Selecting and Evaluating the End Point - Titrations Based on Complexation Reactions

Selecting and Evaluating the End Point

The equivalence point of a complexation titration occurs when stoichiometri- cally equivalent amounts of analyte and titrant have reacted. For titrations in- volving metal ions and EDTA, the equivalence point occurs when C_M and C_EDTA are equal and may be located visually by looking for the titration curve’s inflec- tion point.

As with acid–base titrations, the equivalence point of a complexation titration is estimated by an experimental end point. A variety of methods have been used to find the end point, including visual indicators and sensors that respond to a change in the solution conditions. Typical examples of sensors include recording a poten- tiometric titration curve using an ion-selective electrode (analogous to measuring pH with a pH electrode),* monitoring the temperature of the titration mixture, and monitoring the absorbance of electromagnetic radiation by the titration mixture.

The first two sensors were discussed for acid–base titrations and are not considered further in this section.

Finding the End Point with a Visual Indicator 

Most indicators for complexation titrations are organic dyes that form stable complexes with metal ions. These dyes are known as metallochromic indicators. To function as an indicator for an EDTA titration, the metal–indicator complex must possess a color different from that of the uncomplexed indicator. Furthermore, the formation constant for the metal–indicator complex must be less favorable than that for the metal–EDTA complex.

The indicator, Inm–, is added to the solution of analyte, forming a colored metal–indicator complex, MInn-m. As EDTA is added, it reacts first with the free an- alyte, and then displaces the analyte from the metal–indicator complex, affecting a change in the solution’s color. The accuracy of the end point depends on the strength of the metal–indicator complex relative to that of the metal–EDTA com- plex. If the metal–indicator complex is too strong, the color change occurs after the equivalence point. If the metal–indicator complex is too weak, however, the end point is signaled before reaching the equivalence point.

Most metallochromic indicators also are weak acids or bases. The condi- tional formation constant for the metal–indicator complex, therefore, depends on the solution’s pH. This provides some control over the indicator’s titration error. The apparent strength of a metal–indicator complex can be adjusted by controlling the pH at which the titration is carried out. Unfortunately, because they also are acid–base indicators, the color of the uncomplexed indicator changes with pH. For example, calmagite, which we may represent as H₃In, undergoes a change in color from the red of H₂In– to the blue of HIn2– at a pH of approximately 8.1, and from the blue of HIn2– to the red-orange of In3– at a pH of approximately 12.4. Since the color of calmagite’s metal–indicator complexes are red, it is only useful as a metal- lochromic indicator in the pH range of 9–11, at which almost all the indicator is present as HIn2–.

A partial list of metallochromic indicators, and the metal ions and pH condi- tions for which they are useful, is given in Table 9.16. Even when a suitable indica- tor does not exist, it is often possible to conduct an EDTA titration by introducing a small amount of a secondary metal–EDTA complex, provided that the secondary metal ion forms a stronger complex with the indicator and a weaker complex with EDTA than the analyte. 

For example, calmagite can be used in the determination of Ca2+ if a small amount of Mg2+–EDTA is added to the solution containing the ana- lyte. The Mg2+ is displaced from the EDTA by Ca2+, freeing the Mg2+ to form the red Mg2+–indicator complex. After all the Ca2+ has been titrated, Mg2+ is displaced from the Mg2+–indicator complex by EDTA, signaling the end point by the pres- ence of the uncomplexed indicator’s blue form.

Finding the End Point by Monitoring Absorbance. 

An important limitation when using a visual indicator is the need to observe the change in color signal- ing the end point. This may be difficult when the solution is already colored. For example, ammonia is used to adjust the pH of solutions containing Cu2+ before its titration with EDTA. The presence of the intensely colored Cu(NH₃)₄2+ complex obscures the indicator’s color, making an accurate deter- mination of the end point difficult. Other absorbing species present within the sample matrix may also interfere in a similar fashion. This is often a problem when analyzing clinical samples such as blood or environmental samples such as natural waters.

As long as at least one species in a complexation titration absorbs electro- magnetic radiation, the equivalence point can be located by monitoring the ab- sorbance of the analytical solution at a carefully selected wavelength.* For ex- ample, the equivalence point for the titration of Cu2+ with EDTA, in the presence of NH₃, can be located by monitoring the absorbance at a wavelength of 745 nm, where the Cu(NH₃)₄2+ complex absorbs strongly. At the beginning of the titration the absorbance is at a maximum. As EDTA is added, however, the reaction

Cu(NH₃) 2+(aq)+ Y4–(aq) → CuY2–(aq) + 4NH₃ (aq)

occurs, decreasing both the concentration of Cu(NH₃)₄2+ and the absorbance. The absorbance reaches a minimum at the equivalence point and remains essen- tially unchanged as EDTA is added in excess. The resulting spectrophotometric titration curve is shown in Figure 9.30a. 

In order to keep the individual segments of the titration curve linear, the measured absorbance, Ameas, is corrected for dilution 

where A_corr is the corrected absorbance, and V_EDTA and V_Cu are, respectively, the volumes of EDTA and Cu. The equivalence point is given by the intersection of the linear segments, which are extrapolated if necessary to correct for any curvature in the titration curve. Other common spectrophotometric titration curves are shown in Figures 9.30b–f.