J. Phys. Chem. 1984, 88, 3684-3688
3684
are not too large, we may write
Substitution of these expressions into eq 13 gives
Pzie(E - Czjpjuii) gSx) where K~ = 4 n B e 2 ( C i ~ , z , 2 ) / c . In a similar manner, the contact values for the density profiles at the electrode can be obtained from the general MSA express i o w 8 The result is g,(%/2) =
where Em
= (r/6)Cpiuiim
(21)
1
the summation being over the n components of the bulk solution. The first term in eq 20 is the uncharged hard sphere/uncharged hard wall term. The second term is obtained from -2/32XJr,,/[e(u,, 41 by using the same techniques which were used to obtain eq 1 1 . Comparison of eq 13 and 20 shows that the second term in eq 20 vanishes when the potential difference across the double layer is zero. However, the first term does not vanish and is greater for the larger spheres so that the contact values are qualitatively similar to those 0btained~9~ from the Poisson-Boltzmann approximation. If the difference in diameter of the bulk ions is not too large and if the concentration is not too high, CBU,?/Dis small compared to z p Thus
+
- 2ae~z1p,o,) g , ( a , , / 2 )= 1 -
EK
(22)
We do not neglect 2rexJz,p,uJ,compared to E , since E can be small (and is zero at the pzc). If all of the ions have the same diameter, the MSA density profiles are given by
where go@) is the density for hard spheres near a hard wall and if f ( x - u / 2 ) is a complicated function. Explicit results for go(x) and f ( x - u / 2 ) have been given by Henderson and Smith.g In principle, a general expression for the density profiles, valid for ions of different diameter, can be obtained from the general MSA expressions.* Unfortunately, the result is very complex. However, as long as the concentration and the size differences ~~~
(9) Henderson, D.; Smith, W. R. J . Stat. Phys. 1978, 19, 191.
=-
J
e-x(ra/i/2)
tK
x
> uii/2
(24)
Since f(x)
N
e-Kx
(25)
at low concentrations, eq 23 is of this form at low concentrations. The mean electrostatic potential +(x) may be obtained by using
as may be verified by differentiating eq 26 twice to obtain Poisson’s equation. Both 4 = $(O) and $ ( x ) are unaffected by a change in the sign of the electrode. This symmetry is a result of the linearization inherent in the MSA.
Comments We have given some MSA results for double layers containing an asymmetric electrolyte. Neither the potential q5 nor the difference between the charged hard sphere/charged hard wall density profile and the hard sphere/hard wall density profile vanishes for an uncharged electrode ( E = 0) unless all the hard spheres have the same diameter. This is true in the PoissonBoltzmann theory als0.~9’ It is conventional to interpret a nonzero potential at zero charge in terms of non-Coulombic forces (Le., specific adsorption). However, it is not necessary to invoke such forces, as differences in diameter can also give rise to a nonzero potential at zero charge. This is not to say that specific adsorption is not an important phenomena in double-layer studies. However, estimates of the importance of specific adsorption, obtained by subtracting equal diameter Poisson-Boltzmann theory results from experimental studies, may well be misleading if there are sizable differences in ionic radii. As long as there are no differences in diameter, the MSA predicts that 4 is symmetric under a change of sign of the electrode charge. This is at variance with other s t ~ d i e s . ’ -However, ~~~~~ it is to be remembered that the MSA is valid only near the pzc and that, in this region, the symmetry is valid. The fact that the MSA results are valid only near the pzc is only a minor inconveniencesince away from the pzc the properties of the double layer are, to an excellent approximation, those of a symmetric electrolyte composed of ions of the charge and diameter of the counterions. Acknowledgment. A.F.K. thanks IBM/Brazil for a travel fellowship which made his visit to IBM/San Jose possible. This work was supported in part by NSF grant no. CHE80-01969.
Enthalpies of Hydration of Alkenes. 2. The n-Heptenes and n-Pentenes Kenneth B. Wiberg,* David J. Wasserrnan, and Eric Martin Department of Chemistry, Yale University, New Haven, Connecticut 0651 I (Received: December 6, 1983)
The enthalpies of reaction of the five n-heptenes with trifluoroacetic acid in the presence of a strong acid catalyst have been measured. A combination of these data with the available combustion data for the alkenes allows the enthalpies of formation to be determined with higher precision than previously possible. The differences in enthalpies of formation of the n-pentenes also were determined. The enthalpies of reaction of the three n-heptyl alcohols with trifluoroacetic anhydride were measured, and, when combined with the above data, permits the determination of the enthalpies of formation of the alcohols. Structural effects on the enthalpies of formation are discussed.
