JOURNAL OF T H E AMERICAN CHEMICAL SOCIETY Registered i n U.S.Patenf O f i c e .
@ Copyright,
1964, by the American Chemical Sociefy
AUGUST5, 1964
VOLUME86, NUMBER15
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTION FROM
THE
BELLTELEPHOPI’E LABORATORIES, IKC., MURRAY HILL, NEW
JERSEY]
Ionization and Proton Exchange of Amines in Acetic Acid. I. Kinetic and Equilibrium Properties for Solutions of Methylamine BY ERNESTGRUNWALD AND ELTONPRICE RECEIVED FEBRUARY 28, 1964 Methylamine in acetic acid is largely converted to methylammonium acetate. T h e ionization constant, = [CH3SH~+OAc-]/[CH31CH2], was estimated as 8 X 106. The degree of association of ion pairs was determined from freezing point data. Equilibrium constants (concentrations in mole/kg. ) for the formation of double ion pairs were 0.0 for CH3S“3+OAc-, 0.6 for (CHa)qN+OAc-, 2.7 for CHOKHs+Cl-, and 1.7 for CHsNH3+0Ac- with CH3NH3+C1-. Rates of exchange, R, of “3protons with COOH- protons of the solvent were measured by nuclear magnetic resonance techniques. Kinetic analysis established the rate law as R = k[CHJYH3+OAc-], Kinetic parameters a t 25’ are: k = 230 sec.-l, AH* = 18.41 kcal., A S * = 14.0e.u. A slight decrease of k was observed with increasing concentration and can be interpreted as a viscosity effect. Addition of (CH3)4NOAcproduced a similar effect on k . Addition of CH3NHaClresulted in a larger reduction of k, which was ascribed t o the formation of unreactive mixed ion pairs, C H B N H ~ O A C . ( C H ~ N H I C ~ ) ~ .
K,
The kinetics and reaction mechanisms of fast proton transfer reactions involving oxygen and nitrogen acids and bases have been studied extensively in water and also in a few other solvents of relatively high dielectric constant. We now report nuclear magnetic resonance (n.m.r.) measurements of the rate of proton exchange between amines and acetic acid in glacial acetic acid, a solvent of low dielectric constant (D = 6.22 a t 25°).2 In part I (this paper) we give a kinetic analysis for methylamine in acetic acid and give quantitative estimates of ionization to methylammonium acetate and of the dissociation and association of the latter. In part 113we present kinetic data for a series of amines and discuss the reaction mechanism. Kolthoff and Bruckenstein4 have emphasized that it is necessary to represent base dissociation as occurring in two steps, ionization and dissociation, especially in solvents of low dielectric c o n ~ t a n t . ~These authors report values of the equilibrium constants K i and K d for Ki
B.HOAc
BH+.OAcKd
BH+.OAc-
BH+
4-OAC-
(1) (2)
several amines in glacial acetic acid. Values for methylamine are not reported, but may be estimated as follows. The fairly good success of the method of acidity (1) For a recent review, see L De Maeyer and K. Kustin, A n n . Rev. P h y s . Chem., 14, 5 (1963). (2) W.Dannhauser and R . H.Cole, J . A m . Chem. Soc., 74,6105 (1952). (3) E. Grunwald and E . Price, i b i d . , 86, 2970 (1964). (4) I. M.Kolthoff and S. Bruckenstein, J . A m . Chem. SOL.,78, 1 (1956). (5) In discussions of reaction mechanism it is more useful t o represent the un-ionized base realistically as B.HOAc rather than formally as B .
