Titration Calculations: Practice Questions and Answers

This titration calculator works out an unknown solution concentration from the titrant volume, titrant concentration, sample volume, and balanced reaction ratio. Enter those values to get the analyte concentration in mol/L; use the practice questions below to check how the calculation works.

Formula

At the equivalence point, the reacting amounts follow the coefficients in the balanced equation. If the equation is written as a analyte + b titrant → products, then the analyte concentration is:

C_a = C_t × (V_t / 1000) × (a / b) / (V_s / 1000)

• C_a is analyte concentration in mol/L.
• C_t is known titrant concentration in mol/L.
• V_t is titrant volume delivered at the endpoint in mL; dividing by 1000 converts mL to L.
• V_s is the original sample volume in mL; dividing by 1000 converts mL to L.
• a and b are the analyte and titrant coefficients in the balanced reaction.

The second output is the analyte amount in the sample, n_a = C_t × (V_t/1000) × a/b, in mol. The coefficients are numerical ratios, not units. For a 1:1 reaction, both are 1. For acid-base titrations, do not assume every reaction is 1:1: for example, one mole of sulfuric acid reacts with two moles of sodium hydroxide.

Worked Example

Use the calculator defaults: 0.100 mol/L titrant, a 24.60 mL endpoint volume, a 25.00 mL sample, and coefficients a = 1 and b = 1. The balanced reaction therefore has a 1:1 analyte-to-titrant ratio.

1. Convert the delivered titrant volume: 24.60 mL / 1000 = 0.02460 L.
2. Find titrant amount: 0.100 mol/L × 0.02460 L = 0.002460 mol.
3. Apply the reaction ratio: 0.002460 mol × (1/1) = 0.002460 mol analyte.
4. Convert the sample volume: 25.00 mL / 1000 = 0.02500 L.
5. Divide amount by sample volume: 0.002460 mol / 0.02500 L = 0.09840 mol/L.

The calculator returns an analyte concentration of 0.0984 mol/L (four decimal places) and an analyte amount of 0.002460 mol (six decimal places). The result is slightly below the titrant concentration because the endpoint required a little less than an equal volume of titrant and sample.

Assumptions

• The balanced reaction and its coefficients correctly describe the titration.
• The titrant concentration is known and applies to the solution used.
• The recorded titrant volume corresponds to the equivalence point, or a suitable endpoint close to it.
• Volumes are entered in mL, concentrations in mol/L, and sample volume is the original aliquot volume.
• This is a stoichiometric calculation; it does not model indicator behavior, side reactions, or measurement uncertainty.

How to Set Up a Titration Calculation

A titration determines an unknown concentration by measuring how much of a solution with known concentration reacts with a measured sample. The central idea is mole accounting: use the balanced equation to convert the moles of titrant delivered into moles of analyte, then divide by the sample volume in liters.

• Write and balance the reaction, then identify the analyte and titrant coefficients.
• Record the titrant concentration and the volume delivered at the endpoint. Delivered volume is generally the final burette reading minus the initial reading.
• Convert titrant volume from mL to L and calculate titrant moles using concentration × volume.
• Use the coefficient ratio to calculate analyte moles.
• Divide analyte moles by the original sample volume in liters.

The equivalence point is the stoichiometric point at which reactants have been supplied in the exact ratio in the balanced equation. An observed endpoint, such as a persistent indicator color change, is an experimental signal used to estimate it. Endpoint and equivalence point are related but not identical; a poorly chosen indicator or overshooting the color change can bias the measured volume.

Practice Questions

Try each problem before reading its answer. Assume the endpoint is accurate and the reaction is complete unless the question says otherwise.

1. 1:1 acid-base reaction: A 20.00 mL sample of monoprotic acid is titrated with 0.1500 mol/L sodium hydroxide. The endpoint uses 18.40 mL. What is the acid concentration?
   Answer: 0.1500 × 0.01840 = 0.002760 mol NaOH. The ratio is 1:1, so the acid amount is 0.002760 mol. Divide by 0.02000 L: 0.1380 mol/L.
2. Non-1:1 ratio: A 25.00 mL sulfuric acid sample takes 32.00 mL of 0.1000 mol/L sodium hydroxide. The reaction is H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O. Find the acid concentration.
   Answer: NaOH amount is 0.1000 × 0.03200 = 0.003200 mol. The acid-to-base ratio is 1:2, so sulfuric acid amount is 0.001600 mol. Divide by 0.02500 L: 0.06400 mol/L.
3. Find titrant volume: What volume of 0.2000 mol/L titrant is needed to react with 25.00 mL of 0.08000 mol/L analyte in a 1:1 reaction?
   Answer: Analyte amount is 0.08000 × 0.02500 = 0.002000 mol. The same amount of titrant is needed, so volume = 0.002000 / 0.2000 = 0.01000 L, or 10.00 mL.
4. Triprotic acid: A 10.00 mL sample of triprotic acid requires 30.00 mL of 0.1000 mol/L base for complete neutralization. If one mole of acid reacts with three moles of base, what is the acid concentration?
   Answer: Base amount is 0.1000 × 0.03000 = 0.003000 mol. Acid amount is 0.003000/3 = 0.001000 mol. Divide by 0.01000 L: 0.1000 mol/L.

Common Calculation Mistakes

• Forgetting the coefficient ratio: A diprotic or triprotic analyte may not react 1:1 with titrant. Start with the balanced equation, not a memorized shortcut.
• Mixing mL and L: Molarity uses liters. Convert both measured volumes consistently; the calculator applies division by 1000 to each.
• Using total flask volume instead of aliquot volume: If a sample was diluted in a flask before titration, the amount in the aliquot is calculated using the aliquot volume. Apply any dilution factor separately to recover the original concentration.
• Rounding too early: Keep guard digits through intermediate steps, then round the final value to match the precision of the measurements. Extra calculator digits do not imply extra experimental accuracy.
• Confusing endpoint with equivalence: An indicator color change is an estimate. Overshooting adds excess titrant and typically makes the calculated analyte concentration too high.

Frequently Asked Questions

What is the basic titration formula?
For a reaction a analyte + b titrant, use C_a = C_tV_ta/(bV_s), with both volumes in the same units. If using mL in the calculator, it converts both volumes to liters explicitly.

When can I use C₁V₁ = C₂V₂?
That shortcut applies when the reacting species have a 1:1 mole ratio and concentrations refer to those species. For other ratios, include the balanced-equation coefficients; equal volumes or equal concentrations are not general requirements.

How do I find the titrant volume?
Subtract the initial burette reading from the final reading, using the same units. If a question gives volume at the endpoint directly, use that delivered volume rather than the final reading alone.

Why does a titration result differ from the label value?
Possible causes include endpoint overshoot, inaccurate volume readings, a titrant concentration that has changed or was not standardized, an incorrect reaction ratio, or sample contamination. The calculation cannot correct experimental errors automatically.

How many significant figures should I report?
Use the precision supported by the measured volumes and the stated titrant concentration. Carry extra digits during calculation and round once at the end; follow any significant-figure rules specified by your class or lab.

These calculations support chemistry study and lab planning. For bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

Related

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

in ct | Titrant concentration | mol/L | 0.100 | 0
in vt | Titrant volume at endpoint | mL | 24.60 | 0
in vs | Sample volume | mL | 25.00 | 0
in a | Analyte coefficient in balanced equation | - | 1 | 0
in b | Titrant coefficient in balanced equation | - | 1 | 0
out ca | Analyte concentration | mol/L | ct * (vt / 1000) * a / b / (vs / 1000) | 4
out na | Analyte amount in sample | mol | ct * (vt / 1000) * a / b | 6