We have shown that it is possible to determine the enthalpies of hydration of alkenes via measurements of the enthalpies of 0022-3654/84/2088-3684$01.50/0
reaction of the alkene, the corresponding alcohol, and of water with a reaction medium consisting of 0.25 M trifluoroacetic an@ 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3685
Enthalpies of Hydration of Alkenes
TABLE I: Equilibration of 2-, 3-, and 4-Heptvl Trifluoroacetates T, O C n" ratio 2:4* ratio 2:3 ratio 3:4 40 100 140
4.23 f 0.0SC 4.18 f 0.09 3.98 f 0.06
5 4 7
2.80 f 0.02 2.77 f 0.05 2.69 f 0.04
1.50 f 0.02 1.50 f 0.03 1.48 f 0.03
AH"(4-2) = -158 f 35d cal/mol AP(4-2) = +2.4 eu AHO(3-2) = -36 f 32 cal/mol ASO(3-2) = +0.7 eu AH0(4-3) = -104 f 27 cal/mol ASO(4-3) = +1.7 eu
AH = AH, - AH2 + AH3 hydride in trifluoroacetic acid as shown in Scheme I.' As part of this study, we have measured the enthalpies of reaction of the n-hexenes with trifluoroacetic acid to give a common set of products (2- and 3-hexyl trifluoroacetates) and thereby obtained the differences in enthalpies of formation among these alkenes.' A rather large disagreement was found between our values and those calculated from the previously reported enthalpies of combustioq2 suggesting that some of the latter determinations were in error by as much as 1 kcal/mol. Recent and probably more precise combustion data are now available for the n-heptene~.~We have measured the enthalpies of reaction of these compounds with trifluoroacetic acid. A comparison of the two sets of data would be of value for three reasons. First, if good agreement is found, it would confirm that the accuracy of our procedure is satisfactory. Second, it would allow the two sets of data to be combined in a least-squares sense to yield more precise values of enthalpies of formation. Third, a comparison of the n-hexene and n-heptene series would provide useful information on cis-trans energy differences and on the effect of moving a double bond down a hydrocarbon chain. The reaction of the n-heptenes with the trifluoroacetic acid/ trifluoroacetic anhydride reaction mixture was carried out at 25 "C with 0.002 M trifluoromethanesulfonic acid as the catalyst. The reactions led to mixtures of 2-, 3-, and 4-heptyltrifluoroacetates. Each of the heptenes led to a slightly different product composition. Thus, the initially formed product ratio was determined by allowing the reaction to proceed for 10 min,quenching with sodium trifluoroacetate, and analyzing the composition via I3C N M R spectroscopy. The equilibrium ratio was determined by allowing the reaction mixture to remain at a fixed temperature in the presence of the acid catalyst until equilibrium had been achieved. The ratio was determined as a function of temperature giving the data shown in Table I. The AHvalues thus obtained allow the enthalpies of reaction to be corrected to correspond to the formation of the equilibrium product composition. It is interesting to note that the 3-trifluoroacetate is the preferred product under kinetic control. At 25 "C, the equilibrium ratio of 2,3, and 4-trifluoroacetates is 0.53:0.35:0.12, where the 2-isomer is preferred. Even 1-heptene, which must initially form the 2cation, leads to more 3-trifluoroacetate than the equilibrium amount. A similar observation was made in the case of the n-hexenes.' The results of the calorimetric study of 1-heptene are given in Table 11. It can be seen that high precision may be achieved in these measurements. The reactions of the other n-heptenes proceeded equally well giving the results shown in Table 111. The product ratio was determined as described above. The AHw, are the values obtained after correcting the observed values to cor-
Number of runs. bRatio of 2-heptyl trifluoroacetate:4-heptyl trifluoroacetate. cUncertainties are given as two times the standard deviation from the mean (2s). dThis uncertainty is derived from an estimate of the standard deviation in the slope of the least-squares line. The 2-heptyl trifluoroacetate is the most stable followed by the 3heptyl trifluoroacetate.
TABLE II: Enthalpy of Trifluoroacetolvsis of 1-n-Heptene run 1 2 3 4 5 6
Q,
e,
mmol 0.6080 0.6706 0.5682 0.6035 0.7459 1.3614
AT cal 0.1314 7.172 0.1456 7.942 6.707 0.1230 0.1307 7.118 8.805 0.1615 16.071 0.2934 AH,, = -11808 15 cal/mol" cal/K 54.59 54.56 54.55 54.45 54.51 54.78
*
AH,
cal/mol -11796 -11843 -11804 -11795 -11804 -11805
'Uncertainties are given as two times the standard deviation from the mean (2s).
