Titrations Based on Complexation Reactions
The earliest titrimetric applications involving metal–ligand complexation were the determinations of cyanide and chloride using, respectively, Ag+ and Hg2+ as titrants. Both methods were developed by Justus Liebig (1803–1873) in the 1850s. The use of monodentate ligand, such as Cl– and CN–, however, limited the utility of complexation titrations to those metals that formed only a single stable complex, such as Ag(CN)2– and HgCl2. Other potential metal–ligand complexes, such as CdI42–, were not analytically useful because the stepwise formation of a series of metal–ligand complexes (CdI+, CdI2, CdI3–, and CdI42–) resulted in a poorly defined end point.
The utility of complexation titrations improved following the introduction by Schwarzenbach, in 1945, of aminocarboxylic acids as multidentate ligands capable of forming stable 1:1 complexes with metal ions. The most widely used of these new ligands was ethylenediaminetetraacetic acid, EDTA, which forms strong 1:1 complexes with many metal ions. The first use of EDTA as a titrant occurred in 1946, when Schwarzenbach introduced metallochromic dyes as visual indicators for signalling the end point of a complexation titration.
Chemistry and Properties of EDTA
Ethylenediaminetetraacetic acid, or EDTA, is an aminocarboxylic acid. The structure of EDTA is shown
EDTA, which is a Lewis acid, has six binding sites (the four carboxylate groups and the two amino groups), providing six pairs of electrons. The resulting metal–ligand complex, in which EDTA forms a cage-like structure around the metal ion, is very stable.
The actual number of coordination sites depends on the size of the metal ion; however, all metal–EDTA complexes have a 1:1 stoichiometry.
Metal–EDTA Formation Constants. To illustrate the formation of a metal–EDTA complex consider the reaction between Cd2+ and EDTA
CdCl2 + H4Y ® CdH2Y + 2HCl
where H4Y is a shorthand notation for the chemical form of EDTA. The formation constant for this reaction
quite large, suggesting that the reaction’s equilibrium position lies far to the right.
EDTA Is a Weak Acid. Besides its properties as a ligand, EDTA is also a weak acid. The fully protonated form of EDTA, H6Y2+, is a hexaprotic weak acid with successive pKa values of
pKa1 = 0.0; pKa2 = 1.5; pKa3 = 2.0; pKa4 = 2.68; pKa5 = 6.11; pKa6 = 10.17.
The first four values are for the carboxyl protons, and the remaining two values are for the ammonium protons. A ladder diagram for EDTA is shown
The species Y4– becomes the predominate form of EDTA at pH levels greater than 10.17. It is only for pH levels greater than 12 that Y4– becomes the only significant form of EDTA.
Conditional Metal–Ligand Formation Constants. Recognizing EDTA’s acid–base properties is important. The formation constant for CdY2– assumes that EDTA is present as Y4–. If we restrict the pH to levels greater than 12, then equation provides an adequate description of the formation of CdY2–. For pH levels less than 12, however, Kf overestimates the stability of the CdY2– complex.
At any pH a mass balance requires that the total concentration of unbound EDTA equal the combined concentrations of each of its forms.
CEDTA = [H6Y2+] + [H5Y+] + [H4Y] + [H3Y–] + [H2Y2–] + [HY3–] + [Y4–]
To correct the formation constant for EDTA’s acid–base properties, we must account for the fraction, , of EDTA present as Y4–.
If we fix the pH using a buffer, then is a constant. Combining with Kf gives
where Kf´ is a conditional formation constant* whose value depends on the pH. As shown in Table 9.13 for CdY2–, the conditional formation constant becomes smaller, and the complex becomes less stable at lower pH levels.
EDTA Must Compete with Other Ligands. To maintain a constant pH, we must add a buffering agent. If one of the buffer’s components forms a metal–ligand complex with Cd2+, then EDTA must compete with the ligand for Cd2+. For example, an ammonia buffer (NH4Cl/NH3OH) includes the ligand NH3, which forms several stable Cd2+–NH3 complexes. EDTA forms a stronger complex with Cd2+ and will displace NH3. The presence of NH3, however, decreases the stability of the Cd2+–EDTA complex.
We can account for the effect of an auxiliary complexing agent**, such as NH3, in the same way we accounted for the effect of pH. Before adding EDTA, a mass balance on Cd2+ requires that the total concentration of Cd2+, CCd, be
CCd = [Cd2+] + [Cd(NH3)2+] + [Cd(NH3)22+] + [Cd(NH3)32+] + [Cd(NH3)42+]
* Conditional formation constant is the equilibrium formation constant for a metal–ligand complex for a specific setof solution conditions, such as pH.
** Auxiliary complexing agent is a second ligand in a complexation titration that initially binds with the analyte but is displaced by the titrant.
