ROBERTJ. DAYAND CHARLES N. REILLEY
1588
Rate Constants for Deuterium Exchange of Trimethylammonium
Ion in Heavy Water
by Robert J. Day and Charles N. Reilley Department of Chemistry, University of North Carolina, Chapel Hill,North Carolina 27614 (Received June $7, 1966)
~~~
Rate constants for deuterium transfer in D2O solutions of trimethylammonium ion a t 33’ have been measured by proton magnetic resonance from the collapse of proton-deuterium coupling. The mechanisms advanced by earlier workers to describe the corresponding proton-transfer rates are also adequate for deuterium exchange. The rate of the direct reaction with solvent, BD+ D20 2 B D30+, extrapolated to infinite dilution is k4 = 1.08 sec-l while, for the symmetric reaction B D + OD2 B 2 B DOD DB+, k7 = 1.12 X 108 M - l sec-’. The decrease of k 4 at high D + concentrations interpreted by the mechanism B (DOD), %’ B mDOD gives ~ D = B 8.5 X lo9 sec-l. The direction and magnitudes of the isotope effects on the rate parameters are consistent with the postulated mechanisms.
+
+
Introduction The kinetics of NH proton exchange of the methylamines have been extensively studied in aqueous solution using proton magnetic resonance by following the collapse of the CH3-NH proton coupling and from the line broadening of the H20 proton resonance.’-’ The significant mechanisms of proton exchange for aqueous methylamine-hydrochloride salts at HC1 concentrations in the range 1-10-5 M are
+ HzO -% R3N + H30+ RsN+H + NR3 -% R3N + HN+R3
(1) (2)
€I R3N+H
+
+
+
+
---
R3N+H
+
I + 0-H + NR3 5
where k H is represented as the rate of “breaking of the R3N * (H20), hydrogen bond,” k+/k- = KA,the acid dissociation constant, and
-
k4
=
k+/f 1
+ k-[H’]/k~]
(5)
Because the isotope effectsupon the processes involved in the proton exchange not only should be of interest in themselves but also provide an additional qualitative check on the mechanisms used to describe the proton exchange, this study of the corresponding deuteriumexchange kinetics was undertaken using the exchange collapse of deuterium-proton coupling by proton nmr in a manner similar to the way that proton-proton coupling is used for the study of proton exchange. While as a result of the interaction of the quadrupole moment of deuterium with rapidly fluctuating electric field
H R3N
+ H-0I + HNR,
(3)
Reaction 1 is further delineated by the reactions7
RsN+H. .(HzO),
+ H20
k+ k-
R3N. * * (HzO),
-
R3N. .(HzO),
+ Haof
-% R3N + (HzO),
The Journal of Physical Chemistry
(4)
(1) E.Grunwald, A. Loewenstein, and S. Meiboom, J. Chem. Phys., 27, 630 (1957).
(2)A. Loewenstein and S. Meiboom, ibid., 27, 1067 (1957). (3) E. Grunwald, P. J. Karabatsos, R. A. Kromhout. and E. L. Purlee, ibid., 33, 556 (1960). (4) M.T.Emerson, E. Grunwald, M. L. Kaplan, and R. A. Kromhout, J. Am. Chem. Soc., 82, 6307 (1960). (5) T.M. Connor and A. Loewenstein, ibid., 83, 560 (1961). (6) 2. Luz and S. Meiboom, J . Chem. Phys., 39, 366 (1963). (7) E.Grunwald, J . Phys. Chem., 67, 2208,2211 (1963).
