J. Phys. Chem. 1980, 84, 259-263
and pentanone-3. In the oxidation of butanone-2 the final oxidation1 produds are acetic acid and formic acid whereas in case olf pentanone-B the final oxidation products are acetic acid, propionic acid, and formic acid.
Experinlentall Section Materials. Cerium(YV) sulfate (Chemapol) was used as received. A stock solution of Ce(1V) was prepared in sulfuric acid (Analar, B.D.H.). The acid concentration of the stock solution was determined as described in the The solution of ruthenium trichloride was preparedl by dissolving the sample (Johnson, Matthay Chemical1 Ltd.)in a solution of hydrochloric acid. The final concentrations of HC1 and of RuC1, were 4.00 X low3and 4.76 X lCP M, respectively. Stock solutions of butanone-2 (lab reagent, B.D.H.) and pentanone-3 (purum, Flw) were prepared. by direct weighing. Other chemicals used were either Analar or chemically pure reagents. The temperature of the reaction mixture was kept constant with wn electrically operated thermostat with an accuracy of f O . l “C.
1!59
The progress of the reaction was followed by estimating the remaining amount of cerium(1V) after different time intervals with a standard ferrous ammonium sulfate tictinometer as reported elsewhere.s The method always gave reproducible results. In all kinetic runs the ketone was present in excess. Acknowledgment. M. K. Verma is grateful to U.G.C. for financial assistance.
References and Notes (1) Wlberge, K. B. "Oxidation In Organic Chemistry”; Academic Press: New York, 1965; pp 255-259. (2) (a) Cady, H. H.; Connik, R. E. J. Am. Chem. Soc. 1956, 80, 2846. (b) Connik, H. E.; Fine, D. A. IbM. 1961, 83,3414; 1960, 82, 41t37. (3) (a) Helpern, J.; James, B. R.; Kemp, A. L. W. J. Am. Chem. Ste. 1961, 83, 4097. (b) Harrod, J. E.; Coccone, S.; Heipem, J. Can. J . Chem. lS61, 39, 1372. (4) Harrod, J. F.; Helpern, J. Can. J. Chem. 1859, 37, 1933. (5) (a) Hardwick, T. J.; Robertson, E. Can. J . Chem. 1951, 29, 828. (b) Jones, M. 0.;Soper, F. 0. J. Chem. Soc.Isas, 1802. (6) Krishna, B.; Tiwari, K. C. J. Chem. SOC.1961, 3097. (7) McAuley, A. J. Chem. SOC. 1964, 2545. (8) Sankhla, P. S.; Mehrotra, R. N. Jnd. J. Chem. 1972, 10, 1077.
Ultrasonic Absorption in Aqueous Binary Mixtures. 1. fert-Butylamine-Water at 25 “C 0. Atklnson,’ M. M. Emara,‘ H. Endo,* and B. L. Atklnson Department of Chemistty and Department of Physics, University of Oklahoma, Norman, Oklahoma 73019 (Received August 30, 1979) Publication costs assisted by the University of Oklahoma
The absorption of sound has been measured in aqueous solution of tert-butylamine over the frequency range 1-520 MHz and the concentrationrange 0.065-37 M at 25 OC. In the low concentrationrange, the single relaxation observed is quantitatively explained by a hydrolysis reaction: k
RNH3+ + OH- ’3-L* RNH2 + H 2 0 kb
The analysis of the data yields kf = 1.5 X 1O’O M-l s-l, k b = 3.4 X lo8 8,AVO = 27.8 cm3/mol. In the high concentration range, the broad absorption in excess of the hydrolysis relaxation is fitted to the fluctuation theory of Solov’ev and co-workers. The fluctuation parameters are presented, and the effect is rationalized in terms of a dynamic analogue of the well-known clathrate hydrate of tert-butylamine.
