1552
F. A. Kundell, D. J. Robinson, and W . J. Svirbely
Kinetics of Twelve-Step Competitive-Consecutive Second-Order Reactions. The Alkaline Hydrolysis of Triethyl Citrate F. A. Kundell,' D. J. Robinson,' and W. J. Svirbely" Chemrstry Department, University of Maryland, College Park, Maryland 20742 (Received January 7 7, 7973)
-
The kinetic process for a twelve-step competitive-consecutive second-order reaction involving an unsymmetrical trifunctional molecule, B, reacting with a common reagent, A, can be written as A B C P, A +B-D P, A + B- E + P, A C + F + P, A + C- G + P, A + D-F P, A D-H P,A EG P, A E H P, A F I + P, A + G I P, A + H I P having the rate constants kl, hz, . . .,hlz, respectively. The rate equations have been solved in terms of the variable A, where X = JotA dt. The solution is of the form p = 2,=17G,e - StX where p = ( A - Ao)/Bo + 3 and G, and the S, are constants involving various combinations of the twelve rate constants. If the trifunctional compound has a reaction plane of symmetry, as is the case for triethyl citrate, some of the reaction steps are indistinguishable from others. As a result, the twelve-step case can be treated mathematically as a seven-step case and it becomes a problem of determining seven parameters only. A least-squares solution can be used to calculate these seven rate constants. This procedure was used to determine the k values for the alkaline hydrolysis of triethyl citrate in dioxane-water mixtures of varying composition at 15".
-
+ +
+
+
+
-
-+
+
Introduction The last paper in the series concerned with the kinetics of hydrolysis of multifunctional compounds dealt with the alkaline hydrolysis of diethyl malate, an unsymmetrical difunctional compound.2 In this paper, we shall report on the alkaline hydrolysis of triethyl citrate, an unsymmetrical trifunctional compound. Triethyl citrate may be represented by the formula
OH
0
II
C&OC -CHz-
I C-CHZI
+
The Journal of Physical Chemistry, Vol. 77, No. 12, 1973
(1)
+
+ +
(2)
XT + alcohol
(3)
(4)
x+
OH-
+
xx+
OH-
t alcohol
(5)
+
(6)
X
X
+
alcohol
+ OH- -% x ' M xx + 013- -% xM x x + OH- -% xm x + OH- Ax-+ x + OH-
C -OCZH,
Mathematical Analysis The alkaline hydrolysis of an unsymmetrical trifunctional compound can be represented schematically by the following twelve-step process.
x xx
x'Ix
Xm x
II
Tx + alcohol
m x x + OH- 4 k xm x R + OH- A
+
-- -
0
It is apparent that, as a result of a reaction plane of symmetry passing through the central carbon atom in the formula, the reactions of the two terminal ester groups with a common reactant will be indistinguishable from one another. Thus, the saponification of triethyl citrate will be a special case of the more general one involving a n unsymmetrical molecule which does not have a reaction plane of symmetry. One expects, therefore, seven different reaction steps only for this special case rather than the twelve steps which normally would exist for the saponification of an unsymmetrical triester. A study of the alkaline hydrolysis of triethyl citrate was made in various dioxane-water media at 15" in order to (a) demonstrate the validity of the apparent seven-step kinetic process for this reaction, (b) relate each of the final twelve rate constants to a mechanistic rationalization of the reaction, and (c) extend computer techniques for handling the calculations for shch a complex system.
1, OH[- "
+
T
O=C-OCzHS
I-l-7
-+
+
+ OH- -% + OH- -k
alcohol
alcohol
+ alcohol + alcohol alcohol
+ alcohol + alcohol + alcohol
(7) (8) (9)
(10) (11)
(12)
If one uses the definitions A = LOH] = t h e c o n c e n t r a t i o n of b a s e
B
=
I-[x
- the c o n c e n t r a t i o n of t h e t r i e s t e r -
.=[m xx]- t h e concentration of t h e first diester ion
t h e concentration of t h e second diester ion
(1) Abstracted in part from the Ph.D. Theses of F. A. K. and D. J. R. (2) W. J. Svirbely and F. A. Kundell, J. Amer. Chem. Soc., 89, 5354 (1967).
