Gran Plot - Non-ideal Behaviour

Non-ideal Behaviour

In any titration lacking buffering components, both before-equivalence and beyond-equivalence plots should ideally cross the x axis at the same point. Non-ideal behaviour can result from measurement errors (e.g. a poorly calibrated electrode, an insufficient equilibration time before recording the electrode reading, drifts in ionic strength), sampling errors (e.g. low data densities in the linear regions) or an incomplete chemical model (e.g. the presence of titratable impurities such as carbonate in the base, or incomplete precipitation in potentiometric titrations of dilute solutions, for which Gran et al. (1981) propose alternate approaches). Buffle et al. (1972) discuss a number of error sources.

Because the or terms in the Gran functions only asymptotically tend toward, and never reach, the x axis, curvature approaching the equivalence point is to be expected in all cases. However, there is disagreement among practitioners as to which data to plot, whether using only data on one side of equivalence or on both sides, and whether to select data nearest equivalence or in the most linear portions: using the data nearest the equivalence point will enable the two x-intercepts to be more coincident with each other and to better coincide with estimates from derivative plots, while using acid-side data in an acid-base titration presumably minimizes interference from titratable (buffering) impurities, such as bicarbonate/carbonate in the base (see Carbonate content), and the effect of a drifting ionic strength. In the sample plots displayed in the Figures, the most linear regions (the data represented by filled circles) were selected for the least-squares computations of slopes and intercepts. Data selection is always subjective.