Analytical Chem istry - DePauw University

232 Analytical Chemistry 2.0less ligandCd 2+logK 1 = 2.55Cd(NH 3 ) 2+logK 2 = 2.01pNH 2+3 Cd(NH 3 ) 2logK 3 = 1.34Cd(NH 3 ) 32+logK 4 = 0.84Cd(NH 3 ) 42+more ligandFigure 6.7 Metal–ligand ladderdiagram for Cd 2+ –NH 3 complexationreactions. Note that higherordercomplexes form when pNH 3is smaller (which corresponds tolarger concentrations of NH 3 ).6F.2 Ladder Diagrams for Complexation EquilibriaWe can apply the same principles for constructing and interpreting acid–base ladder diagrams to equilibria involving metal–ligand complexes. Fora complexation reaction we define the ladder diagram’s scale using theconcentration of uncomplexed, or free ligand, pL. Using the formation ofCd(NH 3 ) 2+ as an example2+ 2+Cd ( aq) + NH ( aq) Cd(NH ) ( aq)3 3we can easily show that log K 1 is the dividing line between the areas of predominancefor Cd 2+ and Cd(NH 3 ) 2+ .[ Cd(NH ) ]= = 355 . × 10[ ][ ]2+3K 1 2+Cd NH3log log [ ) 2+K = Cd(NH ] 31log[ ] 255 .2 3[ ]− NH =+Cdlog log [ ) 2+K = Cd(NH ] 31255 .2 3[ ]+ pNH =+CdpNH2+= + [ Cd ]logKlog2552Cd(NH= .+[ ) ]3 1Thus, Cd 2+ is the predominate species when pNH 3 is greater than 2.55 (aconcentration of NH 3 smaller than 2.82 × 10 –3 M) and for pNH 3 valuesless than 2.55, Cd(NH 3 ) 2+ is the predominate species. Figure 6.7 shows acomplete metal–ligand ladder diagram for Cd 2+ and NH 3 .Example 6.9Draw a single ladder diagram for the Ca(EDTA) 2– and Mg(EDTA) 2–metal–ligand complexes. Using your ladder diagram, predict the result ofadding 0.080 moles of Ca 2+ to 0.060 moles of Mg(EDTA) 2– . EDTA is anabbreviation for the ligand ethylenediaminetetraacetic acid.32So l u t i o nFigure 6.8 shows the ladder diagram for this system of metal–ligand complexes.Because the predominance regions for Ca 2+ and Mg(EDTA) 2- donot overlap, the reactionCa 2 +Mg(EDTA) 2 −Ca(EDTA) 2 −Mg2 +( aq) + ( aq) ( aq)+ ( aq)takes place. Because Ca 2+ is the excess reagent, the composition of the finalsolution is approximatelymoles Ca 2+ = 0.080 – 0.060 = 0.020 mol