Donald E. Leyden and W. R. Morgan
University of Georgia Athens, 30601
I
I I
Kinetics of Proton Exchange of Trimethylammonium Ion by NMR A loboratory experiment
Nuclear maglietic resonance has proved to be a valuablo tool for the investigation of fast reactions in solution. Examples of dynamic processes which have been studied include proton exchange ( I ) , hindered rotation about a chemical bond ( 2 ) , nitrogen inversion (5), hydration of carbonyl groups (4), and clectro~itransfer reactions (5). This technique has several advantages when it is applicable to kinetic studies. Principal among these is the fact that the solutions may be studied under equilibrium conditions without the necessity of perturbing the system as is done when one of the various relaxation tcchniques is employed. Also, the theory is well developed and comput,er programs earl he written to simulate the effect of the various parameters upon the spectrum. The experiment described here involves simple preparations of samples and the spectra may be talcen using any commercial high-resolution nuclear magnetic resonance spectrometer. It has, however, an important advantage for instruction in addition to those contained in a similar experiment previously reported in THIS JOURNAL (4). In t,he case of the study of the hydration of pyruvic acid, only one mechanism was proposed and the rate data was treated accordingly (4). I11 this experiment, several plausible reactions are suggest,ed and the student makes use of t,he data to select the most probable ones. This is a more realistic situation, but a t the same time the system is simple enough that an alert student can make good progress. The theory of the effect of rapid exchange of nuclei in different chemical (and therefore magnetic) environments has been adequately reported arid therefore will not be repeated here ( 6 , 7 ) . However, a few basic comments will be made for clarity. Nuclei can exchange their magnetic environments through two general mechauisms: Internal reorientation of the molecule as in internal rotation or nitrogen inversion, or intermolecular exchange of the riuclei as in proton exchangc. In the first case the spectrum observed in the limit of slow exchange is most often that of two separate patterns resulting from the two types of nuclei which have different chemical shift values. As t,he rate of the dynamic process becomes greater, the separate patterns broaden and, in t,he limit of fast exchange, coalesce t,o one pattern representing an averaged spcct,rum. The ratc of the exchange process a t which the patterns coalesce has been shown to be
where 7 is the mean lifetime of a given nucleus befort: exchange and Av is the separation b e t w e n thc t ~ v u patterns in the limit of slow cxcharige (7).
The proton exchange reaction of trimethylami~lerepresents the second case. The three methyl groups in trimethylamine are all equivalent and therefore display a single sharp resonance line. If an aqueous solution of the compound is made i~icreasinglyacidic \ ~ i t hhydrochloric acid, the methyl proton resouancc mill become broad and eventually resolve into a doublet a t high acid concentrations. The doublet is a result of spinspill coupling bet\\-een the methyl protons and the N-H proton. In this case, the effect of the exchange of the N-H proton is to collapse the doublet. to n single peak a s t,he exchalige rate is increased. The exchangc rate a t which the collapse just occurs is given by
where r is as defined earlier and J is the spill-spill coupling constant expressed in cps. The shape of the pattern a t ot,hcr values of r may be comput,ecl using available equat,ions wit,h the aid of a digital computer. I t is important to note that nuclear magnetic resonance lines have finite widths even in the absence of exchange due to the relaxation processes. This "nat,uml" line width is in the greater part a result of the transverse relaxation time, T 2 ,and is directly related to the inhomogcniety of t,he magnetic field in most experimental coiiditions. I t must be taken into account. when using line shape for rate studies. Figure 1 shows the H,O and methyl proto11 nmr lilies a t several pH values. The coupliug constant, J , obtained from the methyl doublet is 5.2 cps. Loewew steiu and Meiboom have proposed the follo\ring aspossible mechanisms for proton exchange (8). Experimcntal evidence given below will permit the evaluation of the relative importance of these reactions.
Figure 1. Nucleor magnetic resonance spectra of t h e methyl and w a t e r protons of o 0.5M aqueous solution of trimethylamine. The pH roiuer used are; [A) 8.00, (81 4.82, (C) 3.45, ID) 2.98, (El 2.50, IF) 2.20.
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I n reaction (1) a water molecule accepts the proton from the amine, whereas in reaction (2) a hydroxyl ion accepts the proton. I n reaction (3) therc is a direct exchange of the proton between amine molecules whilc in reaction (4) a water molecule acts as a bridge for the proton-transfer step. A pseudo-firstorder rate expression may be written as
providc upon request a computer program written in FORTRAN I1 for calculating the line shapes, as well as instructions for use of the program. This program is a straightfor~~ard adaptation of the equations for the line shape of a simple spin-coupled doublet. It may be processed by a small computer such as an IBM 1620 which was used for the data presented here. When an experimental spectrum is a t hand, the peak width or peak-to-valley ratio and the Tzvalue obtained from a reference such as a sample of pure water is entered as data. The program computes the T value by iteration. A plot of the reciprocal mean lifetime, l/r,determined from the methyl resonance pattern, against the reciprocal of the hydrogen ion concentration is shown in Figure 2. Equation (6) shows that the slope of this line is (k,
+
For reaction (I), k = kl. I n a similar manner, the tot,al rate expression may be written as
where Kt, is the ion product constant for water and K. is t,he acid dissociation constant for (CH&NH+. 1Jsing the proposed mechanisms as guides, certain questions may now be considered. For example, is there any evidence in the spectra to indicate an important contribution of mechanism (I)? Because this mechanism is independent of pH, therc should be some exchange broadening of the methyl doublet at low pH values. The doublet shown in Figure 1 is sharp at the lowest pH value used, therefore no significant contribution is made by mechanism (1). lleact,ion (2) mill proceed more rapidly as pH is illcreased. Docs the spectral data indicat,e that this react,ion plays an important role? Before this question is answered it should be pointed out that a plot of l / r versus the product of the total amine concentration and t,he K, valuc is a straight line with an intercept of zero within experimental error. Reaction (2) is not dependent upon the amine concentration and if it were important ~ o u l dlead to a positive intercept. Thercfore, it is concluded that mechanism (2) is not significant. The proton exchange must then be affected by reaction (3) m d (4) or one of these. The fact that the watcr resonance is broadened in certain pH ranges is cvidence that reaction (4) is significant. The evaluation of ka and ka requires quantitative treat,ment.of thc spectral data. The .r values may be obtained from the spectra by using the technique of Loe\venstein and Meihoom (8). The T value for a broadened singlet is obtained from a working curve in which a function of 7 is plotted versus :I function of line 11-idth. A family of curves is given for various values of T2. The curve used is selected on the basis of the experimental Tzvalue. The T value for a doublet is obtained from a similar curve in which a function of r is plotted versus the ratio of the maximum to central minimum amplitude for the doublet. The r value for an experimental measurement is obtained by reading from the graph the T corresponding to thc cxperimental line width or peak-to-valley intensity rat,io depending upon whether the spectrum is a broadened singlet or doublet. Because these worliing curves are small as given in the literature and the data cannot he removed accurately, the present authors will 170 / Journal o f Chemicol Education
Figure 2. A plot of l/r v e r w 1/[H+] where r war obtained from the methyl resonance.
