Intrinsic End-Point Errors in Titration with Ion Selective Electrodes Chelometric Titrations Peter W . Carr Department of Chemistry, University of Georgia, Athens, Ga. 30601
Quantitative errors obtained in chelometric titrations using ion selective electrodes as end-point indicators are presented. The position of the inflection point depends strongly upon p , defined as the product of the equilibrium constant ( K O ' ) and the initial analyte concentration (CO'A), and upon the magnitude of the ionic interference (b). For example, when p = 108 and b = 0.01, an error of -0.38% occurs while under these conditions the analytical precision is 0.05%. The error increases as p decreases or b increases. Titration to a preset potential was examined and shown to be superior to the inflection-point method only under restricted conditions where b and p are both small. The method of Gran plots does not entail any serious determinate errors; however, as ionic interference increases, the precision deteriorates. Under titration conditions, where activity coefficients and liquid junction potentials are constant, Gran's method is preferable.
RECENTWORK ( I , 2) has shown that precipitation titrations with ion selective electrodes can lead to end points which differ substantially from the anticipated equivalence point. These errors are a result of the simultaneous occurrence of a n incomplete reaction and nonideal electrode selectivity. Similar effects may be present in complexometric titrations: consequently, the possible existence of end-point errors in such titrations was tested. Since most modern complexometric titrations are carried out with chelation reagents, only the case of a 1 :1 reaction as indicated below, was studied. A f T 4 A T (1) The major part of the work is concerned with end points located from the inflection point in the potential volume curve; however, the case of titration to a preset end-point potential or by the method of Gran plots is also evaluated. All assumptions involved in these calculations were presented previously ( I ) and insofar as possible the same symbols are used. It is well known (3, 4) that the potential of a n ion selective electrode is given by an equation of the form:
E = const
RT + zxF - In ( y x C x + B )
where Z X , yx and Cx are the charge, activity coefficient, and concentration of the species to which the electrode is principally sensitive. The term, B, which has been discussed previously ( I ) is given below :
B = lZKI(C,yl)Z"Zx
(3)
where I represents all interfering ions sensed by the electrode and Kl is the selectivity coefficient ( I ) . (1) P. W.Carr, ANAL,CHEM.,43,425 (1971). (2) F. A. Schultz,ibid., p 502.
(3) J. W.Ross, Science, 156, 1378 (1967). (4) G. Eisenman, D. C. Rudin, and J. U. Casby, ibid., 126, 831 (1957). 452
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
FRACTION TITRATED
Figure 1. Computed titration curves. Plot of b) us. fraction titrated for the reaction: A T AT
+ +
p
