EDTA Titration Curves

Logarithmic diagrams (Section 3-1) are helpful devices for drawing conclusions about the predominant species in solution at various stages in titrations. Johansson described their application to complexation reactions. 

In analogy to a pH titration curve, pM (— log [M]) may be plotted against the fraction titrated. Under the usual titration conditions, in which the concentration of metal ions is small compared with the concentrations of the buffer and the auxiliary complexing agents, the fractions ay and are essentially constant during the titration. The titration curve then can be calculated directly from the conditional formation constant since it also remains constant. 

EXAMPLE 11-2 Taking the initial concentration of nickel to be 10 M and neglecting dilution, calculate pNi at the following percentages of the stoichiometric amount of EDTA added under the conditions of Example 11-1 0, 50, 90, 99, 99.9, 100, 100.1, 101, and 110%. 

FIGURE 11-5 Titration curves of 10 Mmetal ions with EDTA in a solution withENHa] + [NH +] = 0.1 M at various pH values as indicated. Left, Ni(II) right, calcium (solid lines) and iron (dotted lines). 

The curves for calcium ions differ from those for nickel in two ways, (i) Before the end point the curves are essentially independent of pH because calcium does not form ammine complexes. (2) After the end point the pM value is smaller than for nickel because of the smaller value of the formation constant Kc y-- For the same reason, at low pH values, ay and are so small that no pM break occurs at high pH, ay approaches unity, so it is advantageous to perform calcium titrations at pH 10 to 12. 

Now we calculate the concentration of free metal ion in the course of the titration of metal with EDTA. The titration reaction is 

If K f is large, we can consider the reaction to be complete at each point in the titration. 

In this region, there is excess M after EDTA has been consumed. The concentration of free metal ion is equal to the concentration of excess, unreacted M . The dissociation of MY is negligible. 

There is exactly as much EDTA as metal in the solution. We can treat the solution as if it were made by dissolving pure MY -. Some free M is generated by the slight dissociation of MY  

In this reaction, EDTA refers to the total concentration of free EDTA in all of its forms. At the equivalence point, [M ] = [EDTA]. 

Before the equivalence point, there is excess unreacted Ca24 

At the equivalence point, the major species is CaY2, in equilibrium with small, equal amounts of free Ca2 and EDTA. 

After the equivalence point, virtually all the metal is present as CaY2. There is a known excess of EDTA present. A small amount of free Ca24 exists in equilibrium with the CaY2 and EDTA. 

Now there is excess EDTA, and virtually all the metal ion is in the form MY -4. The concentration of free EDTA can be equated to the concentration of excess EDTA added after the equivalence point. 

Because K f is large, it is reasonable to say that the reaction goes to completion with each addition of titrant. We want to make a graph in which pCa2+ ( = — log [Ca2+]) is plotted versus milliliters of added EDTA. The equivalence volume is 25.0 mL. 

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Now that we know something about EDTA s chemical properties, we are ready to evaluate its utility as a titrant for the analysis of metal ions. To do so we need to know the shape of a complexometric EDTA titration curve. In Section 9B we saw that an acid-base titration curve shows the change in pH following the addition of titrant. The analogous result for a titration with EDTA shows the change in pM, where M is the metal ion, as a function of the volume of EDTA. In this section we learn how to calculate the titration curve. We then show how to quickly sketch the titration curve using a minimum number of calculations. 

Let s see how to reproduce the EDTA titration curves in Figure 12-11 by using one equation that applies to the entire titration. Because the reactions are carried out at fixed pH. the equilibria and mass balances are sufficient to solve for all unknowns. 

The greater the effective formation constant, the sharper is the EDTA titration curve. Addition of auxiliary complexing agents, which compete with EDTA for the metal ion and thereby limit the sharpness of the titration curve, is often necessary to keep the metal in solution. Calculations for a solution containing EDTA and an auxiliary complexing agent utilize the conditional formation constant K" = aM aY4- Kt, where aM is the fraction of free metal ion not complexed by the auxiliary ligand. 

A definitive reference for the theory of EDTA titration curves is... 

Figure 1 7-6 EDTA titration curves for 50.0 mL of 0,00500 M Ca-+ (i cav = 1.75 X 10 ) and Mg2+ = 1.72 X 10 ) at pH 10.0, Note that because of the larger formation constant, the reaction of calcium ion with EDTA is more complete, and a larger change occurs in the equivalence-point region. The shaded areas show the transition range for the indicator Eriochrome Black T.

D-5 The Effect of Other Complexing Agents on EDTA Titration Curves... 

EDTA Titration Curves When a Complexing Agent Is Present... 

A quantitative description of the effects of an auxiliary complexing reagent can be derived by a procedure similar to that used to determine the influence of pH on EDTA titration curves. Here, a quantity am is defined that is analogous to 0 4. 

See Problem 21 for a spreadsheet calculation of the Ca-EDTA titration curve in Figure 9.3 at pH 10. As with calculated acid-base titration curves, the calculations here break down very near the equivalence point due to simplifying assumptions we have made. 

At this point in the chapter, those who want to spend more time on instrumental methods of analysis might want to move to a new chapter. We now consider equilibrium calculations required to understand the shape of an EDTA titration curve. 

The calculation that we just did was oversimplified because we neglected any other chemistry of such as formation of MOH, M(OH)2(a ), M(0H )2(5), and M(0H)3. These species decrease the concentration of available and decrease the sharpness of the titration curve. Mg " is normally titrated in ammonia buffer at pH 10 in which Mg(NH3) also is present. The accurate calculation of metal-EDTA titration curves requires full knowledge of the chemistry of the metal with water and any other ligands present in the solution. 

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