respond to the equilibrium product ratio. The enthalpies of isomerization derived from the present results are compared with the literature values derived from enthalpies of combustion4 in Table 111. The two sets of data agree within their respective uncertainties. It would be of interest to use the present data to obtain more precise values for the enthalpies of formation. We have used a least-squares treatment as follows: The error in the enthalpy of formation for compound i derived from the combustion measurement will be represented by fii, and that for the enthalpy of reaction of compound i with trifluoroacetic acid will be represented by yi. Then 6i = Ai' - Ai yi = Ai 4- Bi'- X
where Ai' is the observed enthalpy of formation, Ai is the true value of AHf,B,' is the observed enthalpy of reaction with trifluoroacetic acid, and X is the constant sum of the true values of Ai and Bi. We wish t o minimize F which is the sum of 6; y; subject to appropriate weighting factors (ai and pi). The latter were taken as 1000/stated error in cal/mol. Thus, we minimize F with respect to the A,'s and X
+
F = C((ui6?+ &y;) which gives n equations of the form: (ai Pj)Aj - @J = '~jAj'- PjBj'
+
where the index runs from 1 to n, and This set of n + 1 normal equations may be solved by matrix inversion, giving the values of Ai shown in Table IV. It is difficult to known what error limits to assign to the corrected values of AHf. We have chosen to use 150 cal/mol which would appear to be conservative. We should like to compare the enthalpies of formation of the C,-C, n-alkenes. It is only recently that precise values for the
(1) Wiberg, K. B.; Wasserman, D.
J. J. Am. Chem. SOC.1981,103,6563. (2) Bartolo, H. F.; Rossini, F. D. J . Phys. Chem. 1969, 64, 1685. (3) Good, W. D. J . Chem. Thermodyn. 1976,8, 67.
(4) ,Cox, J. D.; Pilcher, G. "Thermochemistry of Organic and Organometallic Compounds", Academic Press: New York, 1970.
3686 The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
Wiberg et al.
TABLE 111: Enthalpies of Trifluoroacetolysis of n -Heptenes compd
n"
1-heptene cis-2-heptene trans-2-heptene cis-3-heptene trans-3- heptene
6 4 4 5 4
AH,, cal/mol -11808 -9827 -9003 -10138 -9209
f 15 i 21 f 15 f 25 f 27
AAH(obsd), cal/mol 0 1973 i 27 2799 i 22 1635 f 30 2570 f 32
AHC0l)e
ratiob 0.46:0.44:0.10 0.32:0.58:0.12 0.36:0.52:0.12 0.18:0.52:0.30 0.20:0.54:0.26
cal/mol -11808 i 15 -9835 i 22 -9009 i 16 -10173 i 26 -9238 i 28
AAH(lit.),d callmol 1620 f 300 2670 f 290 1430 f 280 2570 f 320
"Number of runs. Ratio of 2-heptyl trifluoroacetate:3-heptyltrifluoroacetate:4-heptyltrifluoroacetate observed 10 min after mixing. to the equilibrium mixture. dReference 3.
Corrected
TABLE IV: Enthalpies of Formation of Liquid n-Heptenes and n-Pentenes (kcal/mol) comvd 1-heptene cis-2-heptene trans-2-heptene cis-3-heptene trans-3-heptene I-pentene cis-2-pentene trans-2-pentene
lit. -23.51 f 0.21 -25.13 f 0.22 -26.18 i 0.20 -24.94 f 0.19 -26.13 i 0.24 -11.23 f 0.15 -12.78 k 0.15 -13.86 i 0.18
adiusted" -23.35 i 0.15 -25.32 f 0.15 -26.15 f 0.15 -24.99 f 0.15 -25.92 i 0.15 -11.22 f 0.10 -12.75 i 0.10 -13.92 i 0.10
-I
i
" The values for the alkenes derived from combustion calorimetry were combined with the observed differences found in the trifluoroacetolysis studies using the least-squares method. enthalpies of combustion of the n-pentenes have been ~ b t a i n e d . ~ Previous values had been derived by a combination of enthalpies of hydrogenation of a mixture of cis- and trans-2-pentene of uncertain composition, a guess as to the composition of the mixture, and differences in enthalpy of formation obtained in iodine-catalyzed isomerization.6 Again, it seemed reasonable that the combustion data could be improved by combining them with precise values of enthalpy differences. Thus, we also have determined the enthalpies of reaction of these compounds with trifluoroacetic acid giving the data summarized in Table V. Again, mixtures of 2- and 3-pentyl trifluoroacetates were formed, and the equilibrium constant was determined (Table VI), allowing the values to be corrected to the formation of the equilibrium mixture. The results are in good agreement with the energy differences obtained by Egger and Benson6via the iodine-catalyzed equilibration of the n-pentenes, especially considering that their data were obtained at an average temperature of 500 K, and required assumptions concerning heat capacities to convert them to 25 OC. The