Basis of The Calculations
The Gran plot is based on the Nernst equation which can be written as
where E is a measured electrode potential, E0 is a standard electrode potential, s is the slope, ideally equal to RT/nF, and {H+} is the activity of the of the hydrogen ion. The expression rearranges to
depending on whether the electrode is calibrated in millivolts of pH. For convenience the concentration, is used in place of activity. In a titration of strong acid with strong alkali, the analytical concentration of the hydrogen ion is obtained from the initial concentration of acid, Ci and the amount of alkali added during titration.
where vi is the initial volume of solution, cOH is the concentration of alkali in the burette and v is the titre volume. Equating the two expressions for and simplifying, the following expression is obtained
A plot of against v will be a straight line. If E0 and s are known from electrode calibration, where the line crosses the x-axis indicates the volume at the equivalence point, . Alternatively, this plot can be used for electrode calibration by finding the values of E0 and s that give the best straight line.
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