Library / Solution chemistry, equilibria and kinetics / SCH-24
Solution chemistry, equilibria and kinetics
Gran extrapolation for a strong acid titre
Equivalence volume from a Gran plot.
- Ref
- SCH-24
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- Veq [mL]
For a strong acid titrated with a strong base, the Gran function (V_sample + V_base)·10^(−pH) is proportional to the amount of acid left, so it falls linearly with the base volume before equivalence. A straight line fitted to points well before the equivalence point crosses the zero line at Veq = −intercept/slope. The slope is negative, and the volume has the same unit as the base volume in the plot.
Equivalence volume from a Gran plot. Before equivalence, (V_sample + V_base)·10^(−pH) is plotted against base volume for a strong acid titrated with strong base; the straight line crosses zero at the equivalence volume. Needs a negative slope.
Calculator
- Equivalence volume in litres0.025 L
- Magnitude of the slope0.1
- Function value at zero base volume (the intercept)2.5
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.
- Extrapolating the Gran line gives an equivalence volume of 25 mL, found without having to read the steep part of the titration curve.
- Use points from perhaps 80 % of the way to equivalence back to about 20 %; points too close to the endpoint suffer from the electrode’s response and the neglected water term.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mL) | Local step | Change in result |
|---|---|---|---|---|---|---|
| a Intercept of the line | 0.1 to 100 mL | 1 | 1,000 | 999 | +10% | +10 % |
| m Slope of the line (negative) | −1 to −0.01 | 2.5 | 250 | 247.5 | +0.019799999999999998 | +24.7 % |
Sweep of Slope of the line (negative)
| Slope of the line (negative) | Equivalence volume (mL) |
|---|---|
| −1 | 2.5 |
| −0.8762 | 2.853 |
| −0.7525 | 3.322 |
| −0.6288 | 3.976 |
| −0.505 | 4.95 |
| −0.3812 | 6.557 |
| −0.2575 | 9.709 |
| −0.1338 | 18.69 |
| −0.01 | 250 |
Sweep one variable
Variables and how each one contributes
Equivalence volume
What the equation gives you. Everything else feeds it.
Intercept of the line
The intercept of the fitted line, the function value at zero base volume. Raises the equivalence volume in direct proportion. Raising it by 10 % (to 2.75) moves the result by +10 %, from 25 to 27.5 mL.
Slope of the line (negative)
The slope of the fitted line (negative). A steeper (more negative) slope gives a smaller equivalence volume. Raising it by 10 % (to −0.11) moves the result by −9.09 %, from 25 to 22.73 mL.
Worked example with the values above
- The line crosses zero where intercept + slope × V = 0.
- V = −2.5 / (−0.1) = 25.
- Veq = 25 mL.
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
- Using points close to or beyond the equivalence point.
- Forgetting to include the sample volume in the Gran function.
- Mixing the volume units of the intercept and the slope.
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