NMR Titration. The protonation constants K1 and K2 of a diprotic acid H2A were determined by NMR titration. (Protonation constants, for example, H++LHLK1=[HL]/[H+][L] are used in this example because they simplify the equilibrium expressions The chemical shift of a hydrogen near the acidic sites was measured at a number of pH values over the range pH1 to pH11. The data are shown in the following Figure (data table and figure are on the CD that accompanies this book). Figure 14-12. NMR titration. At any pH value there are three acid-base species in solution: H2A,HA and A2; the observed chemical shift is given by the expression calc=00+11+22 where j is the fraction of the species in the form containing j acidic hydrogens and j is the chemical shift of the species. The values can be calculated using the expressions below: j=j[H+]jj[H+]jj=K1K2Kj(0=1)2=1+K1[H+]+K1K2[H+]2K1K2[H+]2 Use the Solver to determine K1,K2,0,1 and 2