2970
ERNESTGRUNWALD AND ELTON PRICE
1.2
0.8
>' 0.4
t
u)
Z
W
-L
o
W
-> 2
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I 0.8
I 1.2
1.2
w J
a 0.8
0.4
0
I -1.2
I
-0.8
I
I
-0.4
0
0.4
AW/J.
Fig. 2. -SH- proton resonance spectrum for (a)0.388 M a n d ( b ) 1.19 M methylammonium chloride in acetic acid a t 25". Solid curves are calculated for ( a ) l / P = 230 set.-'; ( b ) l/T1 = 360 sec. - l . viscosimeter. The measurements were made a t 25 i 0.05" and were precise to 3~0.57,. N.m.r. Measurements.-All n.m.r. measurements were made on the high resolution n.m.r. spectrometer of Meiboom, operating a t 60 Mc./sec. A brief description of the instrument and of methods of frequency stabilization, temperature control, and spin-echo determination of T1 and Tz' relaxation times has been
[CONTRIBUTION FROM
THE
Vol. 86
given e l s e ~ h e r e . ~ I' n measurements of T I and T2' of the carboxyl protons, the radiofrequency field was adjusted according to the method of Alexander28so as to eliminate interference from the CH3--protons of acetic acid. 1-alues of l / T z ' were precise to 1 0 . 0 1 2 set.-', up to about 4 set.-', but the precision decreased rapidly above this value. T'alues of 1/T1 were usually precise to 3~0.005set.-'. Typical values of A ranged from 0.3 to 3 set.-'. The CHI- proton resonance of methylammonium ion (present largely in the form of ion pairs) was recorded under conditions of slow passage and negligible saturation. 1/T2, the effective line width in the absence of exchange, was taken as equal t o the actual line width of the C13H3- proton satellite of acetic acid. The T' relaxation time of Y 4in the methylammonium salts was obtained from slow passage records of the S H - proton resonance under conditions of negligible saturation, In spite of the low signal-to-noise ratio, results were sufficiently precise even a t concentrations as low as 0.2 M . Typical data are shown in Fig. 2. The interpretation of the NH- proton spectra was based on Pople's theory,29and allowance was made for spin-spin interaction with the CH3- protons and for chemical exchange. Pople assumes in his theory t h a t in the absence of T1 relaxation, the NH- proton resonance is a 1 : 1 : 1 triplet of extremely sharp lines. (Line width approaches zero as l / T 1 approaches zero.) Chemical exchange can be introduced into the theory by assuming that in the absence of T 1relaxation the width of each triplet line equals R/( N H ) , where R is the known rate of exchange and ( N H ) is the number of gram-atoms of NH- protons per liter. For any given value of T 1 and R / ( N H ) , a theoretical curve that allows for spin-spin interaction with the CH3- protons can then be constructed by adding a 1 : 3 :3: 1 quadruplet of curves, calculated as described above, and separated by the known C H - S H spin-spin interaction of 6.17 C.P.S. The fit of theoretical curves calculated in this way to some data for methylammonium chloride is illustrated in Fig. 2 . In this case, R / ( N H ) = 0, and TI is defined by the data with a precision of about 109;. However, for methylammonium acetate the precision is less (about 1 2 5 ) because of the relatively large value of R/( N H ) .
______
(27) E . Grunwald, C. F. J u m p e r , a n d S. Meiboom, J . A m Chem Soc., 84, 4646 (1962). (28) S. Alexander, Rev. Sci. Insty., 32, 1066 (1961) (29) J . A. Pople, M o l . P h y s . , 1, 168 (1968).
