always use the equation for the reaction given in the question.

Using Titre Readings and the Calculator

In a practical, several titres may be recorded. A rough first run helps locate the endpoint; repeat runs are then used to obtain concordant titres according to the course or laboratory instructions. The mean is usually calculated from the concordant results, not automatically from every reading. Enter that mean as the titre. The calculator does not decide which readings are concordant or correct a poor endpoint.

Enter the known concentration and the volume of the unknown aliquot in the same units shown. Coefficients must be positive whole numbers from the balanced equation. A coefficient of 1 is not a measured concentration or an extra multiplier unrelated to stoichiometry. Check that the first result is the unknown concentration; the second result is the moles present in the aliquot.

Common Errors and Limits

• Using the wrong volume: the titre is the volume delivered from the burette, while the unknown volume is the aliquot measured for analysis. They are not interchangeable.
• Forgetting the coefficient ratio: multiplying by the known coefficient instead of dividing by it can give the wrong answer. Derive the ratio from the balanced equation.
• Mixing mL and L: using 25.00 as though it were litres makes a result 1000 times too small or too large. Convert explicitly.
• Rounding too soon: keep guard digits during intermediate steps and round only the final result to a precision justified by the data.
• Confusing endpoint and equivalence point: an indicator changes colour over a range. A suitable indicator and careful technique help make the observed endpoint a useful estimate.

The formula assumes the reaction is sufficiently complete and that the titre represents the intended reaction. It cannot account for uncertain concentration, burette reading uncertainty, contamination, an unsuitable indicator, or reactions with interfering substances. For a percentage purity question, calculate the mass of the reacting substance from its moles, then divide by the original sample mass and multiply by 100; the calculator alone does not know the sample mass. For bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

Frequently Asked Questions

How do you calculate concentration from a titration?
Calculate moles of the known solution with n = cV, using volume in litres. Apply the balanced-equation mole ratio to find unknown moles, then divide by the unknown sample volume in litres.

Why do you divide the titre by 1000?
The concentration is in mol/L, so the volume used in n = cV must be in litres. Since 1000 mL equals 1 L, divide a volume in mL by 1000.

Do I use the titre or the pipette volume?
Use the titre as the volume of the known solution delivered. Use the pipette or aliquot volume as the volume of the unknown solution sample when calculating its concentration.

Do titration volumes have to be equal?
No. Equal volumes occur only in some situations. The equivalence point depends on the concentrations and the balanced reaction ratio, not on a rule that the volumes must match.

How many decimal places should I give?
Follow the question’s instructions and the precision of the measurements. Keep extra digits in intermediate calculations, then round the final value appropriately; do not imply greater precision than the measurements support.

Related

• Molecules to Moles Calculator: Divide by the Avogadro Constant
• Mass to Mole Calculator: Grams to Moles From the Molar Mass
• Moles to Grams Calculator: Mass of a Compound From Moles

in va | Titre volume | mL | 25.00 | 0
in cb | Known solution concentration | mol/L | 0.1000 | 0
in vb | Volume of unknown solution | mL | 25.00 | 0
in na | Known-solution coefficient | - | 1 | 1
in nb | Unknown-solution coefficient | - | 1 | 1
out cu | Unknown concentration | mol/L | (cb * va / 1000) * nb / (na * vb / 1000) | 4
out nu | Moles of unknown in sample | mol | (cb * va / 1000) * nb / na | 6