Alkaline Hydrolysis of Triethyl Citrate
1553
E = [ x- =X I t h e concentration of t h e third diester ion
F = [I = x] t h e concentration of t h e first monoester diion
[ T I
G =
=
t h e concentration of t h e second monoester diion
"[X
-
=
I
t h e concentration of t h e third monoester diion
I =
1-
= t h e concentration of t h e triion
then the reactions to be considered are A + B k ' - C + P
(la)
A + B k 2 - D + P A + B k 3 - E + P
(3a)
A + C L F + P
(4a)
A + C k S - G + P
(5a)
A + D k " - F + P
(6a)
A + D k ' - H + P
(7a)
k
A + E A G + P
(sa)
A + E L H + P
(9a)
k
A + F A I + P A + G A I + P
+
+
H *I A If one defines2 a variable X as
P
(1la)
=
+
2LS,
+
(12a)
(S3 k2 - 81)
X = J t A dt
(13)
1.
- SI> (S,kz- Si) + (S,k3 - S,)
k,
(loa)
k
[
(S5
I+
k7 k6 S1) + (S,- SI)
0
then the rate equations in terms of X become
+ k3)B + (h4 + k,)C + + ( k , + kg)E + k1oF +
-dA/dA = ( k , + k , (k6 + k,)D
-dB/dA = ( k , -dC/dA = ( k 4
kllG + k12H (14) k , + k3)B (15)
+ + k5)C + k,)D + kg)E -
k,B k2B -dD/dA = (k6 -dE/dA = ( k , k3B -dF/dA = k i o F - k4C - k6D
(16) (17) (18) (19)
-dG/dA = k , , G - k , C - k 8 E (20) -dH/dA = kl,H - k,D - k , E (21) Equations 14-21 can be integrated. The boundary conditions are X = C = D = E = F = G = H = I = O , A = A o , B = Bo, at t = 0. The results after integration are given by
A
= A0
+ 3(B - Bo) + 2C + 2 0 + 2E
+F +G +H
(22) The Journal of Physical Chemistry, Vol. 77, No. 12, 1973
F. A. Kundell, D. J. Robinson, and W. J. Svirbely
1554
As stated in the introduction, triethyl citrate has a reaction plane of symmetry. Schematically, the triester may be represented by the symbol
Y
rn
x
x
x
It is apparent that because of the reaction plane of symmetry, the reactions of the terminal ester groups with a common reagent would be mathematically indistinguishable from each other. The same situation would exist in several of the succeeding steps. In terms of the symbolism used in eq 1-12 this is tantamount to saying that if k3, k7, k8, ks, and k12 are set equal to zero, then the twelve-step case can be treated mathematically as a seven-step mechanism. Then, after these seven constants k ( i ) have been determined from the data, the rate constants for the twelve-step mechanism can easily be calculated in accordance with the following definitions: k l = k3 = k(1)/2; k2 = k(2); k4 = k s = k(4)/2; k5 = k 8 = k(5j/2; k 6 = k7 = k(6)/2; klo = kl2 = k(10)/2; k11 = k(l1). The procedure for evaluating the constants k ( l ) , k ( 2 ) , k(4), k(5), k ( 6 ) , k(lO), and k(11) through the direct use of eq 30 is in principle the same as the one which has already been described.2 In practice, however, complications arise. Materials and Apparatus Triethyl Citrate. Research grade triethyl citrate was purchased from Aldrich Chemical Co. The ester was vaeuum distilled several times, the center cut being saved. The saponification equivalent indicated a purity of 100 0.1%. A chromatographic analysis yielded one maximum only. Information on an infrared analysis indicated that no impurities were p r e ~ e n tn20D . ~ was 1.4426. Other Details. The apparatus, procedure, and other pertinent factors have already been described.2 Starting concentrations of the triester and of the sodium hydroxide were adjusted so that equivalent amounts were used (i.e., A0 = 3B0, where A0 and Bo are the concentrations in moles per liter of hydroxide and triester, respectively). This restriction is not a necessity but merely a convenience. Triplicate runs were made under identical conditions and the data were pooled for calculation purposes. A partial saponification of triethyl citrate was carried out. The product was a very viscous, syrupy liquid. At low temperatures it formed a clear glassy solid. From this product a solid which was insoluble in N,N-dimethylformamide was recrystallized. Following saponification equivalent determination, it was concluded that the product recovered was disodium ethyl citrate, a monoester. The rate of hydrolysis of this solid was determined at 15” in 30 wt % dioxane-water. The rate constant was 0.0195 M-1 min-1. We will comment on this data later.