DEUTERIUM EXCHANGE OF TRIMETHYLAMMONIUM IONIN HEAVYWATER
gradients, the deuterium TIin many chemical species is frequently so short that any coupling of the deuterium with other nuclei is relaxed, the quadrupole relaxation of deuterium in (CH&N+D is slow enough so that there is an observable coupling between deuterium and the CH3 protons4g8which allows deuterium-exchange rates to be measured by proton nmr for (CH&N+D in D20. I n the proton-exchange studies, k4 and ks k 7 were measured using the CH, proton resonance and k7 separately from the H 2 0 proton resonance. Studies of the analogous deuterium-exchange reactions for (CH3)3N DC1 in DzOby proton nmr are more limited because only the CHI proton spectrum may be used. While kinetic information may be obtained from the residual HOD proton resonance, the measured rate corresponds to the reaction
+
D (CH&N+D
+ 0-H + N(CH3)a -% D (CHa)3N
+ D-0I + "+(CH3)a
(6)
which will proceed a t a somewhat greater rate than the reaction involving DaO. I n the case of (CHa)3NHCl,it was found that as a result of steric effects, ka was too small with respect to k7 to be measurable, and it would be expected that this would also be the case in D20.
Experimental Section Reagents and Solutions. D2O was obtained from Columbia Organic Chemicals Co., Inc., and was of 99.7% isotopic purity. Other reagents were of the highest purity commercially available and were used without further purification. Solutions of DC1 in D20 were prepared by a method similar to that described by Herbergin which SO3 polymer is distilled into D 2 0to produce D2S04 after which NaCl is added, and the resulting DCl is passed into DtO. NaOD in D 2 0 was prepared by adding reagent grade NaOH to DaO. (CHJBNDC1 was prepared by distilling anhydrous (CH&N into a solution of DC1 in D20 until most of the HCl was neutralized, with the concentration of (CH&NDCl being determined potentiometrically by AgN03 titration, correcting for the excess DC1 which was determined by pH titration. The solutions for the kinetic measurements were prepared by a method similar to that used by Loewenstein and R4eiboom2in which two solutions of the same (CHa)3NDC1 content, one acidic (-0.01 F DCl) and the other basic (-0.01 F NaOD), were mixed to give the desired [D+] with the pD being monitored by a glass electrode standardized
1589
with the acidic solution, using a Leeds and Northrup expanded-scale pH meter, while solutions with [DCI] greater than 0.01 M were prepared volumetrically. Dissolved air was not removed from the solutions because of the probable loss of (CH3)3N from samples of low [DCl] during the deaeration. The concentration of residual H in the solutions was measured from the ratios of the integrals of the HOD and (CH&N+D proton resonances by comparison with standard samples. The concentration of HOD varied somewhat for different solutions, but the variation did not appear to have any adverse influence. The HOD concentration was a p proximately 0.5 M in most cases although a few solutions which required somewhat longer periods of time than usual for preparation and were more exposed to H20 contamination from the laboratory atmosphere contained up to 1 M HOD. Effective K A values ( K A = [(CH&N] [D+]/[(CH3)3N+D]) were determined by the differential potentiometric method. l o Activity coefficient corrections were not made because, except for solutions used to determine k4 a t high acidities, the solution conditions other than D + concentration were the same for the pK measurements as those for the rate measurements. To prevent H 2 0 contamination from the reference electrode, the electrode was filled with a 1 M KC1 solution in D2O. For best results, it was necessary to correct for loss of (CH3)3Nafter addition of the NaOD titrant by extrapolating the pD readings back to the time of addition. This correction was minor, normally being about 0.01 pD unit. The precision of the pK measurements is about 0.005 pK unit, but because of possible junction potential errors and other instrumental errors, the accuracy of the effective pK, values is thought to be approximately 0.02 pK unit. Innstrumental Work. The proton nmr spectra were recorded with a Varian A-60 high-resolution instrument at the ambient temperature of the probe which was found to be 33.2'. To increase the stability of the instrument, the magnetic cooling system was made a part of a constant-temperature circulating system; the Fenwall regulator and three-way valve originally used in the coolant regulating system were found to be the major sources of short-term stability problems. This instrumental modification increased the precision of line-width measurements from 0.1 to 0.02 cps. Peak heights and widths were measured directly from precalibrated chart paper, for which the sweep-width (8) D. E. Leyden and C. N. Reilley, Anal. Chem., 37, 1333 (1965). (9) R. H. Herber, Znorg. Syn., 7, 155 (1963). (10) A. L. Bacarclla, E. Grunwald, H. P. Marshall, and E. L. Purlee, J . Org. Chem., 20, 747 (1955).
