Library / Solution chemistry, equilibria and kinetics / SCH-23
Solution chemistry, equilibria and kinetics
Signed relative titration error
Percentage error of a titration, from the observed endpoint volume and the true equivalence volume.
- Ref
- SCH-23
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- ε [%]
The relative titration error is ε = 100(Vend − Veq)/Veq, with Vend the observed endpoint volume and Veq the true equivalence volume in the same unit. A positive value means titrant was overdelivered (endpoint beyond equivalence), and a negative value that the endpoint was reached early. It comes from the indicator choice, not from reading errors, which are separate.
Percentage error of a titration, from the observed endpoint volume and the true equivalence volume. A positive value means excess titrant was delivered past the equivalence point.
Calculator
- Volume error, Vend − Veq0.1 mL
- Error in parts per thousand4 ‰
- Volume error for a 0.1 % tolerance, 0.001 Veq0.025 mL
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The endpoint at 25.1 mL is 0.1 mL past the equivalence volume of 25 mL, an error of 0.4 %.
- A typical analytical target is within ±0.1 %, i.e. about 0.025 mL here, which sets the precision needed in the endpoint detection.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (%) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Veq True equivalence volume | 1 to 100 mL | −74.9 | 2,410 | 2,485 | +10% | −2,280 % |
| Vend Observed endpoint volume | 1 to 100 mL | −96 | 300 | 396 | +10% | +2,510 % |
Sweep of Observed endpoint volume
| Observed endpoint volume (mL) | Relative error (%) |
|---|---|
| 1 | −96 |
| 13.38 | −46.5 |
| 25.75 | 3 |
| 38.13 | 52.5 |
| 50.5 | 102 |
| 62.88 | 151.5 |
| 75.25 | 201 |
| 87.63 | 250.5 |
| 100 | 300 |
Sweep one variable
Variables and how each one contributes
Relative error
What the equation gives you. Everything else feeds it.
Observed endpoint volume
The observed endpoint volume. Raises the error in direct proportion, with slope 100/Veq per unit volume. Raising it by 10 % (to 27.61) moves the result by +2,510 %, from 0.4 to 10.44 %.
True equivalence volume
The true equivalence volume, in the same unit. A larger equivalence volume dilutes the same volume error, so the relative error shrinks. Raising it by 10 % (to 27.5) moves the result by −2,280 %, from 0.4 to −8.727 %.
Worked example with the values above
- Volume error: 25.1 − 25 = 0.1 mL.
- Relative to Veq: 0.1 / 25 = 0.004.
- ε = 100 × that = 0.4 %.
Assumptions and limits
- Complete, fast and well-defined reactions with a clear stoichiometry.
- Volumes in litres or in a single consistent unit, and calibrated glassware and electrodes.
Common mistakes
- Mixing mL and L in one calculation.
- Using the wrong mole ratio of reagent to analyte.
- Using points too close to the equivalence point for a Gran plot.
Statistics and uncertainty
Burette readings are good to ±0.02 to 0.05 mL, so a 25 mL titre has a relative error near 0.1 to 0.2 %, and the endpoint-detection error adds to it.
Where it is used
- Analysing antacids, alkalinity, chloride and other titratable species.
- Estimating the endpoint error of a titration.
Maths you need
- Stoichiometry: mole ratios in a balanced equation
- Equivalence point: where the reagent amounts match exactly
- Titre: the volume of titrant delivered