Complexometric EDTA Titration Curves
The complexometric EDTA titration curve shows the change in pM, where M is the metal ion, as a function of the volume of EDTA.
Calculating the Titration Curve. As an example, let’s calculate the titration curve for 50.0 mL of 5.00 ´10–3 M Cd2+ with 0.0100 M EDTA at a pH of 10 and in the presence of 0.0100 M NH3. The formation constant for Cd2+–EDTA is 2.9 ´1016.
Since the titration is carried out at a pH of 10, some of the EDTA is present in forms other than Y4–. In addition, the presence of NH3 means that the EDTA must compete for the Cd2+. To evaluate the titration curve, therefore, we must use the appropriate conditional formation constant
Kf˝ = ´ ´ Kf = (0.35)(0.0881)(2.9 ´ 1016) = 8.9 ´ 1014
Because Kf˝ is so large, we treat the titration reaction as though it proceeds to completion.
The first task in calculating the titration curve is to determine the volume of EDTA needed to reach the equivalence point. At the equivalence point we know that
Moles EDTA = Moles Cd2+
or
MEDTAVEDTA = MCdVCd
Solving for the volume of EDTA
shows us that 25.0 mL of EDTA is needed to reach the equivalence point.
Before the equivalence point, Cd2+ is in excess, and pCd is determined by the concentration of free Cd2+ remaining in solution. Not all the untitrated Cd2+ is free (some is complexed with NH3), so we will have to account for the presence of NH3. For example, after adding 5.0 mL of EDTA, the total concentration of Cd2+ is
To calculate the concentration of free Cd2+ we use equation
[Cd2+] = ´CCd = (0.0881)(3.64 ´10–3 M) = 3.21 ´10–4 M
Thus, pCd is
pCd = –log[Cd2+] = –log(3.21 ´10–4) = 3.49
At the equivalence point, all the Cd2+ initially present is now present as CdY2–. The concentration of Cd2+, therefore, is determined by the dissociation of the CdY2– complex. To find pCd we must first calculate the concentration of the complex.
Letting the variable x represent the concentration of Cd2+ due to the dissociation of the CdY2– complex, we have
Once again, to find the [Cd2+] we must account for the presence of NH3; thus
[Cd2+] = aCd2+ ´CCd = (0.0881)(1.93 ´10–9 M) = 1.70 ´10–10 M
giving pCd as 9.77.
After the equivalence point, EDTA is in excess, and the concentration of Cd2+ is determined by the dissociation of the CdY2– complex. Examining the equation for the complex’s conditional formation constant, we see that to calculate CCd we must first calculate [CdY2–] and CEDTA. After adding 30.0 mL of EDTA, these concentrations are
Substituting these concentrations into equation and solving for CCd gives
Thus,
[Cd2+] = ´CCd = (0.0881)(5.60 ´10–15 M) = 4.93 ´10–16 M
and pCd is 15.31. Figure and Table show additional results for this titration.
Complexometric titration curve for 50.0 mL of 5.00 ´10–3 M Cd2+ with 0.0100 M EDTA at a pH of 10.0 in the presence of 0.0100 M NH3.
Data for Titration of 5.00 ´ 10–3 M Cd2+ with 0.0100 M EDTA
at a pH of 10.0 and in the Presence of 0.0100 M NH3
|
Volume of EDTA |
(mL) pCd |
|
0.00 |
3.36 |
|
5.00 |
3.49 |
|
10.00 |
3.66 |
|
15.00 |
3.87 |
|
20.00 |
4.20 |
|
23.00 |
4.62 |
|
25.00 |
9.77 |
|
27.00 |
14.91 |
|
30.00 |
15.31 |
|
35.00 |
15.61 |
|
40.00 |
15.78 |
|
45.00 |
15.91 |
|
50.00 |
16.01 |
Selecting and Evaluating the End Point
The equivalence point of a complexation titration occurs when stoichiometrically equivalent amounts of analyte and titrant have reacted. For titrations involving metal ions and EDTA, the equivalence point occurs when CM and CEDTA are equal and may be located visually by looking for the titration curve’s inflection point.
As with acid–base titrations, the equivalence point of a complexation titration 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
1) recording a potentiometric titration curve using an ion-selective electrode (analogous to measuring pH with a pH electrode),
2) monitoring the temperature of the titration mixture,
3) and monitoring the absorbance of electromagnetic radiation by the titration mixture.
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 colour different from that of the uncomplexed indicator. Furthermore, the formation constant for the metal–indicator complex must be less favourable than that for the metal–EDTA complex. The complex are often intensely coloured and are discernible to the eye at concentrations in the range at 10–6 to 10–7 M.