*
Data, Calculations, and Discussion Computing Program. A program4 for the solution of competitive-consecutive second-order rate equations using a least-squares procedure was developed. The cases considered were one-step through three-step reactions involving both symmetrical and unsymmetrical molecules and a four-step reaction involving a symmetrical molecule. The coding for the system has been done in a “neutral” FGrtran IV. Evaluation of Rate Constants. In the least-squares fitting procedure one starts with estimated values for the The Journal of Physical Chemistry, Vol. 77, No. 12, 7973
seven rate constants to be determined. Equation 30 is then expanded around these initial guesses by a Taylor’s expansion. However, when so many parameters are involved the success of the convergence of the k ( i ) values to their true values using the iterative method depends on a good choice for these estimates. One avenue of approach is to utilize a routine in the computer program called SIMPLEX. This is a leastsquares trial and error procedure for generating a set of the desired number of rate constants which are consistent with the kinetic data. While this proved successful in cases where four or less constants were involved, it was not successful in generating seuen rate constants which could be used as estimates which would later lead to convergence and reproduction of the data. Our estimated value for k ( l ) , which is quite large, did, however, come from this approach. Another possibility is to attempt to calculate the rate constants utilizing structure factors for the various compounds. Considerable effort has been expended in the past to generalize existing data and to predict the reaction rates of similar compounds for which no data exists.5 Among the most successful of these has been the Hammett equation which was used to predict rate constants for meta- and para-substituted benzene derivatives. Hammett’s equation was extended by Taft to include aliphatic compounds. Taft also attempted to account for differences in steric hindrance by introduction of a steric factor. Hancock modified Taft’s equation by separation of the Taft steric factor into steric and hyperconjugative contributions. Hancock’s equation is log h / k , = 5 * p * 6E,C h ( n - 3) (39) where u* is a substituent constant specific for the substituent regardless of the reaction under consideration and p* is a reaction coefficient and is dependent upon the type of reaction and the reaction conditions; the product of these two describes the polar or inductive contribution. 6 and h are steric and hyperconjugative factors, respectively, which are reaction dependent, EsC is a corrected steric factor which is substituent dependent, n is the number of hydrogen atoms on the carbon a to the reaction site, and k / k o is the ratio of rate constants for the compound containing a particular substituent and a reference compound, which in our case was ethyl acetate. On referring to Table I, one can see that within the structural formula for triethyl citrate one can locate the substituents analogous to diethyl glutarate, diethyl 3-hydroxyglutarate, diethyl succinate, and diethyl malate. From recent studies made in our laboratory6 on these and other compounds and from data in the literature2,7-8we were able to obtain values for the u*, p * , E,“, 6, and h factors for the substituents on the various species involved in the different reacting steps of the citrate reaction. This permitted us to cal-
+
+
(3) Private communication from the supplier, “A very careful infrared analysis indicates no impurities present.” (4) F. A. Kundell, W. J. Svirbely, and J, M. Stewart, Technical Report No. 68-69, Kinetics 68, Computer Science Center, University of Maryland. (5) (a) L. P. Hamrnett, Chem. Rev., 17, 125 (1935); (b) R. W. Taft, Jr., M. S. Newman, and F. H. Verhoek, J . Amer. Chem. Soc., 72, 4511 (1950); R. W. Taft, Jr., ibid., 74, 3120 (1952); (c) C. K. Hancock, E. A. Meyers, and B. J. Yager, ibid., 83, 4211 (1961). (6) Kinetic studies on the alkaline hydrolysis of ethyl acetate, ethyl propionate, ethyl valerate, ethyl hexanoate, diethyl 3-hydroxyglutarater diethyl glutarate, diethyl 2-methIyglutarate, diethyl 3-methylglutarate, and diethyi 3,3-dirnethylglutarate will be the subject of another paper. ( 7 ) W. J. Svirbelyand A. D. Kuchta,J. Phys. Chem., 65, 1333 (1961). (8) E. Tommila, A. Koivisto, J. P, Lyyra, and S. Heimo, Ann. Acad. Sci. Fenn., Ser. A2, 47 (1952).