functions6”in predicting ~ K for B weak bases in water on the basis of ionization measurements in glacial acetic acid6b suggests that K i in acetic acid is approximately proportional to K B in water. Direct measurements, summarized in Table I, indicate that the proportionality TABLE I
Kg
IN
WATER^ COMPARED WITH Ki IN GLACIAL ACETIC ACID. DATAAT 2Sa Ki KJKB KB
Base
in water
in HOAc
X 10-9
Pyridine 1 . 7 x 10-9 5.4b 3.2 Bis-p-dimethylamino9 x 10-11 0.10* 1.1 azobenzene 3 x 10-13 (4 x 1 0 - 4 ) ~ , ~ ca. 1 2,5- Dichloroaniline Methylamine 4.2 x 8 x lo6 References for K B : H . C. Brown, D. H . McDaniel, and 0. Hafliger in “Determination of Organic Structures by Physical Methods,” E. A . Braude and F. C. Sachod, Ed., Academic Press, Inc., New York, N. \’., 1955, Chapter 14; M . Kilpatrick and C. A. .4renberg, J . A m . Chem. SOC.,7 5 , 3812 (1953); H . H . Jafie, Chem. Rea., 53, 200 (1953). Ref. 7. Assume Kd is equal to Kd for pyridinium acetate. Average for other bases. I t is possible that this estimate of K i / K g is too small since K i for methylamine is so large, see footnote 11 of ref. 3.
’
constant is about 2 X lo9. On this basis, Ki for methylamine is about E; X lo5 and we may conclude t h a t methylamine is almost completely ionized in acetic acid. The available data for K d of acetate salts in acetic acid? suggest that, although K d varies with the nature of the cation, the variation is relatively small. W e (6) (a) L. P. Hammett, Chem. R e v , 16, 67 (1935). (b) S F. Hall and W. F.Spengeman, J . A m . Chem. Soc., 62,2487(1940); H . Lemaire and H J Lucas, i b i d . , 73, 5198 (1951), T L.Smith and J H . Elliott, i b i d . , 76, 3566 (1953), S. Bruckenstein, i b i d . , 82, 307 (1960) (7) S. Bruckenstein and I. M. Kolthoff, ibid , 7 8 , IO, 2974 (1956).
2965
ERNESTGRUNWALD AND ELTON PRICE
2966 1.6
Vol. 86
TABLE I1 FREEZING POINTSTUDIES OF ASSOCIATIONOF ELECTROLYTES IN GLACIAL ACETICACID Solute‘
1.2
ATf
,Ib
Zmi
0.11 0.127 0.42 .27 1 03 ,261 ,417 1.57 .43 .20 (CHI)~N+OAC.25 0.77 .24 .27 0.91 .31 .34 1.17 124 Imidazole ,126 0.44 ,042 .18 CHsNH3CI ( B ) ,048 ,112 .38 ,096 ,162 ,232 .62 ,230 ,392 .87 ,252 ,442 .95 ,312 ,603 1.17 ,353 ( A ) 0 126 ( B ) ,425 1.32 ,257 ( A ) ,126 ( B ) ,218 0.97 ,397 (.4) ,261 ( B ) ,256 1.47 Triphenyl-n-amyl phosphonium iodidec Tetraethylammonium chloridec Tetramethylammonium thiocyanate’ Sodium iodide’ H30+OAc-d IH+OAcI H +OAcCsHsNH + O A C - ~ a ( A ) = C H ~ N H ~ + O A C (- B , ) = CH3NH3’ClRef. 8. formula weights of solute per kg. of solvent. I = bis-p-dimethylarninoazobenzene ; concentrations in CH~NH~+OAC (A) -
e ‘
U‘ v
c’0.8 Q
0.4
0.1 0.2 0.3 MOLAL CONCENTRATION,
0
Fig. 1.-Freezing
0.4
point lowering in glacial acetic acid: 0, naphthalene: 0 , benzoic acid.
