ANALYST, MARCH zyxwvutsrqpo 1985, VOL. 110 291 z Photometric Titration of Group II Metal Ions with EDTA Using Very Precise Linear Extrapolation End-point Location Colin G. Halliday and Michael A. Leonard zyxwvut Department of Analytical Chemistry, The Queen‘s University of Belfast, Belfast BT9 5AG, UK zy Results from the photometric titration of Group II metal ions with EDTA have been linearised using an approach based on Higuchi‘s method. Readily available indicators and pH conditions required to give very precise abscissa intersections have been investigated and a coefficient of variation of 0.04O/0 has been achieved. Keywords: Photometric titration; linearised titration plots; magnesium, calcium, strontium and barium determination The linearisation of indicator weak acid or base photometric tirations was developed by Higuchi zyxwvutsrq et al. with excellent results.’ They implied that such an approach should be applicable to complexometric titrations and this was shown to be so by two other groups of workers who offered a few illustrative examples.2.3 We developed our own theory, though we later found it to be related to that in reference 3, and applied it to discovering which of the readily available metallochromic indicators gave high quality linearised pho- tometric titration curves with individual Group I1 ions. These recommended indicators and pH conditions are, in many instances, rather different from those pertaining to visual titrations. Theory The following are a list of principle symbols used throughout the paper: KMrY, = metal ion - titrant conditional stability constant; KM’In’ = metal ion - indicator conditional stability constant; [MI’ = concentration of metal ion not combined with titrant or indicator in rnol dm-3; [Y]’ = concentration of metal-free titrant in mol dm-3; [In]’ = concentration of metal-free indicator in rnol dm-3; [MY] = concentration of metal - titrant complex in mol dm-3; [MIn] = concentration of metal - indicator complex in rnol dm-3; CM = concentration of metal ion solution to be titrated in mol dm-3; Cy = concentration of titrant solution in mol dm-3; CIn = concen- tration of indicator solution in rnol dm-3; V = volume of titrant added in cm3; VM = volume of metal ion solution taken in cm3; V, = volume of titrant added at the equivalence point in cm3; Vrn = vqlume of indicator solution added in cm3; V, = volume of solution at the start of the titration in cm3; A = absorbance of titrated solution at any stage; A,, = absorbance of free indicator; and AMIn = absorbance of metal - indicator complex. If a metal ion solution is titrated with a complexing agent in the presence of an indicator and only 1 : 1 metal - titrant and metal - indicator complexes form, the following equations apply: The mass balances are: .. , CMVM [MI’ + [MY] + [MIn] = ~ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA v+ zyxwvu vo [Y]’ + [MY] = - .. , CY v v+ vo (3) (4) .. .. * . (5) CIn VIn [In]’ + [MIn] = - v+ vo From equations (3), (4) and (5), (6) CM VM CY V CIn VIn v+ V,) v+ v, v+ v, [MI’ - [y]’ - [In]’ = - - - - - Substituting equation (1) into equation (4) and rearranging gives: . . . . (7) zy CYV [‘I’ = (V + Vo)( 1 + KMiY, [MI’) Similarly substituting equation (2) into equation (5) gives: Substituting equations (7) and (8) into equation (6) we obtain: CYV 1 [MI’ + - V+ V0 [’ -(1 + KM,Y’ [MI’) -0 . . (9) 1 CM VM 11 - (1 + KM~I~,[M]’) 1 v+ Vo If data before the end-point are considered and KM,Y, is large, [Y]’ is insignificant compared with [MI‘ and if CInVIn (( CMVM equation (6) becomes .. . I---- CMVM CYV - v+ V,) v+ v,, Substituting CyV, = CMVM and (2) into (10) and rearranging, Hence a plot of - (V + VO) against Vis linear with slope = KM In zyxwvutsrq I Cy and intercept KM ’In, cy ve. When [In1 (V + V()) = 0 v = v, [In]’ Equation (1 1) is called the “approximate equation.” Let If CI,VIn is not negligible compared with CMVM, e.g., in the titration of a small amount of metal, equation (6) becomes: [MI’ + ~ v clnvln + vo [1 - (1 zyxw 4- CYV~ CYV v+ V,) v+ V,) . . . . (12) --_- - Published on 01 January 1985. Downloaded by Northeastern University on 22/10/2014 13:09:03. View Article Online / Journal Homepage / Table of Contents for this issue