A-Level Titration Calculations: Formula and Example

This A-level titration calculator works out the unknown concentration of an acid or base from the titration volumes, known concentration and balanced reaction ratio you enter. It returns concentration in mol/L, with the mole calculation shown so you can check each step.

Formula

The calculation uses the balanced chemical equation to relate the reacting amounts. First calculate moles of the known solution, then use the mole ratio to find moles of the unknown, and divide by the unknown solution volume in litres:

n_known = c_known × V_known
c_unknown = n_known × (a / b) ÷ V_unknown

• c_known is the known concentration in mol/L.
• V_known is the measured volume of known solution in litres. Convert millilitres to litres by dividing by 1000.
• n_known is the amount of known reactant in moles.
• a/b is the stoichiometric ratio: the equation coefficient for the unknown divided by the coefficient for the known reactant.
• V_unknown is the unknown solution’s titre in litres.
• c_unknown is the concentration sought, in mol/L.

Enter the coefficients as positive numbers in the ratio fields. For a reaction written as aA + bB → products, if A is known and B is unknown, use the coefficient of B for a and the coefficient of A for b. This naming in the calculator keeps the ratio in the required unknown-to-known order.

Worked Example

Suppose 25.0 mL of a 0.100 mol/L known solution reacts with 24.8 mL of an unknown solution. The balanced equation has a 1:1 mole ratio, so enter 1 for each ratio coefficient. These are the calculator’s default values.

1. Convert the known volume: 25 mL ÷ 1000 = 0.025 L.
2. Calculate known moles: 0.100 mol/L × 0.025 L = 0.0025 mol.
3. Apply the 1:1 ratio: unknown moles = 0.0025 mol × (1 / 1) = 0.0025 mol.
4. Convert the unknown titre: 24.8 mL ÷ 1000 = 0.0248 L.
5. Calculate unknown concentration: 0.0025 mol ÷ 0.0248 L = 0.100806… mol/L, which rounds to 0.101 mol/L at three decimal places.

The second output is 0.00250 mol of known reactant. The final concentration is only as precise as the measurements and stated precision justify; the displayed decimal places do not make the original measurements more accurate.

Assumptions

• The balanced equation correctly describes the reaction and the entered coefficients are its mole ratio.
• The known concentration is accurate, and the recorded volumes correspond to the solutions that reacted at the endpoint.
• The reaction proceeds according to the equation without relevant side reactions.
• Volumes are entered in mL and converted to L using the exact factor 1000 mL = 1 L.

How A-Level Titration Calculations Work

A titration determines an unknown concentration by measuring how much of a solution with known concentration is needed to react with a measured portion of the unknown. The endpoint is the observed point at which the indicator changes colour or another measurement signals that the reaction has reached its intended completion. In an ideal calculation, the endpoint corresponds closely to the equivalence point, where reactants have combined in the balanced equation’s exact mole ratio.

The method is not always “moles are equal.” That is true only for a 1:1 equation. For example, in H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O, one mole of sulfuric acid reacts with two moles of sodium hydroxide. If sodium hydroxide is the known solution and sulfuric acid is unknown, the unknown-to-known ratio is 1/2. If the acid is known and the base unknown, it is 2/1. Always identify which substance each volume and concentration refers to before entering the ratio.

Choosing the Ratio and Using the Calculator

• Write and balance the chemical equation first. Do not use an unbalanced equation to infer mole amounts.
• Identify which solution has the known concentration and which has the unknown concentration.
• Use the volume of the known solution that was actually measured, and the unknown solution’s titre from the reaction.
• Enter coefficients in the calculator’s unknown-to-known ratio fields. For a 1:2 ratio, enter 1 for the unknown and 2 for the known.
• Check that both volumes are in mL, the concentration is in mol/L, and the result is chemically plausible.

In common school exercises, a measured aliquot of one solution is placed in a flask and the other is added from a burette. The unknown titre is the volume delivered from the burette, not the burette’s final reading by itself. It is the final reading minus the initial reading.

Endpoints, Repeats and Precision

A single titre can be affected by reading uncertainty, drops left on glassware, incomplete mixing, or adding titrant past the endpoint. In practical work, an initial rough titration is often followed by more careful runs. Concordant titres—measurements close to one another according to the practical’s stated tolerance—are used to obtain a more dependable titre, commonly by averaging the concordant values. Follow the instructions for the specific course or laboratory rather than assuming one universal tolerance.

Use the burette reading difference for each run and keep unrounded values through the calculation. Round the final result to a precision justified by the data and the question. If a question supplies uncertainty or asks for percentage uncertainty, address that separately: the calculator’s concentration result alone does not calculate experimental uncertainty.

Do not confuse the endpoint with the equivalence point. The equivalence point is defined by the reaction stoichiometry; the endpoint is what the experiment detects. A suitable indicator changes colour over a pH range that makes the observed endpoint a reasonable approximation for the reaction being studied.

Common Errors and Limits

• Skipping the balanced equation: this can give the wrong mole ratio, especially for polyprotic acids or reactions with coefficients other than one.
• Mixing up volume roles: divide unknown moles by the unknown solution’s titre, not by the known aliquot unless the unknown is the aliquot.
• Leaving volume in mL: mol/L requires litres. The calculator converts both entered mL volumes by dividing by 1000.
• Rounding too early: retain calculator precision until the final answer, then round appropriately.
• Assuming concentration ratio equals volume ratio: this shortcut works only under particular conditions, including a 1:1 reaction, and is not a general titration rule.

This calculator covers the stoichiometric concentration calculation. It cannot decide whether an indicator is appropriate, correct a poor endpoint, establish the accuracy of a standard solution, or account for side reactions. 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 using concentration × volume in litres. Use the balanced equation’s mole ratio to calculate unknown moles, then divide by the unknown solution’s volume in litres.

Do I need to convert cm³ to dm³?
Yes, when using concentration in mol/dm³ (the same numerical unit as mol/L). Divide a volume in cm³ or mL by 1000 to convert it to dm³ or L.

Why must the titration equation be balanced?
The coefficients give the reacting mole ratio. An incorrect or unbalanced equation can lead to an incorrect concentration even if the volume and arithmetic are right.

What is a concordant titre?
It is a titre that agrees closely with other careful measurements under the tolerance specified for the practical. Concordant results help reduce the effect of random reading variation.

Is the titre the final burette reading?
No. The titre is the volume delivered: final burette reading minus initial burette reading. Use that difference as the volume of titrant added.

Related

• How Many Protons Are in Potassium (K)?
• Moles of Electrons: Formula and Calculator
• Molecules to Liters Calculator: Convert Using Molarity

in c | Known solution concentration | mol/L | 0.1 | 0
in v | Known solution volume | mL | 25 | 0
in w | Unknown solution titre | mL | 24.8 | 0
in a | Unknown-to-known mole ratio | - | 1 | 0
in b | Known-to-unknown mole ratio | - | 1 | 0
out x | Unknown solution concentration | mol/L | c * (v / 1000) * (a / b) / (w / 1000) | 3
out n | Moles of known solution | mol | c * (v / 1000) | 5