may therefore expect to predict unknown Kd values, a t least to the correct order of magnitude, by analogy with known Kd values for structurally related acetate salts. On this basis, Kd for methylammonium acetate is estimated by analogy with Kd for pyridium acetate to be about (mole/l.). In the present work the formal concentrations of amine range from 0.02 to 1 M . Hence the concentrations of the free ion, CH3NH3+, are expected to be no more than 1% of the formal concentrations. On the other hand, the association of ion pairs to higher aggregates (eq. 3 ) might well be considerable in this concentration range Kz
2BH+.OAc-
(BH+.OAc-)* Kll
nBH+.OAc-
(BH+.OAc-),
(3)
The available data for acetic acid solution^^^^ show t h a t this phenomenon is highly specific, but are not sufficiently extensive to permit quantitative predictions of association constants. We therefore decided to study ion-pair association directly for the solutes of interest in the present work. Ion-Pair Association from Freezing Points-In Fig. 1, values of the freezing point lowering, ATf, of acetic acid are plotted vs. the formal solute molality, mf, for the “normal” solutes naphthalene and benzoic acid. The points define a single line. Up to mf = 0.3, AT1 is proportional to mf, the slope being 3.69. A t higher concentrations the plot shows slight negative curvature. On the basis of the heat of fusionga and freezing point of pure acetic acid, the thermodynamically predicted molal cryoscopic constant is 3.58. Assuming that naphthalene and benzoic acid are normal, unassociated solutes, we have used a largescale plot of Fig. 1 to derive actual solute concentrations, Zmi, in solutions of electrolytes in acetic acid. The results are listed in Table 11. I t is seen that ion association is quite insignificant for CH3NHa+OAcand imidazole (largely ionized into C ~ H ~ N +OAc-), ZH barely significant for (CHB)~N+OAC-, but quite con(8) P. Walden, %. p h r s i k . Chem., A94,310 (1920). (9) ( a ) C. S. Parks and K . K . Kelley, J . A m . Chem. Soc., 4 1 , 2092 ( 1 9 2 5 ) : ( b ) E. h‘. Lassettre, Chem. R e v . , 20, 281 ( 1 9 3 7 ) .
+ +
K Qor K (m-1)
0.0
0.6
0.0 2.7
1.7
40 15 10 4 2.0 1.1 ’mf
=
Ref. 7 ; mole/l.
siderable for CH3NH3+ClP. Values of ATf for mixtures of methylammonium acetate and chloride are smaller than additive for the components, showing that there is some mixed association. The solute concentration, Zmi, is expressed as a function of the concentration, ml, of unassociated ion pairs and of association constants by eq. 4. The formal concentration, mf, is expressed similarly by eq. 5 . Dissociation to free ions has been neglected. &ai
mf
+ Kzm12 + . . . + Knmln + . . . = ml + 2Kzm12 + . . . + nKnmln + . . . =
ml
(4) (5)
At moderate concentrations the most important association product is the double ion pair. If we therefore use approximate values for the higher association constants as shown in eq. 6, we obtain eq. 7 and 8 in which K z is the only
- Kzml)
(7)
ml/(l - K ~ I ) ~
(8)
Zlmi = ml/(l
mf
=
Treatment of our data on the basis of eq. 7 and 8 gives adequate fit. Resulting values of K Zare listed in Table 11. Mixed association of methylammonium acetate and chloride was treated as follows. Because of the low tendency of the acetate toward self -association, we assumed that the only mixed association equilibria of importance are of the type shown in eq. 9. BH+OAc-
+ (BH+CI-),
K
BH+.OAc-.(BH’Cl-),
(9)
We further assumed that the data can be represented with a single association constant, K , regardless of n. The average value of K calculated from the data for the mixtures on this basis is given in Table 11. Although
Aug. 5 , 1964
PROTON EXCHANGE OF AMINESIN ACETICACID