Volume 71, Number 6 M a y 1967
ROBERTJ. DAYAND
1590
calibration was checked with a side-band oscillator and a frequency counter. Peak integrals were measured with the A-60 electronic integrator. Because the slowest sweep rate available was 0.1 cps/sec and the minimum useful radiofrequency field was 0.04 mgauss, slow passage and unsaturated conditions could not be strictly achieved. Therefore, the spectra were recorded at radiofrequency fields of 0.04-0.16 mgauss and sweep rates of 0.1-0.5 cps/sec, and the measured parameters (peak to valley ratios, peak to peak ratios, and peak widths a t half-height) were then extrapolated to zero radiofrequency field and zero sweep rate. I n the case of a singlet, the excess line width caused by saturation for slow passage should be linearly dependent upon the radiofrequency field ( H I ) at the values used even in the presence of an inhomogeneous main magnetic field (H0).I1 The theoretical treatment of Jacobsohn and Wangsness12 indicates that the broadening resulting from rapid passage is linearly dependent upon the sweep rate for nonsaturation conditions and a homogeneous Ho. However, because of the presence of inhomogeneities in Ho and both sweep rate and saturation broadening, the correct form of the extrapolations to zero H1 and sweep rate are uncertain. It was found that plots of the line width, Wt,,, against H1 for a given sweep rate were linear within measurement error (0.02 cps) and that a plot of these W 1 l 2values (extrapolated to zero H I ) against sweep rate was also linear. In the case of a triplet, the dependencies of peak to peak and peak to valley ratios and peak to peak separations (apparent coupling constants) upon HZ and sweep rate are also uncertain, but it was found that, within the precision of the measurements, the same type of extrapolations to zero H1 and then zero sweep rate could be used. The exact values of H I are uncertain because a radiofrequency voltmeter with a sufficient band pass (60 Arc) to measure H1 was not available so that the H 1 values had to be taken from the dial calibration of the A-60 radiofrequency field attenuator. While the values of dial calibration are only approximate, the relative values should be sufficiently accurate so that the extrapolation will, in fact, be to zero HI. The only available method for checking this was the use of a spectrum which had several measurable parameters, each exhibiting different dependencies upon HI to see if the corrections agreed. For the CH3 proton triplet, the two pairs of center-peak t o outer-peak ratios and outer-peak to valley ratios are affected differently by Hl because, during the course of sweeping through the triplet, the portion occurring earlier in the sweep is saturated less than that later in the sweep. Hence, if the extrapolation to zero rndiofrequency field is not correct, the two The Journal of Physical Chemistry
CHARLES
N. REILLEY
values will not agree. It was found in most cases, however, that within the precision of the extrapolation, the two values agreed for both pairs.
Kinetic Measurements Of the several available theoretical treatments upon which the calculation of the shape of the CH, proton resonance as a function of the deuterium exchange rate may be based, the most convenient is the equation derived by Sack13for a symmetric triplet I(w)
-
+ 9 p 2 + 18pp” + w 2 ) + 2p”w2 + 4p264 + w262p(4p” - l o p ) + w2p2(3p+ 6 ~ ” +) w4(10p2 ~ + 4pp” + 4p”*) p(6’
w2(62
-
,2)2
(7)
where I ( @ )is the intensity, w is the frequency (sec-l) measured from the center of the triplet, 6 is the deuterium-proton coupling constant (sec-I), p is the spin transition probability of deuterium for I = 0 Ft I = =kl, and p” is the deuterium spin transition probability, I = 1 $ I = - 1 . For chemical exchange, the probabilities of the incoming deuterium being in any given spin state are equal so that p = p” and the contribution of chemical exchange to p and p” is equal to 2/3R, where R is the rate constant for deuterium exchange, { 1/[(CH3)&+D]] (d[(CH3)3N+D]/df].The factor of 2/3 arises because, in one-third of the exchanges, the incoming deuterium will be in the same spin state as the previous deuterium so that there will be no effect on the spectrum. For quadrupole relaxation, p” = 2p,I4 so that the complete transition probabilities are n
n
1
n
where 1 / T Q represents the quadrupole transition probability. The relationship p and p“ to the deuterium T1is given by:14 [ l / T I J= p 2p”. Sack’s equation is not completely adequate to describe real spectra because it involves only the spin interchange of the deuterium nuclei and does not take into account magnetic field inhomogeneities or relaxation effects of the CHs protons. In addition, the treatment is valid only when the deuterium-proton coupling constant and the transition probabilities are small compared to the difference in the resonance frequencies of deuterium and the CHs protons. Obviously, these
+
(11) A. L. Van Geet and D. N. Hume, Anal. Chem., 37, 979 (1965). (12) B. A. Jacobsohn and R. K. Wangsness, Phys. Reu., 73, 942 (1948). (13) R. A. Sack, Mol. Phys., 1, 163 (1958). (14) J. A. Pople, W. G . Schneider, and H. J. Bernstein, “High Resolution Nuclear Magnetic Resonance,” McGraw-Hill Book Co., Inc., New York, N. Y., 1959.
