What a titration calculation finds
In a titration you add a solution of known concentration (the titrant) from a burette to a measured volume of a solution of unknown concentration (the analyte) until an indicator or pH meter shows the equivalence point, where the two have reacted in exactly the proportions of the balanced equation. Because you know how much titrant it took, you can work backward to the analyte concentration. It is the standard way to determine acid strength, vinegar acidity, or the concentration of a prepared base.
This calculator assumes the simplest and most common case: the titrant and analyte react in a 1:1 mole ratio, as with HCl and NaOH or acetic acid and NaOH. Enter the volume of titrant delivered at the endpoint, its molarity, and the volume of analyte you started with, and it returns the analyte molarity. If your reaction has a different ratio, apply the correction described below.
Formula and variables
M(analyte) = M(titrant) x V(titrant) / V(analyte)
This is the 1:1 form of M1V1 = M2V2. The two volumes only need to share a unit, so millilitres work directly.
- M(titrant): concentration of the standard solution in mol/L.
- V(titrant): volume delivered at the endpoint (final burette reading minus initial reading).
- V(analyte): volume of the sample in the flask, from a pipette.
- For other ratios, multiply the result by the analyte-to-titrant mole ratio from the balanced equation. For example, H2SO4 titrated with NaOH uses 1 mole of acid per 2 moles of base, so divide the calculator result by 2.
Worked example
A 25.00 mL sample of hydrochloric acid of unknown strength is titrated with 0.1000 M NaOH, and the endpoint is reached after 24.50 mL. The moles of NaOH delivered are 0.1000 x 0.02450 = 0.002450 mol. HCl and NaOH react 1:1, so the flask held 0.002450 mol HCl in 0.02500 L, giving 0.0980 M. Entering 24.5, 0.1, and 25 in the calculator returns "Analyte Molarity: 0.0980 M".
Common mistakes and how to interpret the result
- Ignoring stoichiometry. The result is only correct for a 1:1 reaction. Diprotic acids, for instance, need the ratio correction.
- Using total volume. Use the burette volume delivered, not the combined volume of flask contents.
- Overshooting the endpoint. Adding too much titrant inflates the calculated concentration. Repeat the titration until results agree within about 0.1 mL.
- Trusting more digits than the glassware supports. Burettes read to roughly 0.05 mL, so report about four significant figures at most.