Прогнозирование конечной точки: график Грана

A Gran plot predicts the equivalence volume or endpoint of a potentiometric or acid-base titration without actually reaching the endpoint. Titration data collected up to a volume less than the equivalence point is converted into linear form. The straight line is extrapolated to the x-axis, revealing the titrant volume required at the equivalence point, saving time and reagents.

For potentiometric titration, the Gran plot is created by plotting the volume-corrected base-10 antilogarithm of the electrode potential against titrant volume. After fitting the best line through the data points, the line is extrapolated to the x-axis. This x-intercept directly indicates the titrant volume at the equivalence point.

In weak acid-strong base titration, the Gran plot equation produces a straight line where the slope equals the negative activity-corrected acid dissociation constant. The x-intercept of this line corresponds to the titrant volume at the endpoint. This relationship allows prediction of both the endpoint and acid strength from a single plot.

Linear extrapolation allows prediction of the equivalence volume from data collected before reaching the endpoint, reducing the volume of titrant needed and minimizing experimental time. Converting titration data into linear form enables accurate endpoint prediction through mathematical regression rather than relying on indicator color changes or potential jumps.

Titration data must be converted into linear form before constructing a Gran plot. For potentiometric titration, the volume-corrected base-10 antilogarithm of electrode potential is plotted against titrant volume. This transformation converts the nonlinear titration curve into a straight line suitable for linear regression and extrapolation.

The x-intercept of the extrapolated Gran plot line directly represents the titrant volume required to reach the equivalence point. By extending the linear regression line to where it crosses the x-axis, analysts can determine the endpoint volume without conducting a complete titration, making the method efficient for routine analyses.

Volume correction accounts for dilution effects as titrant is added, ensuring accurate representation of the system's electrochemical state. Using the base-10 antilogarithm of electrode potential linearizes the relationship between potential and titrant volume. This combination produces a reliable straight line for precise extrapolation to the equivalence volume.