DEUTERIUM EXCHANGE OF TRIMETHYLAMMONIUM IONIN HEAVYWATER
criteria are satisfied in the present case even for rates much larger than those required to collapse completely the coupling within the resolution of the nmr spectrometer. The usual method of including the additional broadening by relaxation and inhomogeneity effects in the GMS15 and similar theories is to insert a phenomenological factor, 1/T2’, into the theoretical equations, Tz’ representing an effective transverse relaxation time in the absence of exchange so that field inhomogeneity is treated as if it were a relaxation process. The treatment of Sack could be modified in a similar manner by inserting a l/Tz’ factor into the original matrix equation and rederiving the above equation or using the matrix equation directly. However, in the present case, the transverse relaxation time for the CHB proton resonance is long (>lo sec) compared to the resolution of the nmr instrument (0.24 cps or 1.3 sec). The resolution is determined by inhomogeneity broadening which arises because there is a distribution of magnetic fields in the volume of the sample and, hence, a distribution of resonant frequencies. Therefore, because the major portion of the nonkinetic broadening of the CH3 proton spectrum is caused by this distribution, it should be possible to account phenomenologically for these effects by taking a theoretical spectrum calculated from Sack’s equation and then applying a shaping procedure that will reproduce the distribution of frequencies in the actual spectrum. The major defect of this method is that the shape of the field inhomogeneity distribution must be known accurately, and it is difficult to measure this distribution because with any spectrum in which the line shape is determined chiefly by the field inhomogeneity, the spectrum is so distorted by sweep rate effects that the line shape cannot be determined. While the lorentzian-shape function is normally used for field inhomogeneity, the shape of the magnetic field distribution will not necessarily follow any specific function and may vary from magnet to magnet. I n addition, the field shape for a given magnet will depend upon the adjustments of the homogeneity controls of the magnet. This is demonstrated for the instrument used in this study by the fact that when one or more of the homogeneity controls are deliberately changed from the most homogeneous settings, the shape of a sharp line becomes very distorted and does not fit any simple distribution function. T i e d 6used the ratios of observed peak widths to the theoretical lorentzian peak widths at various fractions of the peak height as a function of sweep rate as the basis of an argument that the lorentzian shape was adequate for A-60 spectra, but a lorentzian peak with
1591
additional gaussian broadening or a similar shape will also exhibit a similar effect, and the differences in the actual ratio values are not enough greater than the precision of the measurements to provide a sensitive test between different shapes. For the present case, the most sensitive test of the shaping distribution is provided by the peak to valley and peak to peak ratios (corrected to zero radiofrequency field and sweep rate) of the CH3proton spectrum of (CH3)3N+D at slow deuterium exchange rates. After proper adjustment of the various parameters, a gaussian shaping distribution gives calculated ratios which agree with the measured ratios within the precision of the ratio measurements at all DC1 concentrations for which accurate measurements can be made, while with a lorentzian shaping function, a satisfactory fit cannot be obtained for solutions with a DC1 concentration greater than 0.4 M . It is difficult to estimate the error introduced in the rate measurements by an incorrect shaping function. The error will be small at relatively large deuteriumexchange rates and will increase with increasing DCl concentration. A relatively poor choice of shaping function will not give a satisfactory fit at high concentrations, but a somewhat better choice will give a fit although the calculated rate constants will be in error. This error if significant would be apparent in the values ~ of the fact that the increase of the of k - / k ~because error with increasing DC1 