Introduiction There is a continuing interest in the dynamic properties of solutions of simple hydrocarbon derivatives in water. This interest is generated by two factors. The first is the belief that a better understanding of such simple solutions would increase our understanding of water itself. The second is the feeling that an understanding of a variety of simple hydrocarbon moieties in water would eventually enable UEIto understand the aqueous solution behavior of large biomolecules which combine many different such moieties. Unfortunately, the rapidity of all processes in such solutions severely limits our choice of techniques. One technique that has seemed promising is that of ultrasonic absorption. A recent review3 summarizes earlier work using this technique. Many solutions of alcohols, ketones, ethers, and amines have been examinled. In general, the absorptioln behavior is very nonideal, with clear evidence of relaxational processes and strong dependence of the excess absorption on concentration, frequency, and temperature. However, the interpretation of data in terms of molecular dynamics has not been an overwhelming success. 0 0 2 2 - 3 ~ 5 4 ~ a 0 ~ 2 0 ~ 4 - 0 2 15.oo/o 9$0
The two approaches that have been most popular recentll? are the H-bond equilibria model suggested originally by Andreae et al.S and the “concentration fluctuation” model of Solov’ev and his collaborators in the Soviet U n i o i ~ . ~ The first approach attributes the ultrasonic absorption to one or more equilibria of the type It-X + nH20 is RX-(H,O), However, the rate constants obtained by this type of analysis look abnormally slow for the hydrogen bondiing processes. This problem is worsened when more than oine equilibrium must be assumed. The second approach attributes the excess absorption to fluctuations in the thermodynamic properties of the water in the vicinity of the hydrocarbon. This approach utilizes a distribution of relaxation times and assumes that the fluctuations disappear by mutual diffusion of the two components. The fluctuation approach ties the amplitude of the relaxation to the thermodynamics of the system mid needs assume no molecular model. Although these two approaches seem mutually exclusive, some of the same systems have been analyzed both ways 0 1980 American Chemical Society
260
The Journal of Physical Chemistry, Vol. 84, No. 3, 1980 Alcohol
- Amine
5 MHz
Atkinson et al.
1
t
2
$01 80
c1
51 ad
:18
a
,
7
+
+
t
\
i
O’ 6
+
BuNH, 0.652 M
0
I
50
.
40
1
i
I
30 20
0.1
x*
0.2
0.3
Figure 1. Concentration dependence of low-frequency ultrasonic absorption. Contrast of t-BuNH, with t-BuOH.
in a more or less convincing manner. We are presently engaged in an extended effort to look at a variety of well-defined systems so that a more definitive approach to ultrasonic absorption analysis can be made. A few years ago, we examined7 ultrasonic absorption in aqueous solutions of a number of low molecular weight polyamines. The small relaxations observed in the relatively low concentration range studies (less than 1M) could be completely interpreted in terms of amine hydrolysis. This is true in many of the other amine-water and amino acid-water systems e ~ a m i n e d . ~ -In l ~one case, triethylamine-water, Kruus15has attempted an analysis in terms of a hase separation model. In a very brief paper, Bland er16 has looked at a variety of amine-water systems, fitting some to a single relaxation and some to two relaxations. In the higher concentration ranges where a second relaxation was used, the relaxation was attributed to “equilibria involving different clathrate hydrates”. However, no quantitative fitting of the data was attempted. We decided to examine the tert-butylamine-water system over a fairly wide concentration range for two reasons. First, the tert-butylamine hydrolysis reaction is well ~haracterized.’~ Second, we hoped that any water structure effects would be enhanced by the large tert-butyl group. That is, we hoped that the system would give a very large excess absorption as in the tert-butyl alcohol-water system.l8
$n
Experimental Section Solutions were prepared with deionized water. The tert-butylamine (Eastman) was distilled for purification. All measurements were made on freshly prepared solutions. Sound Absorption Measurements. The absorption coefficient, a,which is defined by the equation I, = IOemza‘ in terms of intensities and distance, was measured in the frequency range 1-520 MHz with a standard send-receive pulse apparatus.lg Three cells of different dimensions with crystal fundamentals of 1 MHz, 5 MHz, and 30 MHz were utilized. The electronic equipment was a Matec 6000 mainframe with 700 series plug-ins and a 1235B amplitude monitor. Frequencies were measured by the heterodyne beat method with a Hewlett-Packard 610 signal generator and 5237C frequency meter. The cells were jacketed and the temperature was controlled at 25 f 0.05 “C. A complete set of (a,f ) is available from one of the authors (G.A.) on request. Sound Velocity Measurements. The sound velocity was determined by the “sing-around’’ techniquez0 using an NUS laboratory velocimeter model 6100 with a Hewlett-
1
8
7
6 XMlN 1.00
9
log f
XMPX 1000.00
Figure 2. Frequency dependence of typical low concentratlon tBuNHp solution (ordinate units are nepers cm-’ s2, abscissa units are MHz).