the fit of the data is adequate, the accuracy of K is low. Table I1 also lists some additional values of K z , calculated by us from the data of Walden,8 and some values of K as reported by Kolthoff and Bruckenstein.' I t is seen t h a t the association constants cover a wide range. Judging by this limited sample, ion-pair association is favored by an increase in ion size, particularly of the cation. The strikingly low values of K z for certain acetate ion pairs can be explained on the basis of the following theory. Suppose that the anion in the ion pair forms a stable complex with at least one additional acetic acid molecule, and that the negative charge in the resulting solvated ion pair is dispersed by very rapid proton transfer (eq. 10). B H +.AcO-.HOAc
=
BH +.AcOH.OAC-
(10)
Then, if the rate of charge dispersal is fast compared to the dielectric relaxation time of the ion pairs, the result will be a reduction of the effective dipole moment and, hence, of the tendency toward ion-pair association. Ionized 2 : 1 complexes between acetic acid and amines are known t o be quite stable in carbon tetrachloride and chloroform. lo Furthermore, crystal structures have been determined for several acid salts of empirical formula MA.HA, where M is an alkali metal and HA a carboxylic acid. The interatomic distances deduced from X-ray diffraction indicate generally that there is a strong hydrogen bond between A- and HA, and in some of the solid compounds the A-groups in A- . HA have even been reported to be crystallographically equivalent. l 1 Kinetic salt effects observed in certain acetolysis reactions that involve carbonium ion-pair intermediates are also of interest in this connection. "Normal" salt effects of lithium and diphenylguanidinium acetate in these reactions are appreciably smaller than those of the corresponding perchlorates, indicating that the acetate ion pairs are, in effect, less polar.12*13 Kinetic Results Interpretation of N.m.r. Data.-Rates of proton exchange could be measured conveniently by means of n.m.r. data for the carboxyl protons of acetic acid and, in some cases, for the CH3- protons of methylammonium ion. Values of some relevant chemical shifts and spinspin interactions are summarized in Table 111. The carboxyl n.m.r. line was broadened significantly upon addition of methylammonium acetate, b u t not upon addition of sodium acetate or tetramethylammonium acetate. The broadening was therefore ascribed to NH-COOH proton exchange. For a given solution the broadening increased with an increase in temperature between 15 and 45'. Since the broadening was sufficiently small, it could be treated14 as "lifetime broadening," eq. 11
TABLE I11 X.M.R.CHEMICAL SHIFTS AT 60 Mc./SEC., SPIN-SPIN INTERACTIONS, A N D MEASURES OF VISCOSITY FOR SOLUTIONS OF METHYLAMMONIUM SALTSIN GLACIAL ACETICACID,25" Chemical shift of COOH us. CHa- protons of acetic acid, C.P.S. (a) (b)
CHsNHs+OAc-, 0-0.5 M CHaNHs+CI-, 0-1.2 M
highest values of A / P N n reported in this paper, eq. 1 1 becomes inaccurate b y about 2 7 0 , and corresponding corrections were made.
~ C O O H- ~ C H = ~-576.6 -
~ C O O H-
6caS = -576.6
+
22.5~ 10.66
Chemical shift of COOH- protons us. NH- protons, C.P.S. (a) (b)
CHsNHs+OAc-, 0-0.5 M C H s N H s T - , 0-1.2 M
6COOH
6COOH
-
6NH = 6NH -
-279 -270
+ 35C
-
16c' C H s N H s proton spin-spin interaction, 6.17 C.P.S. (measured in CHsNHaCI) NICH spin-spin interaction, 52 C.P.S. (measured in N H I +OAc-) Bulk viscosity (a) (b)
CHaSHa+OAc-, 0-2.2 M C H a N H a T - , 0-1.0 M
log ( ? / q o ) = 0 . 4 8 0 ~- 0 . 0 2 0 ~ ~ log (?/no) = 0.2656
TIrelaxation time of carboxyl protons; TI' (a) (b) (c)
CHsNHa+OAc-, 0-0.5 M (CHa)r+OAc-, 0-0.2 M CHsNHa'Cl-, 0-0.6 M
T' relaxation time of the (a) (b)
N'4
= 3.12 sec.
log ( T I ' / T I ) = 0 . 4 6 2 ~ log ( T i " / T J = 0 . 3 8 2 ~ fog ( T I ' / T I ) = 0.253~
nucleus in sec.