concentration will lead to a dependence of the rate ratio upon the DC1 concentration, while there will be no dependence if the rate constants are not in error. Since the k - / k ~values ~ obtained in this study are not dependent upon the DC1 concentration within the accuracy of the rate measurements, a gaussian shaping distribution is apparently adequate to describe the field inhomogeneity of the instrument used in this study. The u of the gaussian distribution is chosen so that the half-width of the calculated spectrum a t very rapid rates of exchange will equal the corrected experimental half-width of an actual spectrum. This has the effect of including the proton relaxation broadening in the inhomogeneity broadening, but this does not cause significant error because the relaxation broadening is estimated to be only about 0.03 cps, and the error in treating it in this manner is less than this value and, therefore, less than the precision of the measurement which is 0.02 cps. Another possible source of broadening would be coupling of the CH, protons with the (15) H. S. Gutowsky, D. W.McColl, and C . P. Slichter, J. Chem. Phvs., 2 1 , 279 (1953). (16) G . V. D. Tiers, J . Phye. Chem., 6 5 , 1916 (1961).
Volume 7 1 , Number 6 M a y 1967
ROBERTJ. DAYAND CHARLESN. REILLEY
1592
nitrogen nucleus, but the N-H coupling constant is small for methylamine CH3 protons, and the quadrupole relaxation of the nitrogen is rapid compared to the N-CH3 proton coupling constant for trimethylammonium ion in HzO so that the coupling is almost entirely collapsed. Therefore, the parameters required for the calculation of the theoretical spectra are the rate, the deuterium quadrupole relaxation time, the deuteriumproton coupling constant, and the u of the gaussian shaping distribution. Each series of solutions has a fixed formal concentration of (CH&N+D, D + concentrations which vary M, and one solufrom approximately 0.08 to 5 X M D+. The u of the tion with approximately shaping distribution is determined from the line width of the CH3 resonance of the M D + solution, the kinetic measurements using the CH3 resonance are made from the solutions with D + concentrations greater than 5 X low4M , and the HOD proton resonance measurements were made from solutions with D + concentrations from to 5 X M. The H-D coupling constant is determined from solutions with the higher concentrations of D+ where the CH3 proton resonance has a triplet shape. It was necessary to fit the coupling constant in the calculations because the triplet is partially collapsed even at slow exchange rates because of the deuterium quadrupole relaxation. Once the coupling constant was determined from several spectra, it was not redetermined for the rest of the measurements. After the coupling constant and the shaping u have been determined, outer-peak to valley and peak to peak ratios for the triplets are calculated as a function of exchange rate for various TQ values. The two ratios are affected somewhat differently by T Q and R because exchange tends to broaden all three peaks by the same amount while quadrupole relaxation broadens the outer peaks more than the inner peak. Therefore, there is only a small range of 7Q and R values that will correctly give both ratios. The D + concentrations were chosen such that two solutions in each series gave rise to a triplet line shape, and the average of the two T Q values was used in the calculation of the line widths of the broadened singlets as a function of exchange rate. There is a possibility that r Q might change as the D + concentration is lowered, but this would only be a small source of error for the singlets because R is significantly greater than 1/TQ at these concentrations. In the case of solutions with DCl concentrations greater than 0.1 M , the determination of the shaping u is not as straightforward as for the other solutions because of the large change in solution conditions in The Journal of Physical Chemistry
I
\
I
I
\
5wee~, 7
5 cps
Figure 1. Left: calculated spectrum of (CHa)sN+D for J = 0.79 cps, 78 = 4.7 sec, R = 0.45 sec-1, and shaping width = 0.25 cps. Right: proton nmr spectrum of 1.76 F (CH:,)aNDCI and 0.22 F DCI, recorded a t a sweep rate of 0.1 cps/sec and a radiofrequency field of 0.04 mgauss.