BELLTELEPHONE LABORATORIES, Ih'C., MURRAY HILL, XE\V JERSEY]
Ionization and Proton Exchange of Amines in Acetic Acid. 11. Effect of Structure on Reactivity and the Reaction Mechanism BY ERNEST GRUNWALD AND ELTON PRICE RECEIVEDFEBRUARY 28, 1964 Rates of exchange of S H - with COOH- protons have been measured over a wide temperature range for a series of amines in dilute solution in acetic acid by precise nuclear magnetic resonance techniques. The ionization of these amines is nearly complete in acetic acid, the actual reactant being R3KH+OAc-. Reaction rates were calculated from the n.m.r. data by a rigorous method that requires the d a t a : ( i ) the exchange broadening of the dominant line in the NH-COOH proton system, (ii) the chemical shift of S H - relative to COOH- protons, (iii) the N14-H spin-spin coupling constant of RaSH+OXc-, and (iv) the T 1relaxation time of ?;lr in R 3 K H + OAc-. The rates of proton exchange in all cases were first order in RBSH+O;ZC-,and the rate constant, k, appeared to decrease slightly with increasing concentration. The following kinetic results are reported : for KH4+OXc-, k ( 2 5 ' ) = 6080 set.-', AH* = 19.75 kcal., A S * = 25.0 e.u.; for ( C H 3 ) 3 K H + O A ~ k- , (25') = 945 sec.-l, A H * = 16.95 kcal., A S * = 11.9 e . u . ; for ( H O C H Z ) ~ C X H ~ + O XkC(25') -, = 41,000 sec.-l, AH* = 20.7 kcal., A S * = 32 e.u. Previously reported values for CHaSH3+0Ac-, k ( 2 5 ' ) = 230 sec.-l, AH* = 18.41 kcal., A S * = 14.0 e.u., were also included in the analysis of the effect of structure on reactivity. The preceding rate constants for proton exchange of R3X"+OXc- in acetic acid are very nearly proportional to both rate and equilibrium constants for the acid dissociation of R I S H * in water. Moreover, the variations with structure of A H and A S for the two processes follow similar patterns. These remarkably simple relationships suggest a close analogy of reaction mechanism. Thus in acetic acid the mechanism 13, with B = R3N and with kz > k H , seems to fit these facts as well as some data concerning diffusion control of the reaction of acetic acid with strongly basic amines in water. The order of magnitude of kH is estimated as lo8 sec.-l; kp appears to be so large t h a t the interactions with the surrounding dielectric in the activation step of this reaction cannot be described by a reversible electrostatic model. As a result, it is probable that k2 is greater in acetic acid than in water, in spite of the smaller static dielectric constant of acetic acid.
In water, equilibrium and rate constants for the acid dissociation of the methyl-substituted ammonium ions
are in the well-known and peculiar sequence, NH4+ >> CH3NH3+= (CH&NHz+ < (CH3)3NH+,which
PROTON EXCHANGE OF AMINESIN ACETICACID
Aug. 5 , 1964
2971
1000 I deviates from the order expected for a purely inductive 1 effect.laSb In this paper we extend the previously reported2 nuclear magnetic resonance (n.m.r.) measurements of proton exchange rates in glacial acetic acid so as to provide first-order rate constants and activation parameters for NH-COOH proton exchange for the series of substrates NHdfOAc-, CH3NH3+OAc-, (CH& NH+OAc-, and (HOCHZ)~CNH~+OAC-(TRIS.OAC). We find that for ammonium acetate and the methyl derivatives, the rate constants in acetic acid are in precisely the same sequence as the equilibrium and rate constants for acid dissociation in water and are, in fact, nearly proportional to the latter. Changes of enthalpy and entropy obtained for the two processes likewise display closely similar patterns of substituent effects. We believe that these simple relationships are the result of a'close analogy of the reaction mechanisms and on this basis propose a plausible mechanism for proton exchange in acetic acid. Kinetic results obtained for the highly polar subTEMPERATURE ('C). strate, TRISOAc, in acetic acid fit into the pattern Fig. 1.-Exchange broadening as a function of temperature for established by the methylamines, suggesting that the 0.111 M ammonium acetate in acetic acid. Circles represent experimental points. Smooth curve is calculated from eq. 2, cyclic complex 1, in which there are two intramolecular using 6 = 1915 radians/sec., J = 330 radians/sec., T 1= 0.01 sec., hydrogen bonds, is not a major subspecies.
log 7T
4318/T
-
15.200.
Results Calculation of Reaction Rates from N.m.r. Data.Since in our systems the ratio [B]/[BH+OAc-] of un-ionized to ionized amine is very small, we treat the proton exchange as involving two chemical shifts, that of the carboxyl protons of acetic acid and that of the NH- protons of the ionized amine. We define the proton fraction P B as (NH)/[(NH) (COOH)], where ( ) denotes proton gram-atoms per liter and (NH) is computed on the assumption of complete ionization. Since acetic acid is the solvent, PB > K H , which implies t h a t k = ( k 1 , ' k z ) k ~ = K i - ' k ~ , where Ki is the ionization constant of the amine in acetic acid. I t has been suggested t h a t K, for amines can be estimated by simple proportion from the base dissociation constants in water, the ratio K ~ I K Bbeing --f
- 10.4 0
2.4
2.8
3.2 LOG
3.6
k.
