Analytical Chem istry - DePauw University

480 Analytical Chemistry 2.0Although the Nernst equation is writtenin terms of the half-reaction’s standardstate potential, a matrix-dependent formalpotential often is used in its place.See Appendix 13 for the standard state potentialsand formal potentials for selectedhalf-reactions.Before the equivalence point the titration mixture consists of appreciablequantities of the titrand’s oxidized and reduced forms. The concentration ofunreacted titrant, however, is very small. The potential, therefore, is easierto calculate if we use the Nernst equation for the titrand’s half-reactionErxn= o RT AE −redln [ ]Aox/ Ared nF [ A ]After the equivalence point it is easier to calculate the potential using theNernst equation for the titrant’s half-reaction.Erxnox= o RT BE −redln [ ]Box/ Bred nF [ B ]oxCa l c u l at i n g t h e Ti t r a t i o n Cu r v eIn 1 M HClO 4 , the formal potential forthe reduction of Fe 3+ to Fe 2+ is +0.767 V,and the formal potential for the reductionof Ce 4+ to Ce 3+ is +1.70 V.Step 1: Calculate the volume of titrantneeded to reach the equivalence point.Let’s calculate the titration curve for the titration of 50.0 mL of 0.100 MFe 2+ with 0.100 M Ce 4+ in a matrix of 1 M HClO 4 . The reaction in thiscase isFe 2 +Ce 4 +Ce 3 +Fe3 +( aq) + ( aq) ( aq) + ( aq)9.15Because the equilibrium constant for reaction 9.15 is very large—it is approximately6 × 10 15 —we may assume that the analyte and titrant reactcompletely.The first task is to calculate the volume of Ce 4+ needed to reach the titration’sequivalence point. From the reaction’s stoichiometry we know thatmolesFe= moles Ce2+ 4+M × V = M × VFe Fe Ce CeStep 2: Calculate the potential before theequivalence point by determining theconcentrations of the titrand’s oxidizedand reduced forms, and using the Nernstequation for the titrand’s reduction halfreaction.Solving for the volume of Ce 4+ gives the equivalence point volume asVeqM VFe FeM)(50.0 mL)= V = = ( 0.100 = 50.0 mLCeM (0.100 M)CeBefore the equivalence point, the concentration of unreacted Fe 2+ andthe concentration of Fe 3+ are easy to calculate. For this reason we find thepotential using the Nernst equation for the Fe 3+ /Fe 2+ half-reaction.2+o RT FeE = E3+ 2+− log [ ] =Fe / Fe3+nF [ Fe ]+ 0. 767V−0. log [ 2+Fe05916]3+[ Fe ]9.16For example, the concentrations of Fe 2+ and Fe 3+ after adding 10.0 mL oftitrant are