going to a similar solution with a M D+ concentration. However, the line width of the residual HOD proton resonance is unaffected by the increasing DCl concentration over the range 0.02-1.5 M and, therefore, may be used as a check on the instrumental broadening. Examples of a calculated and an actual spectrum are shown in Figure 1. The parameters for the calculated spectrum correspond to the actual spectrum after correcting to zero radiofrequency field and sweep rate, with the calculated spectrum being normalized for equal areas. The differences in the two spectra illustrate the influence of sweep rate effects and partial saturation. The actual spectrum was taken a t the slowest available sweep rate and the smallest useful radiofrequency field. The rate, R, measured from the CH3 proton resonance in terms of reactions 1-3 is given by
R
= k4
+ (hi4- ~ ~ ) K A [ ( C H ~ ) ~ N + D I / [ (9) D+I
so that k4 is a pseudo-first-order rate constant, and k7 is a pseudo-second-order rate constant. By plotting R against 1/ [D+1, the intercept gives k4, and the slope k7; k D B , the rate of “breaking the R3N. * gives IC6 (DzO), deuterium bond,” which is equivalent to Grunwald’s7k~ is determined by the decrease of k4 at higher concentrations of DCl.
+
DEUTERIUM EXCHANGE OF TRIMETHYLAMMONIUM IONIN HEAVY WATER
The accuracy of R is limited at slow rates because quadrupole relaxation and inhomogeneity broadening are more important than exchange in determining the shape of the triplet while at rapid rates the line width is controlled largely by the inhomogeneity broadening. As a result of the small value of the deuterium-proton coupling constant, the collapse of the triplet into a singlet occurs over a relatively small range of exchange rates compared to the proton-exchange case because the NH-CH, proton coupling constant is 5.15 cps7 or about 6.5 times the deuteriumproton coupling constant. As a result, the accuracy of the rates reported in this communication is not as good as the accuracy of the proton-exchange rates although somewhat lower rates may be measured. The rate of reaction 6 can be measured from the line broadening of the HOD resonance. Using the slowexchange approximation (where the exchange broadening is small compared to the frequency difference between the HOD and N-H proton resonances) ? T W ~=/ , 1/Tze 1/THOD where Wl,, is the line width in cps, Tzethe effective line width of the HOD resonance in the absence of exchange but including field inhomogeneities, and THOD the average lifetime of a proton in HOD before being transferred to a nitrogen. The thirdorder rate constant k7' is given by
+
1593
R
-
400
L
0 6 0
1200
1600
I/IDCI 1
Figure 2. Plots of the experimental exchange rate constant R as a function of the reciprocal of the D + concentration for different concentrations of (CH&N+D: A, 0.439 F; B, 0.878 F; C, 1.32 F; D, 1.76 F. The inset is a magnification of the portion of the plots a t small R.