Fig. 2.-Rate constants ( k ) for proton exchange in acetic acid compared with equilibrium constants ( K A ) and rate constants (kl) for acid dissociation in water: 0, K A ; X , k4,
about 2 X 109.2311Values of K i estimated in t h i s way and the corresponding values of k K i are listed in Table V. In case a the values obtained for k K i , which are of order lo8 set.-', measure k 2 ; in case b they measure k ~ . We believe that case b represents reality and shall present two independent arguments to support this belief. The first is an argument by analogy. We infer from the marked resemblance of substituent effects, noted above, that the reaction mechanisms for proton exchange in acetic acid and for acid dissociation in water are closely similar. The mechanism of acid dissociation in water is represented best by an ionization -dissociation model12 such as t h a t shown in eq. 15, which is closely analogous to t h a t shown in eq. 13. H H BH+,OH.OH
k, k-
H H@ B,HO.HOH
+
H H' B,HO,HOH
i
kd (TZ
- 1)HzO
~
H
+B.HO
structural diffusion
+ (H.TZHZO)+ (15)
The first step in both eq. 13 and 15 is a proton transfer within a hydrogen-bonded complex to produce a conjugate acid-base pair; the second step in both is a diffusional process. The ratio k - i / k d in (15) is therefore analogous to k z / k ~in (13). Now i t is probable that k-i/kd > 1. This follows from microscopic reversibility because the reverse reaction, between amine and hydrogen ion, appears to take place rapidly at each encounter, (11) In view of t h e enormously high rate constants associated with proton transfer in some cases, i t is possible t h a t t h e ratio K ~ / K Bchanges from one constant value for small K i t o a higher constant value for large K , as K , passes through unity. Suppose t h a t the shorter of the two lifetimes in the mobile prototropic system B,HOAc = B H + . O A c - i s shorter t h a n the dielectric relaxation time of the solvent. I t then follows t h a t the interaction of the system with the surrounding dielectric cannot be reversible in the electrostatic sense. If BH+OAc- is the species with t h e very short 11, the effective dielectric constant of the solvent will be t h a t life ( K , resulting from distortion polarization alone. If B.HOAc is the species with l ) , the dielectric interaction will resemble t h e the very short life ( K , model shown in Fig. 3b. Thus, if the irreversible model applies, the stabilieation of B H +OAc- by interaction with the dielectric is greater when K , 1 Since the factor 2 X 100 for K , / K B is based on d a t a with K , 1, the correct factor for Ki 1 could be larger, and the estimates of K Iin Table V could he too small. (12) E.Grunwald. J. P h y s . C h e m . , 67,2211 (1963)
>>
>>
2976
ERNEST GRUNWALD ,4ND ELTONPRICE
(a)
SO LV E N T P O L A R I2 AT10 N BY DISTORTION A N 0 OR IE N TAT ION
SOLVENT P O L A R I 2 AT IO N BY DISTORTION ONLY
(b)
RESIDUAL POLARIZATION (MOSTLY ORIENTATION) JUST BEFORE PROTON TRANSFER
POLARIZATION INCLUDES SOME O R I E N T A T I O N POL ARlZ AT ION
Fig. 3.-Models for the interaction of reactants and transition state in the prototropic system B ' H O A c = BHC.OAc- with a surrounding dielectric.
provided only that the reaction zones are appropriately j ~ x t a p o s e d . ' ~Analogy ~~~ then requires that kz/kH is also greater than unity. Medium Effect on kz. Irreversible Aspects of Dielectric Interaction.-The second argument begins with some kinetic data in water and considers the medium effect on kz. Eigen and Maas15have measured rate constants between acetic acid and a series of amines in water. They find that for weakly basic amines the rate constant increases with the base dissociation constant, but when K B exceeds about lo-', the reaction rate becomes limited by the number of encounters. This means that for ammonia and the alkylamines in water, for which Kg >> IO-', the quantity k2re (which is the analog of k z / k H ) is much greater than unity, where re is the mean duration of the appropriate encounter and k z , as before, is the probability per second of proton transfer during the existence of the encounter. Since K H in acetic acid is not likely to be much greater than l i r e in water (acetic acid is more viscous than water), we may infer that k2/kH > 1 in acetic acid if the medium effect on kz is relatively small. This is probably the case. The simplest argument makes use of a reactivityselectivity relationship. We have seen that in water kz must be very large, almost certainly greater than 10'' sec. - l . Such a high rate constant implies, with a high probability, that the transition state closely resembles (13) M . Eigen and L . De Maeyer, Proc. R o y Soc. (London), A247, 503 (1938); in "Sti-ucture of Electrolytic Solutions," W , J Hamer, E d . . J o h n U'iley and Sons, Inc., New York, N. Y . , 1959, Chapter 5 . (14) I3 G r u n w a l d , J . P h y s . Chem., 67, 2208 (1963). (1.5) M . Eigen and G. Maas, d a t a cited by M . Eigen and L . D e Maeyer, "Investigation of Rates and Mechanisms of Reactions," S. L. Friess, E. S. Lewis. and A . Weissberger, E d , Interscience Publishers, Inc., New York, s.Y , 1963. g . 1040 (16) J E Leffler and E Grunwald, "Rates and Equilibria of Organic Reactions." John Wiley and Sons, Inc., New Y o r k , li. Y . , 1963, pp. 162-168.