1555
Alkaline Hydrolysis of Triethyl Citrate TABLE I: Structural Formulas for Triethyl Citrate and Esters which Can Be Considered as Its Substituents OH
I I
H,C,OOCCH&CH,COOC,NS
Triethyl citrate
COOC2HS H,C,OOCCH,CH,CH,COOC,H, OH
I
H,C200CCH2CHCH2COOC2HS CH,CHpCOOCpH,
I
Diethyl glutarate
Diethyl 3-hydroxyglutarate Diethyl succinate
COOC,H,
TABLE II: Estimates and Least-Squares Values Rate Constant
Estimates
Least-squares values
k(1) k(2) k(4) k(5) k(6) k(10) k(lf)
53.18 8.49 1.11 1.25 12.6 0.018 0.02
49.6 f 1.2 2.92 f 1.1 0.49 f 0.19 1.1 f 0.17 7.4 & 1.4 0.14 0.15 0.011 f 0.006
*
TABLE Ill: Dataa Obtained at 15.07' in 30 wt%
OH
Dioxane-Water Mixtureb
I
YHCH2COOC2H,
Diethyl malate
600C2Hc
I
I
0.000 1 .oa
2.00 3.00 4.01
5.00
OH -00CCH2-C-CH2COOCzH5
a (calcd)
Time, min
culate an approximate value of a rate constant through the use of Hancock's equation. That number then became our estimate for that particular step which would be used in the iterative procedure of our computing program. For example, consider the hydrolysis step
+ OH-
-%
COOCZHS OH
The polar substituent contribution is the summation of the contributions of the carboxylate ion in the glutarate position, -0.208, the ester substituent in the succinate position, 0,199, and the hydroxyl group one methylene group removed from the reaction site, 0.198. u* therefore is the sum of these, or 0.189. EsC was originally estimated from the value for the reaction involving a terminal ester group and an assumption that the steric contributions of the various substituents are additive. The original estimate was revised by an iterative procedure and for the above step calculated as -1.91. The values of p* = 2.22, 6 = 0.567, and h = +0.012 were obtained using regression analysis on the data from the hydrolysis of other esters in this same solvent system a t the same temperaure. There are two hydrogen atoms on the carbon a to the reacting carbonyl carbon of the ester described by eq 5 . Therefore n - 3 = -1. Making these substitutions in the Hancock equation, together with the value of log (ethyl acetate is the reference compound), one calculates k5 = 0.625 in 30% dioxane at 15,07". The same procedure , ke, and klo. The SIMPLEX was used to obtain k ~ kq, routine gave k l = 26.59 and k l l had been determined in this research. However, k(1) = 2k1, k ( 2 ) = kz, k ( 4 ) = 2ka, k ( 5 ) = 2k5, k ( 6 ) = 2k6, k(10) = 2k10, and k.(11) = k l l . The values of the k(i)'s obtained by this procedure were used as initial guesses in the least-squares program and are listed in the second column of Table II. A typical set of time-concentration data is shown in the first two columns of Table 111. Using this data and the estimates given in Table 11, the values of the rate constants were determined by the least-squares procedure. These are listed in the third column of Table 11. The values of a
6.00 7.00
8.00 9.00 11 .oo 13.00 15.00 17.00 19.00 21 .oo 23.00
30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 140.00 150.00 180 200 210
1 .oooo 0.8409 0.7787 0.7281 0.7008 0.6788 0.6632 0.6528 0.6463 0.641 1 0.6294 0.6204 0.61 26 0.6035 0.5970 0.5905 0.5840 0.5633 0.5412 0.5243 0.5075 0.4906 0.4750 0.4634 0.4516 0.4426 0.4335 0.4180 0.41 15 0.3946 0.3855
0.3803
1.000 0.8426 0.7731 0.7270 0.6974 0.6779 0.6634 0.6534 0.6453 0.6386 0.6279 0.6192 0.61 15 0.6045 0.5979 0.5917 0.5857 0.5665 0.5428 0.5224 0.5045 0.4891 0.4754 0.4632 0.4522 0.4424 0.4335 0.4181 0.41 14 0.3946 0.3855 0.3814
% deviation
0.00 -0.21 0.72 0.15 0.48 0.13 -0.10 -0.10 0.16 0.40 0.24
0.20 0.18 -0.16 -0.15 -0.19 -0.29 -0.57 -0.30 0.35 0.56 0.31
-0.07 0.05 -0.11 0.05
0.00 -0.02 -0.02 0:000 0.000
- 0.30
a Only about half of the experimental data for this run are shown. 54.74; A0 = 0.01214 M ; Bo = 1/3 Aot. QME of fit is 0.70%.
D =:
(calcd) in column three of Table I11 were obtained through use of eq 30 and 31 using the final values of the k's. The fourth column in Table 111 represents the deviation between (Y (expt) and (Y (calcd) and is thus a measure of the reproducibility of the experimental data. The agreement is excellent and the random plus and minus deviations lend credibility to this procedure as a solution for the triethyl citrate problem. The program allows for the calculation of the intermediate concentrations of each of the reacting species at each of the recorded times. Figure 1 shows a plot of the intermediate concentrations. One observation from examining this graph is that Pinnows was correct in his state( 9 ) J. Pinnow, Z. Elektrochem.. 24, 21 (1918).
