Gran Plot - Potentiometric Monitoring of Other Species

Potentiometric Monitoring of Other Species

Potentiometric data are also used to monitor species other than . When monitoring any species by potentiometry, one can apply the same formalism with . Thus, a titration of a solution of another species by species is analogous to a pH-monitored titration of base by acid, whence either or plotted versus will have an x-intercept . In the opposite titration of by, the equivalence volume will be . The significance of the slopes will depend on the interactions between the two species, whether associating in solution or precipitating together (Gran, 1952). Usually, the only result of interest is the equivalence point. However, the before-equivalence slope could in principle be used to assess the solubility product in the same way as can be determined from acid-base titrations, although other ion-pair association interactions may be occurring as well.

To illustrate, consider a titration of Cl- by Ag+ monitored potentiometrically: $\frac{v_0 _0-v_i_0}{v_0+v_i} \begin{cases} \approx _i \text{ or } K_{sp} 10^{-b_1E_i+b_0} & \text{ when } v_{0^{ }} _0 > v_i_0 \text{ (before equivalence)} \\ = 0 & \text{ when } v_{0^{ }} _0 = v_i_0 \text{ (equivalence point)} \\ \approx -_i \text{ or } -10^{b_1E_i-b_0} & \text{ when } v_{0^{ }} _0 < v_i_0 \text{ (after equivalence)} \end{cases}$

Hence,

a plot of will have a linear region before equivalence, with slope
and a plot of will have a linear region after equivalence, with slope
in both plots, the x-intercept is

Figure 3 gives sample plots of potentiometric titration data.

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“The question that will decide our destiny is not whether we shall expand into space. It is: shall we be one species or a million? A million species will not exhaust the ecological niches that are awaiting the arrival of intelligence.”
—Freeman Dyson (b. 1923)