VOl. 86
the initial un-ionized state with respect to structure and charge distribution. l7 Medium effects, which reflect differences of the two states with the solvent, should therefore be small. In view of the occasional failure of the reactivityselectivity relationship, we shall develop an alternative argument t h a t does not require the transition state to be essentially un-ionized. Medium effects on the rate constants of polar reactions are normally dominated by interactions depending on the dielectric properties of the solvent. The magnitude of such interactions will depend, among other variables, on the relative values of T D , the dielectric relaxation time of the solvent, and of r*, the mean time required for transition from the initial state to the transition state of the reaction. If r* >> T D , then the interaction with the dielectric can be treated as reversible and the solvent polarization as being in equilibrium with the charge distribution of the reacting system both in the initial state and in the transition state. If T* < TI), then the permanent dipoles of the solvent molecules do not have time to come into equilibrium with the changing charge distribution of the reacting system and the solvent polarization due t o orientation is essentially constant. These relationships are illustrated in Fig. 3a for a model of ionization in which the initial state, B . 'HA, is nonpolar, and the transition state has a dipole moment between zero and that of the product, BH+A-. We now wish to discuss the medium effect on kz due to dielectric interactions according to this model, allowing the transition state to be polar. Dielectric relaxation times are about lo-" sec. for water18 and lo-'" sec. for glacial acetic acid.1° The time required for activation cannot exceed the lifetime of the initial state, and r* must therefore be less than l / k z . In water, l / k z < re, the lifetime of the appropriate encounter, and we therefore have the inequalities r* < l / k z < re. Since relaxation times for diffusional processes in liquids are normally not longer than those for rotational processes, r, is probably a t most of the order of magnitude of T D , and T * is therefore probably less than T D . In terms of Fig. 3a, this implies that the model on the right, in which the transition state is stabilized only by distortion polarization, is probably correct. If we adopt this model, then the transition state will be more stable in acetic acid than in water because acetic acid, which has the greater optical refractive index, will develop more distortion polarization than will water. Figure 3b shows that the dielectric effect of acetic acid might, in the reactions studied in this investigation, be even more favorable than one would expect on the basis of Fig. 3a, because the un-ionized complex B . HA is formed directly from the highly polar ion pair, B H + . A - . The lifetime of B H + . A - is sufficiently long for the polarization of the acetic acid solvent to reach the equilibrium value. On the other hand, the lifetime, l / k z , of B . H A is probably not longer than TD. When B . H A is formed from BH+.A-, the solvent shell surrounding i t will still have some of the orientation polarization originally associated with BIX +. A-, and this polarization will not have time to decay to zero (17) J . E . Leffler, Science, 117, 340 (1953). (18) G. H . Haggis, J B. Hasted, and T J . Buchanan, J . Chem P h y s . , ao, 1452 (1952). (19) P. Girard and P . Abadie, J . chim. p h y s . , 4 4 , 31.3 (1847)
Aug. 5 , 1964
CARBOX-13 MAGNETIC RESONANCE SPECTRA
during the lifetime of B . H A . Since the direction of the residual polarization is such as to favor the formation of the dipole moment in the transition state, as shown in Fig. 3b, we expect a reduction of the free energy of activation from this effect. An analogous reduction would not be expected for the process discussed in water because here the formation of the reactive encounter is preceded by the diffusion of unionized reactants. In summary, if we adopt the model of a polar transition state and of irreversible dielectric interactions resulting from r* < T D , we expect kz in acetic acid to be greater than kz in water. It should be noted t h a t this prediction is opposite to predictions based on reversible electrostatic models. Tris (hydroxymethy1)methylammoniumAcetate.-We were interested in the rate of proton exchange of this substance because of the possibility that the cyclically hydrogen-bonded ion pair (11) is the dominant subspecies.