C H a N H a T - , 0-1.2 M CHaNHS+OAc-, 0.465 M
log ( l / T l ) = 2.28 1/Tl 5 400
+ 0.23~
Here A is the exchange broadening, R the rate of NH-COOH proton exchange (in g.-atom/l. sec.), and [HOAc] the moles of acetic acid per liter of solution; A was obtained from spin-echo measurements of the transverse (T,') and of the longitudinal ( T I ) relaxation times of the COOHprotons in the solutions. The value of Tz' used in eq. 11 was the directly measured value. The quantity T z was taken as TJl.14, since there was a systematic difference of 14 f 2% between T2 and T I for the carboxyl protons in a number of reference liquids. The reference liquids were pure acetic acid over a wide temperature range and dilute solutions of perchloric acid and of sodium acetate in acetic acid a t 25'. We do not know whether this small difference is real or whether it is a systematic instrumental error. A similar difference between T1 and Tz, measured on the same instrument, has been noted for waterLSabut not for methanol.15h The rate of NH-COOH exchange has been compared with the total rate of exchange of NH- protons. The latter is obtained from the n.m.r. spectrum of the CH3- protons of methylammonium acetate, which is a spin-spin quadruplet in the absence of exchange due to interaction with the NHs- protons. Under the present conditions of proton exchange this quadruplet was collapsed into a single broad line, and the rate was calculated as described previously.16 The results are listed in Table IV. The two rates are equal within experimental error and thus show that the NHTABLE IY RATEOF KH-COOH PROTON EXCHAXGE COMPARED WITH TOTAL RATEOF NH- PROTON EXCHANGE FOR METHYLAMMONIUM ACETATEIN ACETICACIDAT 25" [CHaNHa'OAc-1
(10) G. M. Barrow and E . A. Yerger, J . A m . Chem. SOL.,7 7 , 4474 (1955). (11) H. N. Shrivastava and J . C . Speakman, J . Chem. S O L . 1151 , (1961). (12) S. Winstein and E . Clippinger, J . A m . Chem. SOC.,7 8 , 2784 (1956). (13) A. H . Fainbet-g and S. Winstein, ibid , 78,2763 (1956). (14) T h e general relationship between A and R is given in ref 3 For the
2967
0.175 0.465
--Rate of proton exchange, g.-atom/l. sec.----. N H and COOH N H , total
34.6 f 1 . 0 84 f 8
34.1 f 1 . 0 78 f 2
(15) ( a ) Z Luz and S. Meiboom, J . Chem. P h y s . , S9, 366 (1963); ( b ) E Grunwald, measurements a t 2 5 O (16) E. Grunwald, A. Loewenstein, and S . Meiboom, J . Chem. P h y s . , 27, 630 (1957)
ERNESTGRUNWALD AND ELTON PRICE
2968
protons exchange a t a significant rate only with COOH- protons. Kinetic Analysis.-Kinetic results for methylammonium acetate a t 25" are summarized in Table V. In this table and throughout the following kinetic analysis we use the symbol k to denote the pseudo-first-order rate constant, k = R/c, where c is the molar concentration of the formal species, methylammonium acetate. I t is seen that k decreases slightly but significantly with increasing concentration. The theory that this decrease is due to the formation of less reactive ionpair association products must be ruled out in view of the freezing point data (Table 11). Two interpretations therefore suggest themselves: (i) The reaction is precisely first order in BH+OAc-, and the decrease of k is a medium effect; (ii) Proton exchange is significant both for the ion pairs, BH+OAc-, and for the free ions, BH+. TABLEV KINETICRESULTSFOR PROTON EXCHANGE OF METHYLAMMONIUM ACETATE IN ACETICACIDAT 25" Molar concn.
