The Microscopic Protonation Constants An NMR Titration Experiment 0. F. Onasch State University of New York, College of Technology, Delhi, NY 13753 H. M. Schwartz, D. A. Aikens, and S. C. Bunce Rensselaer Polytechnic Institute, Troy, NY 12180-3590
While macroscopic or conventional protonation constants define the overall ability of a polyprotic base to bind protons, microscopic or site-specific protonation constants define the abilities of the individual base sites to bind protons. To predict the distribution of protons among the base sites of a partially protonated polyprotic base, one must know the microscopic protonation wnstants. Since microscopic protonation wnstants define the charge distribution of partially protonated polyprotic bases, they are of special interest in biochemistry, and have been widely studied (I4). If the microscopic protonation constants of individual base sites differ by several orders of magnitude, protonation proceeds almost exclusively by a single pathway, and the microscopic constants for the pathway essentially equal the macroscopic constants. However, if the microscopic protonation constants of two or more base sites do not differ snfiiciently, all the base sites compete for the addition of a eiven nroton. Establishment of the deeree of roto on at ion of each 6ase site in the partially proGated m o l e d e then reouires knowledee of the microsco~ic . .roto on at ion constints. The most &rect way to determine microscopic Protonation constants is to monitor the fractional protonation of individual base sites spectroscopically during the titration. Ultraviolet absorption was used by early workers (57) and is the basis of several undergraduate experiments (8-10). While this approach is attractive because UV spectrophotometers are widely available, the insensitivity of the uv spectra ofmost bases to protonation severely limits the scope of the W titration. 'H NMR spectroscopydoes not suffer this ]imitation, and NMR titration is widely used. N M R titration exploitsthe fact that the chemical shifts of protons on carbons located alpha to a base site vary linearly with the fractional protonation of that base site and are virtually inde~endentof the degreeofprotonationofmorndistant hbsesitns~11, 121. Thc chemical shiR ofthc ind~catorproton for each base site is determined over a pH range that spans protonation of each base site from approximately 0 to 100%.At each point in the titration, the fractional protonation of each base site is determined using equation 1
N
A
-N~H+ kJ+,
NA-
t~
N ~ -
N~H+
".75 +H NA-
NR
-
where fpn is the fractional protonation a t the base site a t the pH of interest, t+,~ is the chemical shift of the indicator a t that pH, 6~ is the chemical shift of the indicator of the deprotonated base site, and &H is the chemical shift of the indicator of the protonated base site. The microscopic protonation constants of each base site are then obtained from Presented at the 19th American Chemical Society Northeast Regional Meeting, Albany, NY, June, 1989;poster CHEMICAL EDUCATION 66.
Microscopic protonation scheme of N,N-dimethyl-1,Sdiaminopropthe plot of fractional protonation against pH by nonlinear (3, The NMR titration has been applied to citric acid (131, lysine, ethylenediaminemonoacetic acid (14), glutathione (151, a-w diamines (161, polyamines and polyaminocarbowlic acids and their metal complexes (17, 18). The significance of microscopic protonation constants and their relationship to macroscopic protonation constants have been discussed (14, 14, 171, as have experimental and c~mp~tational aspects of the NMR titration (3, 4, 7,141. Of basedon the several ~ublishedundergraduateex~eriments the NMR titration (19-211, only one (21) emphasizes the unique power of the NMR titration to determine the microscopic protonation constants of base sitcs of similar basicity. It is a hrief note with little experimental or computational detail. This paper describes the N M R titration of N,N-dimethyl-1,3-propanediamine(DMPD), in which the two amino gropups are nearly identical in basicity. Depending on the NMR equipment available, there are two general approaches to the NMR titration. An FT spectrometer with pulse sequence capability is preferable because it allows measurement of the chemical shifts to within a few thousandths of a ppm, and suppression of the resonance signal of HzO, so that one can use 90% HzO-10% DzO solvent. One can also perform the NMR titration with a CW spectrometer using NaOD and DC1 as titrants and DzO as solvent when chemical shiRs can be measured to about 0.01 ppm. Due to the isotope effect on the pH scale, one must increment the pH values obtained in DzO by 0.4 unit (22) to obtain pK. values consistent with those measured in HzO. Volume 68 Number 9 September 1991
791
