Potentiometry in Analytical Chemistry

This article was published in SPECTRUM, a science magazine published by ChemSA-Central Department of Chemistry, TU in 2005. I do not know whether this magazine is still being published or not. Since this magazine was published in printed copy only and I had its electronic copy, I want to share it with wide range of readers through NepaChem.-Basant Giri

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Potentiometry is one of the methods used for quantitative analysis in analytical chemistry. Here potential of an electrode in equilibrium with an ion to be determined is measured. There are two ways to quantify the given substance using potentiometry. One is direct Potentiometry and other is potentiometric titration. In direct potentiometry a single measurement of electrode potential is used to determine the concentration of an ionic species in solution.

Potentiometric Titration

In potentiometric titration, the end point is determined by measuring the potential of an indicator electrode as a function of the volume of titrant added. Beherend, in 1893 performed potentiometric titration of chloride, bromide and iodide with mercurous nitrate.

In a simple arrangement for a manual potentiometric titration a reference electrode (e.g. saturated calomel electrode or silver-silver chloride) is coupled with an indicator electrode, which is reversible with one of the ions involved in the titration. The emf of the cell containing the initial solution is determined and emf of the cell after each addition of titrant solution is also measured. Sufficient time should be allowed after each addition for the indicator electrode to reach a reasonably constant potential (~ 1-2 mV) before the next increment is introduced. In this procedure, we are concerned with changes in emf of the cell which is due to the change in concentration of ions reversible to the indicator electrode. Advantages of potentiometric titrations over 'classical' visual indicator methods are:

1. Can be used for coloured, turbid or fluorescent analyte solution.
2.  Can be used if there is no suitable indicator or the colour change is difficult to ascertain.
3. Can be used in the titration of polyprotic acids, mixtures of acids, mixtures of bases or mixtures of halides.

Types of Potentiometric Titration

Depending on the type of the reactions involved to which potential measurement can be applied for end point detection, potentiometric titrations can be classified into followings.

(a) Acid-Base Titration: An electrode, reversible to hydrogen ion (e.g. glass, quinhydron, antimony etc.) is employed in order to follow the progress of acid-base reactions. The potential of such electrode at 25 deg C is given by an equation of the form E = E^o + 0.0591pH., Where E^o is a constant potential depending on the experimental arrangement, the liquid junction potential(s) and reference electrode. Satisfactory results are obtained in all acid-base titrations except (a) where either the acid or the base is weak (K<10^-8) and solutions are very dilute and (b) where either the acid or the base are weak.

(b) Complexometric Titration: Complexometric titration can be followed with an electrode of the metal whose ion is involved in complex formation. For instance a number of ion selective electrodes can be used to monitor the titration of metal ions potentiometrically by EDTA. A silver electrode may be used to follow the titration of cyanide ion with a standard silver solution. The potential of the silver electrode may be expressed at 25 ^oC by E = E^o + 0.0591 log [Ag⁺].

(c) Oxidation-Reduction Titration: Such titrations involve the transfer of electrons from the substance being oxidized to the substance being reduced. Oxidized form + n electrons = reduced form. For such reaction the potential (E) acquired by the indicator electrode at 25^oC is given by E = E^o + (0.0591/n)*log([ox]/[red]).

The potential is controlled by the ratio of these concentrations terms. It is possible to titrate two substances by the same titrant provided the standard potentials of the substances being titrated, and their oxidation or reduction products, differ by about 0.2 V.

(d) Precipitation Titration: In this case, the titration reaction results in the formation of precipitate. A precipitation titration that involves insoluble salts of metals such as mercury, silver, lead and copper may be followed potentiometrically. The indicator electrode may be made of the metal involved in the reaction, a silver electrode for the titration of halides for instance, or may be an electrode whose potential is governed by the concentration of the anion being precipitated.

The potential of the silver electrode used as a cathode with SCE as anode in the titration of potassium iodide with silver nitrate will be governed by following Nernst equation: E_Ag+/Ag = E^o_Ag+/Ag + 0.0591 log [Ag⁺]. The concentration of silver ion is related to the concentration of iodide ion as K_AgI = [Ag⁺][I^-], where K_AgI is the solubility product of silver iodide. Hence, the electrode potential can be expressed in terms of the iodide ion concentration as: E_Ag+/Ag = E^o_Ag+/Ag + 0.0591 logK_AgI - 0.0591log[I^-]

In potentiometric titration the electrode potential over most of the titration range varies gradually, but near the equivalence point the electrode potential changes very abruptly even by the addition of small amount of titrant.

The magnitude of the potential change at the end point depends on the solubility of the substance being precipitated as well as on the concentration of the active ionic species involved. It has been found that potential change of silver electrode for the titration of 0.1M KI with 0.1M AgNO₃ is greater than for the titration of 0.01M KI with 0.01M AgNO₃.

In precipitation based potentiometric titration a number of components differing in solubility product could be analyzed. For example mixture of potassium iodide, potassium bromide and potassium chloride could be titrated with silver nitrate solution using silver electrode and silver-ISE. Among three halides, the solubility product of iodide is least (10^-16) and of chloride is highest (10^-10); silver iodide precipitates first, then silver bromide and at last silver chloride. But due to co-precipitation, adsorption the end points in halide mixture contains error.

Location of the End Point

a) Titration Curve: It is obtained by plotting the successive values of the cell emf on ordinate and corresponding values of volume of titrant added on the abscissa. This gives an S-shaped curve. The central portion of this curve which shows the steeply rising portion corresponds to the volume for the end point of the titration. When there is a small potential change at the end point like in the titration of weak acid with strong base, titration of very dilute solution etc, it is difficult to locate end point by this method. 

