Titration Calculator - Find Analyte Concentration

What Is a Titration Calculator?

A titration calculator finds the concentration of an unknown solution, called the analyte, using data from a titration. In a titration, a solution of known concentration, called the titrant, is added slowly to the analyte until the reaction between them is complete. Measuring how much titrant was needed lets a chemist work out how concentrated the analyte was.

Titration Formula

The calculator uses the standard titration formula for a reaction where titrant and analyte react in a 1:1 ratio:

$C_2 = \frac{C_1 \times V_1}{V_2}$

• $C_1$ = concentration of the titrant (mol/L)
• $V_1$ = volume of titrant used (mL), equal to the final burette reading minus the initial reading
• $C_2$ = concentration of the analyte (mol/L)
• $V_2$ = volume of the analyte (mL)

The formula comes from a basic rule of titration: at the point where the reaction is exactly finished (the equivalence point), the moles of titrant added equal the moles of analyte present, as long as the reaction consumes them in a 1:1 ratio. Moles equal concentration multiplied by volume, so:

$C_1 \times V_1 = C_2 \times V_2$

Solving for $C_2$ gives the formula above.

How to Calculate Analyte Concentration

1. Record the initial burette reading. This is the starting volume in the burette, in mL. It is 0.0 mL if the burette was filled to the zero mark.
2. Record the final burette reading. This is the volume shown when the reaction just finishes, usually spotted by a color change from an indicator.
3. Subtract to get the titrant volume. Final reading minus initial reading, in mL.
4. Enter the titrant concentration. This is the known concentration of the standard solution, in mol/L.
5. Enter the analyte volume. This is the volume of the unknown solution used, usually measured with a pipette, in mL.
6. Apply the formula. Multiply the titrant concentration by the titrant volume, then divide by the analyte volume.

The final reading must be equal to or greater than the initial reading, and the analyte volume must be greater than zero. The calculator checks both conditions and shows an error message if either fails.

Worked Example

Suppose a burette starts at 0.0 mL and ends at 10.0 mL after the reaction is complete. The titrant is 0.1 mol/L, and the analyte volume is 25 mL.

1. Titrant volume: $10.0 - 0.0 = 10.0$ mL
2. Apply the formula: $C_2 = \dfrac{0.1 \times 10.0}{25} = 0.04$ mol/L

The analyte concentration is 0.04 mol/L.

Titrations That Are Not 1:1

Some reactions consume titrant and analyte in a ratio other than 1:1. For example, sulfuric acid reacts with sodium hydroxide as $\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}$, so one mole of acid needs two moles of base. The formula above must be adjusted with the stoichiometric coefficients:

$C_2 = \frac{C_1 \times V_1 \times n_2}{V_2 \times n_1}$

Here $n_1$ is the coefficient of the titrant in the balanced equation and $n_2$ is the coefficient of the analyte. For the sulfuric acid example, $n_1 = 2$ (NaOH) and $n_2 = 1$ (H₂SO₄), so the titrant volume needed is effectively divided by an extra factor of two.

Types of Titration

• Acid-base titration. A strong or weak acid reacts with a strong or weak base. Used to test vinegar acidity, water alkalinity, and antacid tablets.
• Redox titration. Based on electron transfer between titrant and analyte. Used to measure hydrogen peroxide concentration or dissolved oxygen in water.
• Complexometric titration. A chelating agent such as EDTA binds to metal ions. Used to measure water hardness from calcium and magnesium content.
• Precipitation titration. The reaction forms an insoluble solid. Used to measure chloride concentration with silver nitrate.

Sources of Error

• Overshooting the endpoint. Adding titrant too quickly can push past the point where the indicator changes color.
• Misreading the meniscus. The burette should be read at eye level, looking at the bottom of the curved liquid surface.
• Air bubbles in the burette tip. A trapped bubble makes the recorded volume larger than the volume actually delivered.
• Degraded titrant. Sodium hydroxide solutions absorb carbon dioxide from air over time, which changes their concentration.
• Dirty glassware. Residue in the burette or flask can react with the solutions and change the result.

Frequently Asked Questions

What is the difference between the titrant and the analyte? The titrant is the solution with a known concentration, added from the burette. The analyte is the solution with the unknown concentration being measured.

What is the difference between the endpoint and the equivalence point? The equivalence point is the exact moment the reaction is stoichiometrically complete. The endpoint is the moment an indicator changes color, signaling that the reaction is done. Good indicator choice keeps the two very close together, but they are rarely identical.

Why does the calculator require the final reading to be at least the initial reading? The titrant volume equals the final reading minus the initial reading. Since a burette is read as it drains, the volume added cannot be negative, so the final reading cannot be smaller than the initial one.

How is a titration with a non-1:1 stoichiometry calculated? Multiply the standard result by the ratio of stoichiometric coefficients between titrant and analyte, as shown in the formula above. A reaction where two moles of titrant react with one mole of analyte needs the titrant term divided by two.

Can titration be used on colored or cloudy solutions? Yes. When a color-change indicator is hard to see, a pH electrode (potentiometric titration) or a conductivity meter (conductometric titration) can locate the endpoint instead.

How precise are titration results? With calibrated glassware and careful technique, titration can reach a precision of about ±0.1%. Most of the error in a titration comes from measurement and technique, not from the arithmetic.

References

1. Harris, D. C. (2015). Quantitative Chemical Analysis (9th ed.). W. H. Freeman and Company.
2. Skoog, D. A., West, D. M., Holler, F. J., & Crouch, S. R. (2013). Fundamentals of Analytical Chemistry (9th ed.). Cengage Learning.
3. IUPAC Compendium of Chemical Terminology (Gold Book).
4. NIST Chemistry WebBook, U.S. National Institute of Standards and Technology.