Carolyn S. Handloser, M. R. Chakrabarty, ond Melvyn W. Mosher Marshall University Huntington, West Virginia 25701
Experimental Determination of pK. Values by Use of NMR Chemical Shifts
In a protic solvent heterocyclic bases are known to exist in two forms, according to eqn. (1).
The concentration of each of these is dependent upon the value of the equilihrium constant, K,, which is usually determined by p H titration and by spectrophotometric methods. In this paper we wish to describe a new technique for the determination of the pK, of this type of compound using nuclear magnetic resonance spectrometry. The ionization constant for these pyridinium ions as acids is given by eqn. (2). This equation can be rewritten
into the form of eqn. (3), which gives the relationship to thepK.. pK, = pH
Figure 1. NMR spectra of 4-cyanopyridine in acid and base. Spectra obtained relative to tetramethylammonium chloride on a Varian A60A NMR.
+ log-(BH+) (B)
The proton chemical shift of the cationic and uncharged species are expected to he significantly different due to the differences in electron densities and magnetic anisotropy of the lone pair of electrons on the nitrogen atom. If the proton exchange is rapid compared to the nmr time scale, which is the case in the system, only one set of signals will appear. The observed chemical shifts of a set of protons could then be expressed by eqn. (4)
where v B H . and vB represent the chemical shift of the protonated and the unprotonated forms, and P B ~ and + Ps represent the fractional populations of these two species. At very low pH values it can be assumed that nearly 100% of the material is in the uncharged form. Hence the values of v B H * and vE can be determined with reasonable accuracy. As might be expected the resonance lines of the protonated form appear downfield compared to the uncharged form (Fig. 1). In all cases the line due to the protons alpha to the nitrogen shifted less by approximately lh that of the lines due to the protons a t the beta position. The explanation for this difference in the amount of change in these protons has been reported.1 The relationship between the two fractional populations can be seen in eqn. (5).
Substitution of this ratio of the charged to the uncharged forms, which can be determined from the nmr chemical shifts, into eqn. (3) gives eqn. (6).
This equation has a number of advantages, the greatest 510
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DH Figure 2. Plot of chemical shift in ppm of the ring and methyl protons of 4-acetylpyridine as a function of p H . Chemical shifts were obtained at 37'C on aVarian A60A NMR.
being that the actual concentrations do not occur and only the relative amounts of each is involved. So long as the ionic strength of the solutions are kept constant, the reagent concentrations may vary by up to a factor of two without any effect upon the chemical shifts of the two forms. A plot of the observed chemical shifts relative to an inert standard, such as tetramethylammonium chloride, versus p H of the solution results. in a smooth titration type curve (Fig. 2). The values for the individual fractional populations are determined from this plot as follows. The values of the chemical shifts in strong acid and base are taken from the corresponding initial and final flat parts of the curve, respectively. The fractional population of BH' and B are calculated from the change between these two forms, by eqn. (7). 'Mosher, M . W., Sharma, C. B., and Chakrabarty, M. R., J. Mag. Res., 7,247 (1972).
PK. Values for a Number of Substituted Pyridines. All Values Obtained on a Varian A60A NMR with a Normal Operating Probe TemDerature of 37% Substrate
3-chloropyridine 4-pyridinecarboxaldehyde
isonicotinie acid*
Our Values*
4.09 -t 0.11 4.72 f 0.37 4.60 + 0.12
Student
4.32 + 0.11 4.73 + 0.08 4.01 + 0.06
~Exprrimtmrnlwmr is thr rnnx:rnurn qmad of rhr arrrayr cxperirnentsl value r a l c u l ~ t ~f dn m ~all thr paints u 4 in the derrrrninnrmn In all rase5 t h w~ e r n e ~16 the d w r d e ~"in1 h s t 6 ewerlmentalpK. values. b Saturated solution of the acid in 1MHCl used. Results of at least 2 student determinations. No student determination has heen omitted.
Once this value is obtained, all the values including the pK, can be evaluated by use of eqns. (5) and (6). The observed chemical shifts can either be the experimental points or a point (or points) taken from the plot of chemical shift versus pH. Taking both chemical shifts and pH values from the plot however, does have the large advantage of previously balancing the experimental weight of all the points, hence cutting down the possibility of incorporation of experimental errors into the calculations. I n selecting any point to be used from the plot, it should be in the rapidly changing area of the curve. Points too close to either end of this region will often have values of PRs* or Pe that are either extremely large or small, the log then of the ratio will vary greatly with a small difference in the actual chemical shift, making an even larger difference in the log term. Points in the center of the curve will have and PB of the same order of magnitude. both PBHThe values calculated for the pK,'s of a series of substi-
tuted pyridines using this method are presented in the table, along with the average experimental errors in their determination. In all cases the values determined by this method are consistent with those reported in the literature.l.2.3 This technique of calculating pK, values is suitable for advanced physical organic, physical, and/or instrumental laboratories, and has been used with good results (see the table) in the instrumental and auantitative . analysis lahoratoried a t ~ a r s h a luniversity. l The onlv limitation that we have encountered is that 30 MHz nm; are not suitable for the experiment. The two oroblems with these small instruments are (1) the differences in the chemical shift of the charged and uncharged forms are not pronounced, and (2) many of the pyridines studied have the water peak obscuring either the standard, or the ring protons. Experimental
Dissolve between 1.5-2 g of the nitrogenous base or its hydrochloride salt in 1M hydrochloric acid to a final volume of exactly 25 ml. (The ionic strength of this solution is approximately 1.0.) The only requirement upon the nitrogenous base is that its uncharged form is water soluble at the concentrations used over the pH range under investigation. The acid should be added slowly to avoid splattering and fuming. With a volumetric pipet, 10 ml of this solution is added to 1 ml of a saturated solution of tetramethylammonium chloride in water. The pH of the solution is obtained with any laboratory pH meter which has a scale expander. A sample af the solution is removed and placed in an nmr tube. The pH of the solution is adjusted by the addition of 0.5-1M sodium hydroxide, the pH redetermined, and a sample placed in an nmr tube. This process is repeated until the pH of the test solution is at least 10. The nmr spectrum of each of the pH paints is determined with a 60 MHz nmr spectrometer and the chemical shift of the protons is calculated relative to the inert standard, tetramethylammonium chloride. The pK, is determined by use of eqns. (3) and (5)-(7). Acknowledgment
The authors wish to thank Marshall University and the
C. W. Benedum Foundation for a Summer Research grant to Melvyn W. Mosher. We would also like to acknowledge the International Nickel, Allied Chemical Corporation and other Huntington area industries which supported Carolyn S. Handloser for the summer 1970. 2Perrin, D. D., "Dissociation Canstanti of Organic Bases in Aqueous Solutions," Butterworth, London, 1965. 3Handloser, C. S., Chakrabarty, M. R., and Mosher, M. W., unpublished results.
Volume 50, Number 7, July 1973
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