tion for various (CH&N+D concentrations, and the results are shown in Figure 2. The experimental points a t higher D+ concentrations have been corrected for the decrease of k4 via reaction 4 using eq 5, after k+ and k-/kDB have been determined by succesh' = P[D+I/[(CH~)~N+D]~KA~HOD (10) sive approximations. A portion of the plots a t low The statistical factor p arises because a portion of the R values has been expanded in the inset for increased exchanges involving HOD transfers a deuterium to clarity. These plots are linear within experimental (CH&N rather than a proton so that the factor p error, and the rate constants evaluated therefrom are must be applied to obtain a rate constant which will given in Table I. The agreement of the k7 values, which be comparable to k7 for DzO or HzO. An effective pseudo-second-order rate constant, k7HOD,for comparison with the IC7 measured from the CH, proton Table I: N-D Deuterium-Exchange Rates for resonance, is obtained by multiplying kTf by the conTrimethylammonium Ion in D20 a t 33.2' centration of DzO, 55 M . The accuracy of the HOD (k8 + k ? ) K A , line-width measurements is limited because the signal I(CHs)aN+D], h, 888-1 X KA, M - 1 8ec-1 'I'IQ,~ to noise ratio is poor for the broadened resonance, so M sec -1 10' M X 10" X 10-8 sec that the precision is approximately lO-l5%. The 0.439 1.00 3.85 3.46 1.11 4.0 [D+] values are also not as accurate as those of the 0.878 0.85 3.56 3.04 1.17 2.2 solutions in which the CH3 proton resonance is studied 1.32 3.17 2.80 0.80 1.13 1.8 0.74 2.68 1.76 2.55 1.05 1.6 because the [D+] must be lower to get a measurable broadening, and in this concentration range, the solua Assuming ks < < k,. * TlQ is the contribution of deuterium tion is poorly buffered; hence, the [D+] is sensitive to quadrupole relaxation to the N-D deuterium TI (TIQ= T Q / ~ ) . acidic or basic impurities adsorbed on the nmr sample tubes and to the possible loss of (CH,),N from the solution. are not expected to have a significant salt effect, is well within experimental error, the average deviation Results and Discussion being only 3%, while the estimated error is 10% for Values of the experimental rate constant, R, deterk d and k7. A plot of log k4 against total concentration mined from the CH, proton resonance were plotted is linear with a slope of -0.090 and intercept which against the reciprocal of the deuterium ion concentragives a k40 value of 1.08 sec-'. Log K A is linearly Volume 71,Number 6 May 1967
ROBERT J. DAYA N D CHARLES N. REILLEY
1594
dependent upon [(CH3)3N+D]"2with the intercept giving KAO to be 4.76 X lo-"; therefore, taking k+O = k40, k-O = 2.3 X loloJ4-I sec-I. Table I1 gives the effect of higher D + concentrations ~ calculated from eq 5 on k,, The ratio k - / k ~was assuming, as did G r u n ~ a l dthat , ~ there is no salt effect upon the ratio and that the salt effect of D + upon k+ is the same as that of (CH3),NDCl. The agreement of the ratios is satisfactory in view of the accuracy of k, in this range which is only 1525%. The average
Table 11: Rate Constants for Deuterium Exchange a t Higher Acidities I(CHa)sN +Dl, ,lf
[DCll,
kr
M
8ec -1
0.44 0.44 0.44 0.44 0.50 0 ,50a 1.76
1.10 0.88 0.66 0.44 0.22 0.22 0.22
0.22 0.26 0.29 0.44 0.57 0.45 0.45
k-/kDB, IM -1
Tig.
2.5 2.4 3.0 2.4 2.9 3.1 2.7
0.8
sec
0.8 0.8 1 .O 1.3 1.1 0.9
proton resonance, extrapolated to infinite dilution, are summarized in Table I11 along with the corresponding proton-exchange rates and isotope effects calculated at 33.2" from the empirical rate equations for proton exchange given in ref 7. These isotope effects are in agreement with mechanisms used to describe the exTable I11 : Isotope Effects for Exchange of Trimethylammonium Ion at 33.2' at Infinite Dilution Rate parameter
kHzOa
kao, sec-l k+, M-l sec-l KAO, M k-Q, M-l sec-l kao, sec-l
7.2 3 . 8 X IO8 2 . 4 0 x lo-'' 3 . 0 X 1Olo 1 . 2 X 1Olo
a
kDzO
1 .og 1.12 x 108 4 . 7 6 X lo-" 2 . 3 X 1Olo 8 . 5 X lo0
kHz01 kDiO
6.7 3.4 5.0 1.3 1.4
Calculat.ed from ref 7.