Figure 1: Titration method of locating end point 

b) Analytical or Derivative Method: The end point can be more precisely located from the first or second derivative curves. The first derivative curve involves the plot of slope of the titration curve (ΔE/ΔV-ration of change in emf and change in volume added) against the volume of the titrant added. Most frequently ΔE/ΔV is plotted against the average volume of titrant added corresponding to the values of emf taken. Volume on the x- axis corresponding to the peak of the curve is the end point of the titration.

In second derivative curve we plot the slope of first derivative curve (Δ²E/ΔV) against volume. The point on volume axis where the curve cuts through zero on the ordinate gives the end point. This point corresponds to the largest steepest point on titration curve and maximum slope of the ΔE/ΔV curve. 

Figure 2: First derivative Curve 

Above mentioned methods need values of potential corresponding to very small change in volume of titrant added near the end point for good result. In the immediate vicinity of the end point the concentration of the original reactant becomes very small, and it usually becomes impossible for the ions to control the indicator electrode potential. The cell emf becomes unstable and indefinite because the indicator electrode is not longer bathed with sufficient quantities of each electroactive species. Therefore the above methods may not give satisfactory results. Again also, results obtained by above methods may be in error if the reaction is not symmetrical e.g. in titration of silver ions with chromate ions.

Figure 3: Second derivative curve

c) Gran Plot: This is a new method of end point location in potentiometric titration developed by G. Gran in 1952 and modified by others. This method does the numerical manipulation of titration curves into linear straight lines intersecting at the equivalence point.During the potentiometric titration of KI with AgNO₃ following reaction occurs: KI(aq) + AgNO₃(aq) → AgI(s) + KNO₃(aq). The cell for the titration is SCE//KI,AgI/Ag and the emf of the cell is given by E_cell = E^o_cell - 2.303*(RT/F)*log(I^-) . The emf of the cell increases during potentiometric titration of KI with AgNO₃. By manipulating above equation one can derive the following equation for locating the end point by Gran's method.

Where V₀ = Initial volume of KI taken, V = Volume of AgNO₃ solution added, V_e = Volume of AgNO₃ solution at end point, C_Ag+ = Concentration of AgNO₃ solution added, F = Faraday's constant, R = Gas constant, T = Temperature, γ = Activity coefficient.

In above equation the term  

is called Gran's function. When Gran's function is  plotted against volume of AgNO₃ added 'V', a straight line will be obtained. Such a plot is called Gran Plot.

Above equation best fits for the data points taken only before the equivalence point. The end point can also be obtained from the data points after the end point by plotting 

against the volume of titrant added.

Figure 4: Gran Plot of Locating End Point

Thus the end point from Gran Plot can be obtained either taking the points before the end point or taking the points after the end point. It is obvious that the results obtained from linear curves would be more accurate than from the non-linear ones. The linear straight lines can be extrapolated to the volume axis to locate the end point. By the development of calculator, later on computer and using ion selective electrode, use of Gran Plot is increasing.

The advantages of using Gran's method of locating end point are: Simplicity of measurement, Simplicity of Calculation, Versatility and Precision.

This author had reported (see my MSc thesis) the titration errors and uncertainty in locating the end point using Gran method is reduced when a large portion (nearly 60%) of the titration curve is represented either before or after the equivalence point. One could use data points near equivalence points, neglecting the points at beginning for best result. It has been found that accurate end point from Gran plot can be obtained by using last 40% of data points near the end point.

Conclusion

Two ways of end point location in potnetiometric titration are mainly in practice in our lab. First is the titration curve and second is the first derivative curve. In these methods greater weightage is given to the data points near the end point and for better and accurate result large number of data points corresponding to very small change ion volume of titrant added near the end point must be used. But near the end point influence due to chemistry of reaction is high. In Gran's method of locating end point in potentiometric titration, the above errors can be removed because in this method greater weightage should not be given to readings near the end point. At last following points can be said on behalf of Gran method:

It is superior method than others. Removes all difficulties associated with classical methods, can be used to unsymmetrical reactions.

• Gran's method does not need values of emf near the end point. Therefore this method is more precise and accurate.
• Extrapolations of linear straight lines are used to locate the end point. Data points only before the end point can be used to locate the end point.
• Small numbers of data points give accurate end point.
• End point from Gran plot can be obtained even with last 40% of data points from near to the equivalence point with best result.

References

1. Vogel's textbook of "Quantitative Chemical Analysis" sixth edition.
2. Kolthoff, Sandell, Mechan, Bruclcenstin "Quantitative Chemical Analysis" forth edition.
3. Wilson, C.L.; Wilson, D. W.; "Comprehensive Analytical Chemistry" 2^nd A, Electrical Methods, Elsevier Publishing Company, 1964.
4. Day, R.A.; Underwood, R.L.; "Quantitative Analysis" sixth edition Prentice Hall of India, 1993.
5. Williard, H.H.; Merritt, L.L.; Dean, J.A.; Settle, F.A.; "Instrumental Methods of Analysis", sixth edition, Van Nostrand, 1981.
6. Gran, G.; Analyst (London), 1952, 77, 661.
7. Dick, J.G.; Analytical Chemistry, International Student Edition, McGraw - Hill Kogakusha, Ltd. 1973.
8. Gran, G.; Acta. Chem. Scand., 1950, 4, 559.
9. Sorenson, P.; Kem Maanedsbl.; 1951, 32, 73.
10. Burden, S.L. and Euler, D.E.; Proc. Indiana Acad. Sci.; 1973, 82, 167.
11. Burden, S.L. and Euler, D. E.; Analytical Chemistry, 1975, 47, 793.
12. Giri, B.; M. Sc. Dissertation, Central Department of Chemistry, T.U. 2004.