The microscopic protonation of DMPD is describedin the posable Pasteur pipets, approximately 0.8 mL of the DMPD figure. NArepresents the tertiary nitrogen and NB represolution is removed and placed in an NMR tube, which is capped to prevent entry of COz. With a Varian XL-200 sents the primary nitrogen. The equilibria corresponding to the four microscopic protonation constants ( k ~k, ~k, ~ , spectrometer, the Hz0 resonance is suppressed by preirradiating the Hz0 protons with a 6-s pulse from the and keA)are defmed by eqs 2-5. The hydrogen ion concendecoupler before the normal excitation pulse (25). The trations are derived from conventional pH values with a NMR spectra exhibit two downfield triplets for the alpha version of the Davies equation (23), a s we described premethylene groups, a complex upfield multiplet for the cenviously (24). tral methylene p u p , and a strong singlet for the methyl group. Since the two nitrogens of DMPD are very close in basicitv. the two aloha methvlene resonances exhibit verv pH 3 and pH 12, the; ~ i m i l a r depeniencies. '~~ appear as two relatively well defined triplets, but near pH 8, they cross. Since the chemical shift of the methyl singlet responds to the protonation of NA,the fractional chemical shiWpH behavior of the methyl group corresponds very closelv to that of the methylene located alpha to Na This Equations 6 and 7 define the relationships between the microscopic constants and the stepwise macroscopic conprovides a simple way to kstabtish that the alpha hethylene resonance that is furtherdownfield at pH 3 and further stants, Kl and Kz.Equations 8 and 9 define the dependence offAand fB,the measured fractional protonation of NAand upfield at pH 12 is associated with NA. NB, on the microscopic constants and the hydrogen ion Curve-Fitting Considerations concentration. To account for the effect of the 10%D20 on the measured pH, one must increase each pH value by 0.04unit (22). Then the four microscopic protonation constants are determined by simultaneously fitting the fractional protonation1pH data sets for NAand NBto equations 8 and 9 respectively. A In essence, one fmds the values o f k ~k, ~k, ~and , ~ B which minimize the variance of the chemical shiR values. Fitting equations 8 and 9 is a problem in nonlinear regression analysis (71, for which discussions and subroutines are given in several texts on scientific statistics (26-28). Most mainframe computers have subroutines users can call for Experimental nonlinear regression, and we used one based on Shor's Titration of the dihydrochloride with NaOH is preferable ellipsoid method. to titration of the base with HCl because the ionic strength changes less during the titration and the dihydrochloride Results salt is easier to purify than the base. The dihydrochloride We obtained essentially equivalent values for the microsalt is prepared by dropwise addition of aqueous HCI to a scopic constants using either methylene or methyl reso10% aqueous solution of DMPD,and the solutionis concennance to monitor the protonation of NA.The table reports trated in a rotary vacuum evaporator. The dihydrochloride the microscopic constants obtained by the former approach, is recrvstallized from 80% (v/v) ethanol. dried. and stored the macroscopic constants calculated from them using R m a vakumdesiccator. Solut~ons[or F T ~ spectroscopy equations 6 and 7, and the macroscopic constants obtained were 0.010 M In DMPD In 907 H?O-10%I),O and 0.080 M d&ectlyby conventional pH titration. The microscopic conin NaCl to adjust the ionic strength to 6.100 M a t the stants agree reasonably well with those of Hine (161,which half-titration point. They contained 2,2-dimethyl-2-silawere obtained under somewhat different conditions. In pentaned-sulfonate as an NMR internal standard. All pH addition, the microscopic constants agree fairly well with measurements were made at 25.0 f 0.05 'C in a 30-mL those estimated using model compounds (29). Macroscopic thermostated titration vessel using a digital pH meter with constants calculated from microscopic constants agreed a resolution of 0.001 pH units calibrated with NBS stanwell with those obtained directly by pH titration. dard buffers of pH 4.008,6.865, and 9.180. The NMR titration curves are adequately defined by Literature Cited 20-25 approximately equally spaced points from pH 3 to 1.EdoaU, J. T.;Wymsn, J.Biophysiml Chemistry;AoademicPmss: New York. 1958:pp 477604. pH 12. After adjustment of the pH to each desired value by dropwise addition of concentrated NaOH or HC1 with dis-
n ear
Microscopic and Macroscopic Logarithmic Protonation Constants of N,N-Dimethyl-l,3-propanediamine
Constant
Predicted
NMR Titrationa
pH
Titration log kn log k~ log ~ A B log ~ B A log Ki
-
104 Kz
9.73
9.72
10.22
10.09
9.04
8.75
8.55
8.38
10.34
10.24
10.27
8.43
8.23
8.26
elhe maximum uncertainty estimated from the sum of squares forthese results averages 0.07 pKunits.