TABLE I: Ultrasonic Parameters for Low Concentration Aqueous t-BuNH, at 25 “ C
X , , mol C, M fraction 0.0650 0.00117 0.130 0.00234 0.326 0.00584 0.652 0.0116 0.973 0.0172
A x 1017, neper, cm-’ s2 54.6 i. 1.5 55.3 i. 1.2 58.0 i. 2.9 60.5 i. 0.9 62.0 t 6.0
B x 1017, neper, cm-’ s* fr, MHz 16.4 i. 1.5 67.3 i. 4.4 20.5 i. 1 . 3 77.8 f 3.8 20.8 * 3.2 109.1 f 8.9 22.8 i. 0.8 122.1 i. 1.2 32.4 t 6.9 108.8 ?: 18.1
Packard 5237C digital frequency meter. The temperature of the solutions was maintained at 25 f 0.05 “C with a Forma temperature bath. Results and Analysis Measurements were made at ten amine concentrations in the range 0.065 to 37 M. Figure 1 shows a plot of a/f2 vs. mole fraction of amine at a frequency (5 MHz) below the relaxation region. The PSAC (‘‘peak sound absorption concentration”) phenomenon appears with a lower amplitude and at a lower X 2 than in the tert-butyl alcohol system. In the low concentration region (less than 1 M amine, X 2 < 0.02), ultrasonic data can be fitted to a single relaxation of the conventional form:
where a = absorption coefficient, f = measured frequency, f, = relaxation frequency, A = relaxation amplitude, and B = background absorption. Figure 2 shows a typical set of data fitted to the single relaxation equation. Table I gives the fitting parameters for the five concentrations for which this is an appropriate approach. However, the higher concentration relaxations are too broad to be fitted to a single relaxation. Low Concentration Analysis. The increase off, with amine concentration and some qualitative measurements showing a strong dependence of absorption on pH persuaded us that the low concentration relaxation is due to the amine hydrolysis process. In this case, OH- + t-BuNH3+ 7-1
= 27rfr = kb
k
t-BuNH,
+ kfl*2uC
[+ 2
~
+ H20
(2)
(3)
where yh = mean ionic activity coefficient, u = degree of
The Journal of Physical Chemistry, Vol. 84, No. 3, 1980 261
Ultrasonici Absorption in Aqueous Binary Mixtures
TABLE 11: Comparison of Amine Hydrolysis Reaction Parameters
H yd rol y s is
-
8
kfX
lo-'',
kb
M-I
lo-,,
s-l
s-l
tert-butylamine
1.5
3.4
em3/ mol 27.8
tert-butykmine is0 butylamine n-butylamine ethylamine diethylamine triethylamine ethylenediamine diethylenetriamine triethylenetetramine tetraethylenepentamine trieth ylenediarnine
1.9 1.2 4.1 3.2 2.1 1.I 2.9 2.6 2.4 2.3 5.0
2.1 3.2 1.4 0.14 0.26 0.095 0.11 0.15 0.04 0.13 0.018
24 29 32 24 24 22 25.5 25.5 25 25 31.3
amine ~~
Figure 3. Analysis of low concentration relaxation data by hydrolysis mechanism.