The Journal of Physical Chemistry, Vol. 77, No. 12, 1975
1556
F. A. Kundell, D. J. Robinson, and W. J. Svirbely
TABLE IV: Summary of the k(i) Values at 15.07" in Various Dioxane-Water Mixtures Dioxane, wt % 20.0
30.0
70.0
80.0
36.25
18.71
11.27
37.2 6.4 0.90 0.62 8.2 0.022 0.0058
36.7 3.9 3.0 4.2 3.8 0.11 0.093 0.83
46.4 5.1 20 5.4 1.5 2.1 0.24 1.8
50.0
Dielectric constant 63.97 k(1)
57.4
k(2) k(4) k(5)
1.54 0.78 1.12 56.2 0.030 0.007 0.63
k (6) k(10) k(11) YOQME of fit
54.74 49.6 f 1.2 2.92 f 1.1 0.49 k 0.19 1.1 f 0.17 7.4 f 1.4 0.14 k 0.15 0.011 f 0.006 0.70
0.50
TABLE V: Test for Uniqueness of the k Values in the 30% Dioxane- Water System
41
Rate constant
Accepted value
k(l) k(2) k(4) k(5) k(6) k(10) k(11)
49.6 2.92 0.49 1.1 7.4 0.14 0.01 1
QME
0.70
Trial value 40 3
New value
50.6
0.05
2.28 0.47 1.06 7.85 0.038
0.01
0.0051
0.5 1.o 2.0
%
difference 2 22 4 4 6 17 54
0.50
TABLE VI: Summary of Rate Constantsa at 15.07' in Various Dioxane- Water Mixtures Dielectric constant 63.97
54.74
36.25
18.71
11.27
Dioxane, wt YO Figure 1. Plot of intermediate species vs. time (min).
concentrations of the reacting
ment that the first step of the alkaline hydrolysis of triethyl citrate involves one of the side groups and that the reaction essentially proceeds to completion before the next step begins. Another observation is that species F and G are present in reasonably large quantities and this mixture is most probably what we isolated in our partial saponification of triethyl citrate and it was on this mixture of isomers of disodium ethyl citrate that we ran our hydrolysis measurements to determine a rate constant. We used existing data2 and a computer program for regression analysis to calculate the three Hancock reaction parameters p * , 6, and h for three additional solvent systems, 20, 50, and 70% dioxane. Using these values, the substituent parameters F* and E s C which had previously been determined and values of log ko determined from the work of Tommilas we then calculated, with aid of the Hancock equation, trial values for the k's for each of the three new solvent compositions. Using these trial k's the calculations quite quickly converged to the values shown in columns 2 , 4 , and 5 of Table IV. Extrapolation of plots of log k us. 1OO/D then permitted us to extend all of our data to the 80% dioxane solvent system. Reaction parameters were calculated and trial k's were calculated and after some 120 iterations the calculations converged to the values listed in the sixth column of Table IV. The Journaiof PhysicalChernistry, Voi. 77, No. 12, 1973
a
20.0
30.0
50.0
70.0
80.0
28.7 1.54 28.7 0.39 0.56 28.1 28.1 0.56 0.39 0.015 0.007 0.015
24.8 2.92 24.8 0.25
18.6 6.4 18.6 0.45 0.31 4.1 4.1 0.31 0.45 0.01 1 0.006 0.01 1
18.4 3.9 18.4 1.5 2.1 1.9 1.9 2.1 1.5
23.2 5.1 23.2
0.55 3.70 3.70
0.55 0.25 0.07 0.01 1 0.07
0.055 0.093
0.055
10.0 2.7 0.75 0.75 2.7 10.0 1.05 0.24 1.05
In units of I. mol-' min-'.
Reference to the fifth column of Table IV shows that in 70% dioxane the magnitudes of k ( 2 ) , k(4), k ( 5 ) , and k ( 6 ) are all nearly the same. Similarly the values for k(10) and k(11) are also very similar. These conditions tend to cause singularities in the matrices involved in the least-squares calculations. Original difficulties in getting convergence in the calculations for this solvent system are now explainable. It was desirable to see if the seven constants calculated for a triethyl citrate run are unique, or if some other set might be found which would fit the experimental data equally well. We had set as criteria of acceptability of rate constants the following conditions.