The indicator, Inm–, is added to the solution of analyte, forming a coloured metal–indicator complex, MInn-m. As EDTA is added, it reacts first with the free analyte, and then displaces the analyte from the metal–indicator complex, affecting a change in the solution’s colour. The accuracy of the end point depends on the strength of the metal–indicator complex relative to that of the metal–EDTA complex. If the metal–indicator complex is too strong, the colour change occurs after the equivalence point. If the metal–indicator complex is too weak, however, the end point is signalled before reaching the equivalence point.
Eriochrome Black T is a typical metal-ion indicator that is used in the titration of several common cations. Eriochrome Black T forms red complexes with more than metal ions, but the formation constant of only a few are appropriate for end-point detection. Except, Eriochrome Black T behaves as an acid-base indicator as well as metal ion indicator:
The metal complexes of Eriochrome Black T are generally red. Until the equivalence point in a titration, the indicator complexes the excess metal ion, so the solution is red. When EDTA becomes present in slight excess, the solution turns blue as a consequence of the reaction:
MIn– + HY3– « HIn2– + MY2– (Yn– – EDTA ions)
red blue
A limitation of Eriochrome Black T is that its solutions decompose slowly with standing.
Most metallochromic indicators also are weak acids or bases. The conditional 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 colour of the uncomplexed indicator changes with pH. For example, calmagite, which we may represent as H3In, undergoes a change in colour 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 colour of calmagite’s metal–indicator complexes are red, it is only useful as a metallochromic 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 conditions for which they are useful, is given in Table. Even when a suitable indicator 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 analyte. 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 presence of the uncomplexed indicator’s blue form.
Selected Metallochromic Indicators
|
Indicator |
Useful pH Range |
Useful for |
|
Calmagite |
9–11 |
Ba, Ca, Mg, Zn |
|
Eriochrome Black T |
7.5–10.5 |
Ba, Ca, Mg, Zn |
|
Eriochrome Blue Black R |
8–12 |
Ca, Mg, Zn, Cu |
|
Murexide |
6–13 |
Ca, Ni, Cu |
|
PAN |
2–11 |
Cd, Cu, Zn |
|
Salicylic acid |
2–3 |
Fe |
Quantitative Applications
With a few exceptions, most quantitative applications of complexation titrimetry have been replaced by other analytical methods.
Selection and Standardization of Titrants. EDTA is a versatile titrant that can be used for the analysis of virtually all metal ions. Although EDTA is the most commonly employed titrant for complexation titrations involving metal ions, it cannot be used for the direct analysis of anions or neutral ligands. In the latter case, standard solutions of Ag+ or Hg2+ are used as the titrant.
Solutions of EDTA are prepared from the soluble disodium salt, Na2H2Y ´ 2H2O. Concentrations can be determined directly from the known mass of EDTA; however, for more accurate work, standardization is accomplished by titrating against a solution made from the primary standard CaCO3. Solutions of Ag+ and Hg2+ are prepared from AgNO3 and Hg(NO3)2, both of which are secondary standards. Standardization is accomplished by titrating against a solution prepared from primary standard grade NaCl.
Inorganic Analysis. Complexation titrimetry continues to be listed as a standard method for the determination of hardness, Ca2+, CN–, and Cl– in water and wastewater analysis. The determination of Ca2+ is complicated by the presence of Mg2+, which also reacts with EDTA. To prevent an interference from Mg2+, the pH is adjusted to 12–13, precipitating any Mg2+ as Mg(OH)2. Titrating with EDTA using murexide or Eriochrome Blue Black R as a visual indicator gives the concentration of Ca2+.
Titration with inorganic complexing agents. Complexometric titrations with inorganic reagents are among the oldest volumetric methods.
Cyanide is determined at concentrations greater than 1 ppm by making the sample alkaline with NaOH and titrating with a standard solution of AgNO3, forming the soluble Ag(CN)2– complex. The end point is determined using p-dimethylaminobenzalrhodamine as a visual indicator, with the solution turning from yellow to a salmon colour in the presence of excess Ag+.
Now sometime is used the titration of halide ions with mercury(II) ions, called mercurimetry. Chloride is determined by titrating with Hg(NO3)2, forming soluble HgCl2:
Hg(NO3)3 + 2NaCl = HgCl2 + 2NaNO3
The sample is acidified to within the pH range of 2.3–3.8 where diphenylcarbazone,
which forms a coloured complex with excess Hg2+, serves as the visual indicator, or sodium nitroprousside Na3[FeNO(CN)5]. Xylene cyanol FF is added as a pH indicator to ensure that the pH is within the desired range. The initial solution is a greenish blue, and the titration is carried out to a purple end point.
Quantitative Calculations. The stoichiometry of complexation reactions is given by the conservation of electron pairs between the ligand, which is an electron-pair donor, and the metal, which is an electron-pair acceptor; thus
This is simplified for titrations involving EDTA where the stoichiometry is always 1:1 regardless of how many electron pairs are involved in the formation of the metal–ligand complex.