.change processes. The large isotope effect on kq is consistent with the hypothesis7 that the position of the a Also contains 1.0 F LiCI. transition state of reaction 1 along the reaction coordinate is not very far from the products so that there would be a significant difference in the zero-point enerratio is 2.7 so that ~ D is B 8.5 X lo9 sec-'. The congies between transition state and the reactants. In tribution of quadrupole relaxation to the deuterium T1 the case of k7, the rapidity of the symmetrical reaction of (CH3)3K-+Dis not a simple function of concentraindicates that the transition state is not very different tion. This arises because changes in concentration from the reactants (or the products); thus, the difof the various species in solution can affect T1,( T1,= ference in zero-point energies would be smaller; hence, T Q / ~ )by two different mechanisms, one involving the the isotope effect on k7 should be smaller than that on correlation time for molecular rotation, T C , and the k4. Because k- is considered to be diffusion controlled, other involving the electrical field gradient about the the isotope effect should be determined by the difdeuterium nucleus. The effect of concentration ferences in diffusion between HzO and D 2 0 so that the changes of 'rc can be considered as a viscosity effect, ratio of rates should be given approximately by the and a plot of log TI, against concentration should be mobility ratio of H+/D+ which is 1.4," within experiapproximately linear with the effect of changes in mental error of the measured value of 1.3. The cal(CH3)J +D concentration being much greater than culation of the theoretical isotope effect on k ~ the , rate changes ill :D+ concentration. However, plots of log of "hydrogen bond breakage," may be based on the TI, against concentration are not linear; furthermore, treatment of Conway, Bockris, and Linton,I7 who the effect of DCl is greater than that of (CH3)3NDC1 considered the rate-determining step in proton conor LiCl. The greater influence of DCl us. LiCl indiductance in HzO to be the reorientation of the hycates that this is not a simple anion effect leading to drogen-bonded HzO molecules. In the mechanism increased ion pairing. Therefore, at the relatively suggested by Grunwald, the rate step should also be large concentrations required for this study, there is the reorientation of H2O molecules so that the theoapparently a change in ion pairing or some other factor, retical ratio of k H / k D B would also be 1.4, in agreement leading to a significant alteration of the microscopic with the experimental value of 1.4. structure of the solution about a (CH3)3N+Dmolecule The results from the line broadening of the HOD as the concentrations of the various species are changed, proton resonance using eq 10 are given in Table IV, leading to changes in the electric field gradient about the deuterium nucleus. (17) B. E. Conway, J. O'M. Bockris, and H. Linton, J. Chem. Phys., The kinetic parameters determined from the CH, 24, 834 (1956). The Journal of Physical Chemistry
DEUTERIUM EXCHANGE OF TRIMETHYLAMMONIUM IONIN HEAVYWATER
taking 1.45 as the d u e for the statistical factor p . This value was determined by assuming that k7 for deuterium transfer from HOD has the same value as k7 for deuterium transfer from D20 so that p is given Table IV : Proton-Exchange Rates Measured from the HOD Proton Resonance
x
M
0.439 0.878 1.32 1.76
104
1.7 1.0 1.2 1.2
+
x
10-0
5.2 3.4 4.2 4.6
x
10-0
2.9 1.9 2.3 2.6
by [kTHoD k7h0]/k~HOD (hHoD refers to proton transfer from HOD). This wumption should be valid within the experimental error. The average deviation of the kTHODvalues is 12%) which is within the esti-
1595
mated experimental error of 20%. The isotope ratio approximately half that of k7H20/ kTDlo in D2O; this is in agreement with a concerted reaction. The rate parameters were not measured at other temperatures because the reproducibility of the instrumental broadening was not sufficient to permit accurate rate measurements; this is caused primarily by poor temperature control of the variable-temperature probe. I n addition, the triplet shape is collapsed a t higher temperatures for D + concentrations below 0.1 M so that the determination of TI, values becomes difficult. k l ~ ~ o / k 7is~ 01.6, ~
Acknowledgment. The authors are indebted to Drs. L. B. Anderson and D. E. Leyden for their assistance in the preparation of the computer program for the calculation of the theoretical spectra. Research was supported in part by National Institutes of Health Grant GM-12598-01 and by the Advanced Research Projects Agency.
Volume 71,Number 6 M a y 1967
