Gran Plot
Definition and meaning of Gran Plot in chemistry.
A Gran plot is a linearized graph of potentiometric titration data, typically volume of titrant times an exponential function of the measured electrode potential or pH, plotted against titrant volume, used to locate the equivalence point precisely from a straight-line x-intercept rather than from the curve's inflection point.
In more detail
Ordinary titration curves are sigmoidal, and near the equivalence point the slope can be shallow for weak acids/bases, dilute solutions, or poorly buffered systems, making the inflection point hard to pinpoint by eye or by simple derivative methods. Gran's transformation exploits the linear relationship between titrant volume and a rearranged form of the equilibrium expression (derived from the mass-action and mass-balance equations) that holds strictly only before or after the equivalence point, well away from the curved region. Because the transformed data are linear over an extended range, a simple linear regression and extrapolation give a far more precise and less subjective equivalence volume than direct curve inspection. The method is named for Swedish chemist Gunnar Gran, who introduced it in 1950, with a widely cited follow-up paper ("Part II") in 1952.
Key facts
| Field | Analytical Chemistry |
|---|---|
| Introduced by | Gunnar Gran (1950; Part II, 1952) |
| Typical function plotted | V × 10^(−pH) vs. V (titrant volume) |
| Common application | Potentiometric acid–base and redox titrations, especially weak/dilute analytes |
In titrating a weak monoprotic acid with standard NaOH, the quantity V(NaOH) × 10^(−pH) is plotted against V(NaOH) for volumes before the equivalence point. The data fall on a straight line that decreases toward zero; extrapolating this line to where it crosses the volume axis gives the equivalence-point volume directly, without needing to identify the steepest part of the S-shaped titration curve.
Frequently asked questions
Why use a Gran plot instead of just reading the titration curve?
Because it linearizes the data before (or after) the equivalence point, giving a straight-line extrapolation to the endpoint that is far more precise than judging the inflection point of a shallow or noisy sigmoidal curve.
Is a Gran plot limited to acid–base titrations?
No. The same linearization approach applies to any potentiometric titration, including redox and precipitation titrations, wherever the electrode response follows a known logarithmic (Nernstian) relationship to concentration.