amine dissociation, C = stoichiometric amine concentration, anld (4) 2Tfr = k b + k@(C)
I
We have calculated e(C) by using the known pKB of tBuNHz ,and the Davies equation for yI. This is done easily by a small iterative computer program. Figure 3 shows a plot of 2 r f r vs. e(C) to be quite linear in this low concentration range. This analysis yields the rate constants kf = 1.s4X 1O'O M-ls-' and k b = 3.36 X 10' s-l. The amplitude is given by 280
340
where d = solution density, u = sound velocity in solution, V = molar volume of solution, (Y = expansibility of solution, C, = specific heat of solution, AH = enthalpy change in reaction, AV := volunie change in reaction, and [OH-]
--)
-1
(6)
[RNH3+] 1 + [R"d
Considering the rather small AH and the large AV typical of such reactions, we can probably ignore the AH term. This enribles us to calculate AVO for the reaction from the measured amplitudes. The extrapolated AVO (infinite dilution) is 27.8 cm3/mol, and the AV for the low range can be given by an equation of the form AV = 27.8 - 2.44C '
One would expect a C1I2rather than a C dependence, but the above equation fits quite well. Table I1 compares the results of this work with a variety of other amine hydrolysis data. All of the k f values are in the diffusion-controlled range. There are no obvious trends to be noited in them or in the AVO values. If one examines the &, values obtained from the ultrasonic data by using eq 3 and Kb = (kb/kf:l,one finds the ultrasonic & to be generally larger than the accepted values obtained by using a conventional thermodynamic approach. This has been attributedll to the fact that proton transfer is inherently a two-step process, but no quantitative interpretation along these lines has been attempted. We feel it is just as likely to be due to the difficulty of obtaining kb with any precision from the ultrasonic data. High (ConcentrationAnalysis. Figure 4 shows one of the high concentration data sets fitted to a single relaxation and to a double relaxation of the form
A T ,
I I I I 12
I
I I, '
100
ref this work 11 11 10 8 8 8
""'7
6
XMlN 1.00
X M A X 1000.00
'
'
'
" " "
log F
a
9
Figure 4. Frequency dependence of typical high mcentratbn t-Bu", solution (ordinate units are io-" nepers cm-' s2,abscissa units are MHz).
It is clear for this and for the other four high concentration sets that the double relaxation does fit the data. However, we are still left with problems. We have another relaxation to attribute to some believable process. Worse yet, neither of the relaxation frequencies found in this fitting process can be easily correlated with the single hydrolysis relaxation found in the low concentration range. Therefore, we have taken a somewhat different approach. If we define (a/f)excessI (a/f)exptl - (a/f)hydrolysia
(8)
we can calculate the "excess" quantity by using the derived AV, kf, and kb values to calculate the expected contribution from ( a / f ) h d at any concentration and frequency. We, then, havevoocd at various ways to fit (a/f)excess* I3ut (a/f)excesa cannot be fitted to a single relaxation. It can be fitted well to a two-relaxation fit. However, that would leave us with two relaxations for which to find cogent explanations. Therefore, we decided to try the fluctuation approach. If (a/f2)excess is due to fluctuations in the water, then it should be given by (see ref 3 for details)
2
where P = molar volume of solution, u = sound velocity in solution, 0, = compressibility of solution, a = expansibility of solution, C, = specific heat of solution, G" =
262
Atkinson et ai.
The Journal of Physical Chemistry, Vol. 84, No. 3, 1980
F”
Plot
TABLE 111: Ultrasonic Fluctuation Parameters for High Concentration Aqueous t-BuNH, at 25 “C C.M 0.652 3.17 3.67 4.37 6.20 37.0
X , , mole
Q X loz6
D X 105
0.0116 0.054 0.062 0.073 0.100 0.400
0.40 f 0.01 1.72 f 0.04 1.88 f 0.03 2.29 f 0.05 2.89 -i. 0.09 7.40 i. 2.6
3.40 f 0.15 1.79 ?: 0.05 1.88?:0.04 2.53 ?: 0.06 4.57 i. 0.16 32.4 f 12.2
r-
x
1,
fraction
107
1.18 1.18 1.18 1.18 1.18 1.18
tBuNH2 3.17M fluctuation c
Figure 5. Fluctuation square root plot for 3.17 M t-BuNH, solution (ordlnate units are IO-’’ nepers cm-I s2, abscissa units are MHz).
(a2GE/aX2)+ RT/[XZ(l- XJ], V” = a2VE/aX?, H” = a2HE/aX2, YE = excess thermodynamic property, and
3 0 0 .
200.
