complexes part6

When spectrophotometric absorbance is used as the phys¬ical property, the observed values obtained at various mole fractions when complexation occurs are usually subtracted from the corresponding values that would have been expected had no complex resulted. This difference, D, is then plotted against mole fraction, as shown in Figure 11-8. The molar ratio of the complex is readily obtained from such a curve.
If the magnitude of the measured property, such as ab¬sorbance, is proportional only to the concentration of the complex M An, the molar ratio of ligand A to metal M and the stability constant can be readily determined. The equation for complexation can be written as
(11-3)
M + nA = MAn
And the stability constant will be
[MAn ] is the concentration of the complex, [M] is the concentration of the uncomplexed metal,  [A]  is the concentra¬tion of the uncomplexed ligand, n  is the number of moles of ligand combined with 1 mole of metal ion, and K is the equi¬librium or stability constant for the complex.
The concentra¬tion of a metal ion is held constant while the concentration of ligand is varied, and the corresponding concentration, [MAn], of complex formed is obtained from the spectrophotometric analysis. If log [MAn] is plotted against log [A], the slope of the line yields the stoichiometric ratio or the number n of ligand molecules coordinated to the metal ion, and the intercept on the vertical axis allows one to obtain the stability constant, K, because [M] is a known quantity. This method is restricted to the formation of a single com¬plex..
pH titration method
This is one of the most reliable methods and can be used whenever the complexation is attended by a change in pH. The chelation of the cupric ion by glycine, for example, can be represented as
 Because two protons are formed in the reaction of the last equation, the addition of glycine to a solution containing cupric ions should result in a decrease in pH.
Titration curves can be obtained by adding a strong base to a solution of glycine and to another solution containing glycine and a copper salt and plotting the pH against the equivalents of base added. The quantity of alkali added (potentiometric titraration) is exactly equal to the concentration of ligand bound at any pH. The results of such titration are shown in Figure 11-9. The curve for the metal-glycine mixture is well below that for the glycine alone, and the decrease in pH shows that complexation is oc¬curring throughout most of the neutralization range. Similar results are obtained with other zwitterions and weak acids (or bases). The Schwarzenbach method can be used instead of the potentiometric method when complexes are unusually stable.