k, set.-'
0.0208 0466 ,0922 175 267 465
230 + 10 21; i 6 202 f 6 198 f 6 197 f 10 180 f 20
k q / ? o , sec.-l
176
23 5 228 224 240 265 300
+ 8,17c-'/2 233 214 206 196 192 188
According to hypothesis ii the rate law is given by eq. 12
k
=
R;/c = k'
+ k"Kd1i2c-1/z
(12)
where k' and k" are rate constants for BH+OAc- and BH +, respectively. Judging by data for structurally related acetate ion pairs,' K d = (BH+)(OAc-)/ (BH+OAc-) is about As a matter of fact, the empirical eq. 13 fits the data well, as shown in the last column of Table V. We
k
=
176
+ 8.17~-"'
(13)
doubt, however, that the formal resemblance of eq. 13 to 12 implies the corresponding mechanism. If i t did, we would infer from the coefficient of c - ' l z in eq. 13 that k" = 8 . 1 7 K d - 1 / 2 = 8000 sec.-l. This value seems implausibly high compared to the value 0.9 set.-' of the first-order rate constant for proton exchange of methylammonium ion with water.17a We regard the value as implausible because acetic acid is much less basic than water and methylammonium ion does not have unshared electron pairs.17b To obtain further evidence, we have measured the rate of N H proton exchange for 0.8 ill CH3NH3C1in acetic acid. Judging by data for model substance^,^ the lower limit to K d for CH3NH3Cl is If k" were indeed bOO0 set.-', the lower limit to R would therefore be 2.3 g.-atoms/l. sec. The actual rate is just below the threshold of easy measurability by the n.m.r. method. However, the experimental u p p e r limit to the rate of NH proton exchange is I .O g.-atom,'l. sec. Furthermore, a rate of the order of 0.1 to 0.3 g.-atom/l. sec. is to be expected under these conditions due to CH3NH3+OAc(17) (a) E. Grunwald, P. J . Karabatsos, R. A. Kromhout, and E. L. Purlee. J . Chem. P h y s . . 3 3 , 5 5 6 (1900); (b) A . I. Brodskii, Z h Obshch. K h i m . ,
ar, 413
(19.~).
Vol. 86
ion pairs produced by acetolysis.ls It seems safe BH+C1- -I- HOAc
=
HCI
+ BH+OAc-
(14)
to conclude that hypothesis ii is inconsistent with the facts. Assuming, therefore, that the NH-COOH proton exchange rate is precisely first order in the ion pair CH3NHa+OAc-, we regard the two-step kinetic scheme, eq. 15 and 16, as the most plausible representation of the reaction mechanism.'S' ki
BH +.OAcAcOH*
+
Jr B.HOAc kz
(15)
kH
B,HOAC+.4cOH*.B
+ HOAc
(16)
The reaction rate is then given by eq. 17. If k~
R
=
kl[BH+.OAc-]
kH ~
k2 f
kH
(17)
>> kz, the observed rate constant k is equal to kl. If k2 >> k H , k = k l k ~ / k z = kH/& where K i is the ionization constant (see eq. 1). We believe the second inequality to be correct but shall postpone discussion to the next paper. Dependence on Viscosity-In this section we shall suggest that a theory in which k = k H / K i could be correct by showing that the decrease in k parallels that of the viscosity, v / q o , up to moderate concentrat i o n ~ . ' ~Furthermore, ~ we shall show that the ionpair aggregates, BH+OAc-. (BH+Cl-),, are apparently unreactive. We have obtained three separate measures of the viscosity: (i) 7, the macroscopic viscosity of the solution; (ii) TI,the longitudinal relaxation time of the carboxyl protons, a rather complex measure of the microscopic viscosity opposing the tumbling and diffusion of the acetic acid molecules in their various microscopic environments ; and (iii) T', the longitudinal relaxation time of the NI4 nucleus. l / T 1 is a rather good index of the microscopic viscosity opposing the tumbling of the molecular species containing the N14 nucleus.2n In the concentration range of interest, plots of log ( v / ~ ~log ) , (Tlo/Tl),or log ( l / T 1 ) v s . c are linear, and