Analytical Chem istry - DePauw University

Chapter 9 Titrimetric Methods463shape of a complexometric EDTA titration curve. In section 9B we learnedthat an acid–base titration curve shows how the titrand’s pH changes as weadd titrant. The analogous result for a complexation titration shows thechange in pM, where M is the metal ion, as a function of the volume ofEDTA. In this section we will learn how to calculate a titration curve usingthe equilibrium calculations from Chapter 6. We also will learn how toquickly sketch a good approximation of any complexation titration curveusing a limited number of simple calculations.Ca l c u l at i n g t h e Ti t r a t i o n Cu r v eLet’s calculate the titration curve for 50.0 mL of 5.00 10 –3 M Cd 2+ usinga titrant of 0.0100 M EDTA. Furthermore, let’s assume that the titrand isbuffered to a pH of 10 with a buffer that is 0.0100 M in NH 3 .Because the pH is 10, some of the EDTA is present in forms other thanY 4– . In addition, EDTA must compete with NH 3 for the Cd 2+ . To evaluatethe titration curve, therefore, we first need to calculate the conditionalformation constant for CdY 2– . From Table 9.10 and Table 9.11 we find thata Y 4– is 0.35 at a pH of 10, and that a Cd 2+ is 0.0881 when the concentrationof NH 3 is 0.0100 M. Using these values, the conditional formationconstant isStep 1: Calculate the conditional formationconstant for the metal–EDTA complex.K′′16= K × α 4−× α = ( 29 . × 10 )( 037 . )( 0. 0881) = 95 . × 10 14f f Y Cd 2+Because K f´´ is so large, we can treat the titration reactionCd 2 +Y 4 −CdY2 −( aq) + ( aq) → ( aq)as if it proceeds to completion.The next task in calculating the titration curve is to determine the volumeof EDTA needed to reach the equivalence point. At the equivalencepoint we know thatStep 2: Calculate the volume of EDTAneeded to reach the equivalence point.molesEDTA = moles Cd 2+M × V = M × VEDTA EDTA Cd CdSubstituting in known values, we find that it requiresVeqM VCd Cd( 500 . × 10 −3M)(50.0 mL)= V = =EDTAM0.0100 MEDTA= 25.0mLof EDTA to reach the equivalence point.Before the equivalence point, Cd 2+ is present in excess and pCd isdetermined by the concentration of unreacted Cd 2+ . Because not all theunreacted Cd 2+ is free—some is complexed with NH 3 —we must accountfor the presence of NH 3 . For example, after adding 5.0 mL of EDTA, thetotal concentration of Cd 2+ isStep 3: Calculate pM values before theequivalence point by determining theconcentration of unreacted metal ions.