use kb). Because only ka involves the water mo~ecu~ks, of the water resonance will provide kp. The basic equation used is lira = s ( W ' m - Wla) (7) where r , is the mean lifetime of a proton in water before being transferred to the amine, Wm is the water line width a t half height in the absence of exchange (at low pH), and W'W is the water line width under exchange conditions. The mean lifetime of the NH+ group before the proton is transferred to water, r', is given by
The fraction p of exchange by reaction (4) is then given by
where k is the rate constant obtained from the methyl resonance at the same pH and ammonium salt concentration at which r , is measured. The results can be compared with those in reference (8) which give k, = 0.0&0.3 X 108l~ec-~M-'and kr = 3.1 k 0 . 3 X 1081sec-' MJ. This experiment is simple to perform. One set of working curves can be provided to a class for the data treatment. However, an excellent opportunity to utilize computers in teaching is present. The experiment also provides insight into an invaluable application of
nuclear magnetic resonance aud an exercise in selecting the important kinetic processes from a number of possible ones. The use of the technique describcd here has beeu extended to t,he study of deuterium exchange (9). Using t,hese results, kinetic isotope effect,s can be introduced. Experimental
Although t,he experimental procedure for the study out,lined here is simple, a few suggestions may be of interest,. St,ock solutions of t,rimethylamine hydrochloride may be prepared by room temperature distillat,ion of the aminc into a solution of hydrochloric acid. This is conveniently done by placing the receiving container on a t,riple beam balance and addirig the amine dist,illate until a predetermined weight has been transferred. A solution which is 1.25 M in amine hydrochloride is convenient. From this stock solution, a pair of solutions of equal ami~ieconccnt~ratio~i is made for each amine concentration desired. One of the two solutions is adjusted t,o about 0.01 M excess hydrochloric acid and t,he other t o about 0.01 M potassium hydroxide. These two solutions may be mixed to give the desired pH values ~ ~ h i should ch range from approximately 2.2 t o 8.0 whereas the amine concentration is constant,. Similar sets of solutions can be prepared with different amine concent,rations ranging from 0.25 M. to 1.25 M. Each student may obtain data for a given amine concentration and the results combined for t,he complete experimeut. Because the K , is conccntrat,ion dependent, it must be measured or those tabulated may be used (8).
The data shown in this report was obtained a t 2Q°C. However, a temperature study of the exchange rate over the range 0 to 80°C may be performed provided a nmr spect,rometer equipped v i t h a variable t,emperature probe is available. Because the doublet under ohservation is a result of spin coupling, the shape of the spectrum a t a given exchange rate is independent of the magnetic field strength. Thc T2 value should be checked frequently by recording a reference peak such as a sample of distilled water. The T2value should be about 0.3 seconds for most commercial instruments (T,= l/?r W112). The authors wish to acknovledge C. N. lteilley for his discussions in connection with this experiment. Literature Cited
LOEWENSTEIN, A,, AKU MEIBOOM, S., J . Chon. Phys., 27, 630 (1857). (2) NAIR,P. M., A N D ROBERTS, J. D., J . Am. Chem. Soc., 79,
(1) GRUNWALD, E., 4565 (1RIi7) \-.--,.
BOTTINI, A. T.,A N D ROBERTS, J. D., .I. Am. Chem Soe., 78, 5126 (1956);80,5203 (1958). (4) Socn.vm:s, G., J. CHEM. EDUC.,44, 575 (1967). M. W..A N D WABL. A. C.. J . Chem. Phvs.. (5) DIETRICH. .. . 38.. 1591 (1963). (6) H. S.. ANI) HOLM.C. H.. J. Chem. Phi,s.. , . GUTOWSKY. ., , 25.. lzzs (ia57j. (7) POPLE, .J. A , , SCHNEIDER, W. G., ANDBERSTEIK, H. d., "Highrcsalution Kurlcar Magnetic Resonance," McGraw-Hill Book Co., Inc., Ncn York, 1959, Chap. 10. ( 8 ) LOWI:NSTI:TN, A,, .\ND M111100~, S., 3. Chem. f'hys., 27, 1067 (1957). C. N., J. Phys. Chem., 71, 1588 (9) U.LY,R. J., .\NO RIXLLKY, (1967). (3)
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