the empirical slopes are listed in Table 111. For both CH3NH3C1 and C H ~ N H ~ O A the C , slope obtained for the concentration dependence of log (71'70) is very nearly equal to that obtained for the logarithm of the microscopic viscosityz1 as measured either by 1)'Z-l or by l/T1. We therefore believe that the bulk viscosity is also a fairly good index of the kind of microor IO-' on (18) T h e equilibrium constant for eq. 14 is of the order of the basis of data in ref. 4 and 7. (19) (a) Bimolecular reaction between free B H + and free OAc- ion is kinetically indistinguishable from a first-order reaction of t h e ion pair. However, it is necessary t o make a distinction between t h e two processes only if the transition state for t h e reaction cannot be reached directly from the ion pairs but must be reached by way of t h e free ions. This is evidently not the case here, since in the ion pairs t h e functional groups COz- and H N C are already connected by a hydrogen bond. Furthermore, we can show t h a t the assumption t h a t t h e transition state can be reached only from the free ions leads t o a n improbably high value for the rate constant of the reverse HOAc + B H + OAc-. (b) See, for example, M . T . Emerreaction, B son, E. Grunwald, bl L. Kaplan, and R. A . Kromhout, J . A m . Chem. Soc., Ea, 6307 (1960). (20) W. B. Moniz and H. S. Gutowsky, J . Chem. P h y s . , 38, 1155 (1963). (21) T h e similarity is not so good for t h e temperature dependence of q and of TI for pure acetic acid. Between 15 and 45'
+
+
log
(poise) = 568/T
- 3.858
-log T , (sec.) = 4 1 7 j T - 1.896
PROTON EXCHANGE OF AMINESIN ACETICACID
Aug. 5 , 1964
scopic viscosity opposing the replacement of one acetic acid molecule by another in the solvation shell of B as shown in eq. 16. Values of kq/qO for methylammonium acetate are listed in column 3 of Table V. I t is seen that the factor q 'qo compensates quite well for the decreasing trend in k , up to c 0.2 M. At higher concentrations, values of k q , qo seem to increase. Preliminary results indicate that this increase might be due t o an additional reaction of higher than first order in methylammonium acetate. For example, a t c = 5 .lfj the NH- and COOH- proton resonance is collapsed into a single sharp line with Tz' = Tz, and k > 1 x 105sec.-l a t 25,' Kinetic data for mixtures of electrolytes are given in Table VI. Addition of (CH3)4N"OAc- decreases the value observed for k , but kv/qo is again quite constant, being independent of the concentration of added salt. I t will be recalled that, on the basis of the freezing point data, (CH3)&+OAc- does not have a strong tendency to form ion-pair aggregates.
-
TABLE VI SALTEFFECTS OK PROTON EXCHAXGE RATESFOR METHYLAMMOSIUM .kCETATE I S ACETIC ACID AT 25' ----Concentration of-[BH+OAc-I [Added salt]
1. .idded salt 0.0963 0963 0963 0963 267 ,267 267 267
....
0.0328 ,0721 1377 . . .
0,0372 ,0881 ,163
2. Added salt 0.0544 0.0934 0934 1250 274 0934 ,63 ,175 a Calculated from log q / q o slopes a l , a2 from Table 111. * Calculation of 01 ( = fraction B H +Cl-) 01
=
kdvo, sec. - l a
k, sec.-l
(CHI)~?YT+O-~C207 230 204 234 188 223 179 225 197 265 191 265 185 269 177 274
a-'kq;'qa,
sec.-lb
=
. . . . . .
. . . . .
. . . . . .
.
,
.
.
= CH3KH3'CI195 223 239 168 201 232 123 165 213 76 136 205 = alcl U Z C Z , Values of the a = 0.382 for (CH3)4SCOAc-. of BH'OAc- not complexed to
+
(1 + 1 1,7m' 2.7ml
>-'
where ml = molal concentration of uncomplexed BH+Cl-, 1.7 = K , 2.7 = K Z(Table 11). Calculate rnl by successive approximations from: ml(1 4- 1.7am,~~o.4,. f o r m a l ) = ?nBHCl. f o r m dl 2 . 7rn1)%.