792
Journal of Chemical Education
4. Sameski. J. E.; Rdley, C. N. inEssoys o n A d y f i m 1 Chemislry;Pergamrm: Orford, UK,1977;pp 35-48. 6. Beneseh, R. E.;Benesch, R. J.Am. Chem S n I965,77,5877. 6. Edasll, J. T.;Manin, R. B.;Hallmgawarth, B. RPm. Nall. A d Sei. USA,19.58.44, cnz ""*. 7. Niebergall P. J.:Sehnaare, 5.L.: Sugita,E. T. J. P h m Sei 1912,61,232. 8. Clement, 0.E.; Hart., T. P.J. C k m Edw. 1911,48,395. 9. Fun& H. L.; Cheng, L. J Chem. Educ.1914,5I, 108. lo.Aike"a,D.A.;Bail&%R.k; Ciachino, 0.0.:M00re,J.b;Tompkins, R. P. htqmfrd E r p ~ t i m n t a lChemLlfq: Allyn and Bacon: Baston, MA, 1978;Val. 2,pp 431-439. ll.Gutows!%H.S.;Saika.A J. Chem.Phy8.1968,21,1688. 12. Cmwald. E: Lowenstein:Meiboom, S. J.Chem.Phya 1961,27,641. 13. Lowenatein,A,; Roberts, J. D.J Amr. Chem. Soe. 1860,82,2705. 14. Pahenstein, D. L.; Sayer, T. L A M 1 C k m . I916,48,1141. 15.Rabenetein,D.L.JA-P. Chem Sa. 1913,95,2797. 16.Him, J.;Via, F. A,; Jensen, J.H. J Org. C h . 1971,36,2926. 11.Sudmeier. J. L.: Paillev. C. N.Anol. Chem. 1864.36 . . 1698. 18.Letkern&, P.i ~hem:~due. 1919,56,348. 19. Handloser, C. 8.;Chskrabarty, M. R.;Mosher. M. W . J Chem. Educ 197s.50,510.
20.Waller. F.J.; Hartart, I. S.;Kwong, S.T.J C b m . Educ. 1877,54,447. 21.Burt.C.T. J. Chem. Educ 1982.57. 1056. 22. Bates, R. G. D e h r m i ~ t i mofpH, Theory and Procth; 2nd. ed;Wiley: New York, 1973;pp374376. 29. Meites, L. Handbook ofAnolytlm1 Cbmist~;MeGraw-Hill: New York,1961; p 1. 2 4 Onsaeh. 0.F.;A*ens,D.A.; Bunee,S. C.; SEhw&,H.;Nsim, D. andHunritz, C. BiophyaicalCh~m.1984, 29,245. 25. Rabenstein, D. L.;Fan.S.;N&ashima,T. T.J.Magn. R e s o m m 1985,M. 541.
26. Johnam, K D. N u m e r i d Methods in Chemistry; M. DeBer: New York, 1980; pp 27b293. 27.ha8,W.H.;Flannery,B.P.;Teukalsky. S.A.;Vetterliog,W.T.NvmaricolRpeipes. Cambridge University Press: Cambridge, 1986; pp 521428. 28.J0hnston.M.D.. Jr.Camputa~io~ICbmisfry:Elaevier:NewYork,1988:pp482-508. 29. ALkem, D. k: Bunce, S. C.; Onsaeh, 0. F.: Parker, R.;Hunvltz, C.;Clemana,S. Biophysicd Ckem. 1983, 27.67.
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