2977
ammonia would have the acyclic structure 111. In the cyclic complex IV, the amine molecule is bonded to the adjacent acetic acid molecule by two hydrogen bonds, whereas in I11 i t is held less firmly by a single hydrogen bond. Since displacement of the adjacent acetic acid molecule by acetic acid from the bulk solvent is the probable rate-determining step in proton exchange. and since the rate constant for that displacement is measured by M i , we would expect a marked decrease in kKi if I1 were the dominant subspecies.2n The relevant data for TRIS.OAc are included in Table V. It is seen that the value of kKi is not exceptional, being nearly the same as that obtained for trimethylamine. Moreover, the activation parameters AH* and A S * for TRIS.OAc continue the systematic trends established by ammonia and the methylamines when compared with AH" and A S " for acid dissociation in water. It therefore appears that the mechanism of proton exchange for T R I S Orlc is entirely analogous to that for the other amines. As a corollary, the cyclic ion pair I1 is not the dominant subspecies. Experimental
HOAc
I RzCNH3'.
. .Oe
\
I / /
CHzOH. . .O
C-CHI
+ 2HOAc
I1 RzC-NHp.
.HOAC.HOAC RzCiXHz.. . H O I \ I C-CHI
II
Acknowledgment.-It is a pleasure to thank Dr. 2 . Luz and Dr. S.Meiboom for helpful discussions and for their advice concerning the n.m.r. measurements.
CHzOH
HOAc
I11
The product of proton transfer of I1 would also have a cyclic structure (IV), whereas the analog of solvated
[CONTRIBUTION FROM
THE
Ammonia and trimethylamine were obtained as compressed gases from the Matheson Co. Trimethylammonium chloride ( Eastman) was recrystallized twice from absolute ethanol. Sodium acetate (Baker) was dried a t 120" for 36 hr. Tris(hydroxymethy1)aminomethane (Fisher) was dried in an 2,Z-DiAbderhalden pistol over PzOba t 80"; m.p. 171.5-172'. methyl-1,3-propanediol was recrystallized from benzene; m.p. 130.5-131.1" (reportedz1 130'). Solutions were prepared exactly as described previously. The experimental and n.m.r. techniques are the same as described in paper I . 2
(20) For example, for t h e cyclically hydrogen-bonded dimel- of c-caprolact a m , t h e rate constant for breaking only one of the two hydrogen bonds is about 109-10'0 sec. -1; t h a t for breaking both hydrogen bonds is 10s sec - 1 , d a t a reported by M . Eigen, Chem. En! News, 41, Dec. 2 , 38 (1963). (21) R. W . Shortridge, R A . Craig, K W Greenlee, J . M Derfer, and C. E . Boord, J . A m Chem. SOL.,70, 948 (1948).
DEPARTMENT O F CHEMISTRY, UNIVERSITY OF UTAH, SALT LAKECITY, UTAH]
Carbon-13 Magnetic Resonance. I. Improved Carbon-13 Magnetic Resonance Spectra Obtained by Proton Decoupling and Rapid Sample Spinning B Y EDWARD G. PAULA N D DAVIDI f . GRANT RECEIVED JASUARY 2, 1964 Experimental methods for improving the observation of carbon-13 magnetic resonance spectra are presented. Saturation effects common t o the carbon-13 nuclei resulting from its relatively long relaxation time can be partially circumvented with proton decoupling and sample spinning. In addition to improved signal heights realized from multiplet collapse, a nuclear Overhauser enhancement of the resonant peak allows carbon-13 magnetic resonance spectroscopy to be extended to considerably larger molecules and more dilute samples. Spinning of the sample also results in greater resolution and enhanced signal intensity. By accurately determining the proton decoupler and carbon-13 transmitter frequencies, the chemical shift of a given peak can be determined within an error of f 0 . 0 7 p.p.m. a t 15.1 Mc.p.s. Optimum operating conditions are discussed
I. Introduction The combination of a low natural abundance and a relatively long nuclear relaxation time for the carbon-13 magnetic isotope has offered a formidable obstacle in the study of its magnetic resonance Use of adiabatic rapid passage techniqueson the dispersion has been relatively SUCCeSSfUl in the study Of compounds
of low molecular weight which are neat liquids or solids of high solubility in some solvent. The sensitivity of (1) P. C . Lauterbur, J . Chem. P h y s , 26, 217 (1957); A n n . S. Y . Acad. s c i , 70, 841 ( 1 ~ 5 8 ) :J ~m Chem S O C . . 83. 1839. 1846 (19611 J . Chem P h y s , 38, 1406, 1415 1432 (1963) ( 2 ) C H Holm ,bad 26, 707 (1957) (3) H Spiesecke and W G Schneider tbtd 36, 722 (1960) (4) H Spiesecke and w G Schneider, Teiuahed?oia Leileis 468 (1961)