Addition of CH3NH3C1 causes a marked reduction in k , which is only partially compensated by the factor q: vo. Since methylammonium chloride has been shown to form complexes with methylammonium acetate, with the assumed formula BH +OAc-.(BH+Cl-)n, we attempted to account for the additional decrease in k on the basis that the mixed complexes are completely unreactive. Accordingly, the fraction, e , of uncomplexed BH+OAc- was calculated ,for each solution, using the association constants in Table 11. As shown by the last column in Table VI, the values of kql avoare indeed quite constant. Activation Parameters.-For 0.09 M methylammonium acetate, k was measured a t 15, 25, 35, and 45'. The plot of log ( k , ' T )v s . T-' was nicely linear, T being the absolute temperature. Values of the activation
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parameters, calculated according to the transition state theory, are: AH* = 18.41 kcal., A S * = 14.0 e.u. Experimental Materials.-Glacial acetic acid (Merck) was dried and purified in a n all-glass apparatus by refluxing for 12 hr. over chromium trioxide ( 2 g./1000 ml.) and acetic anhydride, followed by distillation.z' The acetic anhydride was just sufficient t o react with the water in the unpurified reagent. The first fraction of 20yo ) used as solvent to was rejected, and the next fraction ( 2 0 q G was prepare solutions. The water content of the acid was determined by titration with Karl Fischer reagent in the presence of excess nethanol ( 5 : The methanol was titrated first; then acetic acid was added and the mixture titrated. Acetic acid, taken directly from the bottle, was usually between 0.03 and 0.04 M in water. However, after purification, 1 drop of Karl Fischer reagent was sufficient to produce an end point (H?O < 0.005 M). Reagent grade methylamine hydrochloride was recrystallized twice from pure ethanol and dried in zacuo a t 250 Methylamine was obtained from Matheson and Co. in the form of a compressed gas. Tetramethylammonium acetate was preparedz4by neutralizing a solution of the hydroxide with acetic acid. Isolation of dry solid product was difficult, however, because of the great hygroscopicity of this substance. ilfter evaporation of the solution on a steam bath, the product was dried for 2 weeks over magnesium perchlorate at a pressure of 0.01 mm., a t which time it still had not reached constant weight. The material was then dried in 37 hr. to constant weight in 3n Abderhalden pistol at 80" over phosphorus pentoxide a t pressures below 0.01 mm. : equivalent weight, determined by acid-base titration in glacial acetic acid: obsd. 140 i 14, calcd. 133. Solutions Preparation.-A stock solution of 3 M methylammonium acetate in glacial acetic acid was prepared by bubbling methylamine into purified acetic acid in a special all-glass apparatus designed t o protect the solution from atmospheric water. Subsequent solutions of the desired concentration were prepared from this stock solution by dilution. The solutions were then standardized by titration with 0.5 NHCIOa in acetic acid, using bromophenol blue indicator.25 Mixtures of methylammonium acetate and methylammonium chloride of the desired concentrations were prepared by adding the required volume of the acetate of known concentration to a weighed quantity of the hydrochloride. In the same manner, solutions of methylammonium acetate and tetramethylammonium acetate were prepared, but tetramethylammonium acetate was dried in vacuo until a constant weight (within 0.2 mg.) was obtained. The total acetate concentration of the final solutions was checked by titration with 0.5 S HC104 in glacial acetic acid. All experiments were done with air-saturated solutions. Freezing Point Determinations.-Freezing points were determined in an apparatus of the Beckmann type. The thermometer was graduated in 0.1" intervals and could be read to 0.02'. The freezing point of each solution and of pure acetic acid was determined from a temperature a's. time plot.26 The molal concentration, m , of each solution was corrected for the fraction,f, of acetic acid that had solidified (eq. 18, 19).
f
=
AT.Cp'Lf
=
0.0lATfor HOAc
mcor = muneor/(l - f)
(18) (19)
In eq. 18, AT is the amount of supercooling (in " C . ) of theliquid prior t o freezing, C, is the molar heat capacity of liquid acetic acid, and Lf is the molar heat of fusion. Values of A T were usually less than 1 '. The freezing point of pure acetic acid was found to be 16.56' (reportedg 16.6"). Viscosities.-The viscosities of solutions of methylammonium acetate and methylammonium chloride relative to t h a t of pure acetic acid were determined in the standard way from densities and flow times, using an Ostwald modification of the Poiseuille (22) K . J. P. Orton and A. E . Bradfield, J . Chem. SOL.,983 (1927) (23) A. H Fainberg and S. Winstein, J. A m . Chetn. SOL, 78, 2776 (1956) (24) W. E . Thompson and C . A. Kraus, i b i d . , 69, 1016 11947). ( 2 5 ) S . Winstein, E Grunwald, and L. L. Ingraham, ibid, 70, 827 (1948) (26) A. R Glasgow, Jr., A J Streiff, and F. D . Rossini, J Res S o l i Bur. Std , 36, 8 5 5 (1945).
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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