100
2[tan-l ( d a l ,
+ 1) + tan-1 (Gal,- I)] (11)
where a = w/2D, w = 2rf, D = mutual diffusion coefficient, and 1, = minimum interaction length. For a detailed description of the inherent model and asumptions, see the original Solov’ev papers. Equation 9 is basically a four parameter fit (Q, l,, D, B ) one of which ( E ) can be estimated from the experimental data and two others (Q, D)which in principle can be obtained by nonkinetic measurements. Q is completely determined by the equilibrium thermodynamic properties of the mixture. D can be obtained using NMR methods. Only 1, is not clearly related to other available data. Equation 9 is difficult to use as a fitting equation for data. This is because of the tight coupling between the 1, and D parameters. Even very sophisticated nonlinear least-squares programs have great problems. However, as a start we can take advantage of an interesting property of the fluctuation approach-its zero frequency limit. discrete relaxation
fluctuation
Figure 5 is a plot of [ ( a / f ) e x c e sBs] vs. PI2. The data clearly approach linearity with f112 as we approach low frequency. By using an estimated 1, from such plots, it is possible to fit the (a/fL)excess data with a nonlinear least-squares program. We have arbitrarily fixed 1, at the “best” value for minimizing the standard deviation of fit for the “best” set of data. Then, for the remaining sets of data we have fixed 1, at this same value and allowed the least-squares program to determine Q and D. Table I11 gives the fluctuation parameters determined in this way. Figure 6 shows a set of data fitted with the fluctu-
i
s
u
Figure 6. Fluctuation theory fit of 3.17 M t-BuNH, solution (ordlnate units are lo-’’ nepers cm-I s2,abscissa units are MHz). Fluctuation
-
Parameters
-4
Q
-3 1-
D
-2
Figure 7. Fluctuation theory parameters as a function of amine concentration. ation equation, and Figure 7 shows and Q and D values as a function of mole fraction of amine.
Discussion The low concentration results are clearly consistent with a hydrolysis interpretation. The rate constants and AVO value obtained are in good agreement with those obtained previously on this and other amine systems. However, the high concentration analysis is a somewhat different matter. This is, in fact, true of all the similar aqueous nonelectrolyte systems that have been examined by ultrasonics. In the range of very large absorptions if the data covers a reasonably wide frequency range, it cannot be fitted to a single relaxation. The data can be fitted either to a double relaxation or to a fluctuation equation. If one fits to a double relaxation, one is left with the difficulty of proposing two kinetic processes that make some chemical sense. We do not feel that this has been done convincingly. We believe that the fluctuation equation fit is a better approach. In a system where complications such as hydrolysis do not occur, it should be possible to do a complete analysis of the frequency and concentration dependence using only one “free” parameter, l, the minimum inter-
J. Phys, Chem. 1980, 84, 263-267
action distance. The D values can be obtained by NMR methods. The Q values should be directly related to the equilibrium thermodynamics of the system. It clearly takes a very large amount of good data to attempt such a fit. We are pursuing this approach on some well-characterized systems. At the same time, we have examined a large number of systems using data on aqueous amines, alcohols, and ethers from our own and other laboratories. In every case, ( a / p - B ) approaches linearity with f 1 2 if the data cover a wide enough frequency range and go to a relatively low frequency (15 M Hz). We feel that thns is strong evidence for the fluctuation approach. One of the main conceptual problems with the fluctuation approach is that it does not provide a simple “chemical” kinetic process like A B C for the audience. Instead, we obtain parameters purported to describe a thermlodynamic fluctuation. It is useful to consider how such a fluctuation could arise. We note that the amplitude of the sound absorption phenomenon in such systems is governed by the ratio of hydrophobic to hydrophilic area on the molecule. That is, as we go from MeOH to t-BuOH, the effect goes up in amplitude dramatically. If we go from EtOH to ethylene glycol, the effect is diminished. So our fluctuation is related to the response of the water to the introduction of a hydrophobic moiety, and the thermodynamic properties of the water in the vicinity of the hywater’ In effect’ drophobic moiety are different from we are seeing a dynamic version of the well-known propensity of such organic molecules to form clathrate hydrates. t-BuNE[, is well-known21 to form such a hydrate. It is probably not coincidental that the hydrate formula (tBuNH2.9.75H20)is not far removed from the “peak sound
+
-
26a
absorption concentration”. It, thus, seems at least possible to conceive of a hybrid theory which has the virtues of a “chemical” model and still has the quantitative advantages of the fluctuations approach. Acknowledgment. The authors acknowledge the support of the National Science Foundation under Grant OCE-7814527.