Solvent Isotope Effects on pKa of Anilinium Ions
(1) The quadratic mean error (QME) of fit. This was set to be less than 1% and we have succeeded in most cases in obtaining it. (2) The experimental data must be reproducible with only small scale and random plus and minus variations between the values for the experimental concentration and the calculated concentration obtained a t each of the experimental times. The uniqueness of a particular set of rate constants was checked in the following way. For the 30% dioxane-water solvent system, we changed the time-a input data for 25 of the 54 data points in a roughly Gaussian distribution about 3.5 times the standard deviations for these points to see what would be the effect of these changes on the rate constants. We used trial k(i)’s which were quite far from those we believed to be the true values (but still within what we believed to be the convergence sphere). The new set of rate constants obtained is shown in Table V along with the “estimates” and with the “accepted values” listed in Table IV for ease of comparison. It can be seen from Table V that while the value for k(1), k(4), and k ( 5 ) remained essentially unchanged, the values of the other rate constants were changed from 6% to as much as 54% of their original values. The QME of fit was improved. These “new” values are therefore no less reliable from the standpoint of our criteria than are the accepted values. However, the overall picture of the kinetic steps in terms of magnitude of the rate constants is essentially the same. We therefore believe that our results are unique and represent a true picture. There is an option in the computer program which allows for grouping one or more rate constants together and refining by the iterative process successively on the members of these groups in turn, instead of allowing all of the rate constants to be varied simultaneously during each iteration. This process is slower, but it avoids the possibility of missing the minimum in the least-squares fit and
1557
very often aids in convergence, particularly if singularities in the matrices could occur. Group refinement was used in all of the triethyl citrate calculations. The members of the groups were changed from run to run and between cycles to avoid any bias in the r e s u l k Table VI is the final summary of our rate constants in terms of the twelve steps postulated for the reaction. The effect of solvent variation on each step is very apparent. However, an analysis of the solvent effect is not easy to evaluate. We believe that in addition to polar and ionic effects which have been commonly observed, both steric and hyperconjugation effects make themselves more felt as the dioxane concentration increases. Steps leading to the rate constants k2, k d , kg, and k11 have reactant species in which there are no hydrogen atoms on the carbon CY to the carbonyl carbon. These steps therefore would preclude any contribution from a hydrogen bonding and consequently no hyperconjugation effects. These are also the steps when the reactant species are most highly steric hindered due to the ester group on the center carbon. It is possible that in high dioxane concentration media, the above-mentioned effects override the polar effects. In the steps leading to the rate constants kl, k3, ko, and k?, polar effects predominate and the general behacior is similar to what has been previously observed in studies involving simple molecule-ion and ion-ion reactions as a function of the dielectric constant. In the steps leading to the rate constants kg, ks, klo, and klz an inductive effect is added to the polar effect. This type of behavior we had reported previously.2 Acknowledgments. We wish to express our appreciation to the Computer Science Center of the University of Maryland and the National Aeronautics and Space Administration Grant No. NsG-398 for computer time, and to Professor James Stewart for helpful discussions relative to the computer program.
Solvent Isotope Effects on pKa of Anilinium Ions in Aqueous Sulfuric Acid J. L. Jensen” and M. P. Gardner Department of Chemistry, California State University, Long Beach, California 90840 (Received December 13, 1972) Publication costs assisted by the California State University, Long Beach Foundation
Solvent isotope effects on K , of a variety of anilinium ions are reported. As anilinium ion pKa changes from 5 to -6.5, Ka(H20)/Ka(D20) changes from 4.6 to 1.4. These isotope effects consist of primary, secondary, and solvation isotope effects. In buffer solutions of constant ionic strength, it appears that changes in secondary isotope effect predominate over changes in primary isotope effect with changing substituents on the aryl group of the aniline. The solvation isotope effect does not appear to be extractable from the secondary isotope effect, except perhaps in the case of 2,4-dinitroaniline.
Two investigations of Hammett indicator behavior in deuteriosulfuric acid have recently been reported.lJ It is now that the Hammett acidity function determined using primary anilines as Hammett indicators in
aqueous sulfuric acid, Ho‘, is virtually identical with the analogous function, DO,determined in deuteriosulfuric (1) E. Hogfeldt and J. Bigeleisen,J. Amer Chem. Sac., 82,15 (1960). (2) J. Sierra, M. Ojeda, and P. A. Wyatt, J Chem. SOC.,1570 (1970).
The Journalof Physical Chemistry, Val. 77, No. 12, 1973