References and Notes (1) Department of Chemistry, Al-Azhar Unlverslty, Calro, Egypt. (2) DeparbTlent of physics, Natlonal Defense Academy, Yokosuka, Japan. (3) M. J. Blandamer and D.Waddlngton, A&. M I . Relawatbn Rccesws, 2, 1 (1970). (4) M. J. Blandamer, In “Water-A Comprehenslve Treatlse”, Vol. 2, F. Franks, Ed., Plenum Press, New York, 1973. (5) J. H. Andreae et ai., Acustica, 15, 74 (1965). (6) V. P. Romanov and V. A. W e v , Sov. phys.-Acoust. (fngl.Transl.), 11, 68 (1965). (7) M. M. Emara, G. Atklnson, and E. Baumgartner, J. Phys. Cheim., 78, 334 (1972). (8) M. E m , G. Maass, and G. Schwarr, Z . phys. Chem., 74,319 (19171). (9) R. S. Brundage and K. Kustln, J . Phys. Chem., 74, 672 (1970). (10) S. Nisklkawa et al., Bull. Chem. Soc.Jpn., 46, 1098 (1973). (11) S. Niskikawa et at., Bull. Chem. SOC. Jpn., 52, 655 (1979). (12) R. E. Verrell, personal communication. (13) M. J. Blandamer et ai.. Trans. Faradav SOC..63.66 (1967). i i 4 j K. Applegate, L. J. slutsky, and R. C. Pirker, A ~ I cbm. . ’s~oc., 90, 6909 (1968). (15) P. Kruus, Can. J . Chem., 42, 1712 (1964). (16) . . M. J. Blandamer. N. J. Hidden, and M. C. R. SYmons, Trans. Fanidav SOC..86. 316 (1970). (17) “Stability Constants oiMetaCIon Complexes”,2nd ed., The Chemical Society, London, 1964. (18) K. Tamura, M. Maekawa, and T. Yasunaga, J. Phys. Chem., 81, 2122 (1977). (19) R. Garnsey and D. W. Ebdon, J . Am. Chem. Soc., 91, 50 (1969). (20) R. W W Y , R. J. m,R. M b Y , and T. A. m o a , J. Chem. W S . , 50, 5222 (1969). (21) R. K. McMullan, 0. A. Jeffrey, and T. H. Jordan, J. Chem. Phys., 47, 1229 (1967).
i.
Use of Regular Solution Theory for Calculating Blnary Mesogenic Phase Diagrams Exhibiting Azeotrope-Like Behavior. 2. Maxima Formlng Systems‘ G. R. Van Hecke,” 1.S. Canlu, Department of Chemistry, Harvey Mudd College, Claremont, Callfornia 9171 I
M. Domon, and J. Blllard Laboratoire de Dynamique Ues Cristaux Moleculars, Unlversit6 des Sciences et Techniques de Lille, B.P. 36, 59650 Viileneuve D’ Ascq, France (Recelved July 12, 1979) Publlcatlon costs assisted by Harvey Mudd College
Many binary phase diagrams of mesomorphic components exhibit maxima azeotrope-like phase behavior. Regular solution theory is successfully applied to calculate four such diagrams arising from binary mixtures of three cholesterol esters and a tolane with enantiomeric p-nitrobenzalaminocinnamicacid 2-methylhexyl ester.
Introduction While more tmd more phase diagrams of binary mixtures of crystalline materials are appearing in the literature, little work calculating such diagrams by some thermodynamic means has appeared.2‘4 Regular solution theory has been successfully applied to calculating the fluid two phase region between the nematic and isotropic phases exhibited in binary mixtures of homologous symmetric azoxybenzene^.^ We report here the results of applying the regular solution approximation to relatively complex phase diagrams, which, in some cases, exhibit three phases in 0022-3654/80/2084-0263$0 1.OO/O
equilibrium, for example, smectic A, cholesteric, and a crystal, or smectic A, nematic, and isotropic. The method does indeed appear to be a successful means for calculating even complex phase diagrams.
Experimental Section The four phase diagrams discussed here were obtained for combinations of three cholesterol esters and one tolrme with a common reference compound, enantiomeric p nitrobenzalaminocinnamic acid 2-methylhexyl ester (I).6 The cholesterol esters were nonanoate (pelargonate, .[I), 0 1980 Amerlcan Chemical Society