enthalpy differences obtained in this investigation were combined with the enthalpies of formation derived from the combustion studies as described above. The values are given in Table IV. Considering the excellent agreement, it seems reasonable to assign an uncertainty of f0.1 kcal/mol. The effect of structural changes on the enthalpies of formation of the n-alkenes is best seen in a plot of relative enthalpies with respect to the 1-alkenes (Figure 1). The enthalpy differences among the n-hexenes and n-heptenes are quite similar, except that the latter are shifted to lower values by 300-400 cal. The more precise relative enthalpies now available show a relatively simple trend with increasing chain length. The differences in enthalpy for the 2- and 3-hexenes and heptenes are shown in Figure 2. In both series, the trans compounds having a CH,, and an alkyl group are more stable than those having a C,H5 and an alkyl group. This is presumably an electronic effect since the groups are trans. The cis-trans isomerizations had the same enthalpy change when both groups were larger than methyl, but when one substituent was methyl, there was a small effect from the size of the other substituent. The second part of the determination of the enthalpies of hydration involves the measurement of enthalpies of reaction of water and 2-, 3-, and 4-heptanol with trifluoroacetic anhydride in the (5) Good, W. D.; Smith, N. K. J . Chem. Tbermodyn. 1979, 1 1 , 111. (6) Egger, K. W.; Benson, S . D. J . Am. Chem. SOC.1966, 88, 236.
-31
1 -1 --- i
Figure 1. Relative enthalpies of formation of the n-alkenes. + -
-265f42
w
-492f40
+737+41
+935f38
-229+32
-338f34
+E26227
Figure 2. Enthalpy changes for double bond isomerization and migration for the n-hexenes and n-heptenes.
reaction medium. These reactions are rather slow in the presence of a strong acid, presumably because water and the alcohols are converted to their conjugate acids which are no longer nucleophilic. The reaction did proceed satisfactorily in the absence of the acid catalyst, and the enthalpies were determined under these conditions. The results are presented in Table VII. Again, satisfactory precision was obtained. Since the differences in enthalpy among the trifluoroacetates is known from the equilibration experiments, the differences in enthalpy among the alcohols may be obtained directly from these data. The 2- and 3-heptanols differ in energy by only 43 f 38 cal/mol, but 3- and 4-heptanols differ by a larger amount, 223 f 40 cal/mol. Neither of these differences is large, and may be compared with the difference between 2- and 3-hexanol, 278 f 62 cal/mol. In order to determine the enthalpies of hydration of the alkenes, it is necessary to have the same final state for the trifluoroacetolysis of the alkenes and the esterification of the alcohols. However, as the experiments were performed, the first reaction was carried out in the presence of strong acid, whereas the latter was not. In order to correct the data to a common final state, the enthalpies of solution of the equilibrium mixture of the trifluoroacetates and
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3681
Enthalpies of Hydration of Alkenes
TABLE V Enthalpies of Trifluoroacetolysis of Liquid n-Pentenes (cal/mol) compd nQ AH, ratiob 4 -12464 f 28 62:28 1-pentene cis-2-pentene trans-2-pentene
4 4
-10918 f lge -9743 f 13
50:50 53:47
AH,," -12476 f 29 -10946 f 19 -9767 f 14
AAH(obsd)
AAH(lit.)d
0
0
1530 f 35 2704 f 32
1660 f 70 2590 f 80
aNumber of runs. bRatio of 2- to 3-pentyl trifluoroacetates. cCorrected to the equilibrium mixture of trifluoroacetates at 25 OC. dData of ref 6 obtained at an average temperature of 500 K and corrected to 25 OC by using approximate heat capacities. eThe observed AH was 10891 f 14. Correcting for 0.25 f 0.05% of inert impurity (pentane) gives 10918 f 15. The uncertainty in the AHr of the isomeric pentene impurity raises the uncertainty interval to f 1 8 .
TABLE VI: Eauilibration of 2- and 3-Pentyl Trifluoroacetates T, O C K" Kb4 23.7 87.7 148.2
2.35 f 0.05 2.23 f 0.03 2.17 f 0.05
2.45 f 0.02 2.32 f 0.03 2.33 f 0.03
"Based on ratio of NMR methyne hydrogen bands for the two trifluoroacetates. bBased on ratios of areas of groups of bands. cAH(2-3) based on both sets of equilibrium constants is 133 f 33 cal/ mol.
AH,, cal/mol -21813 f 22 -21881 f 23 -21991 f 18
n 5 5 5
AHwr: cal/mol -21845 f 25 -21888 f 29 -22111 f 27
Corrected to the equilibrium mixture.
TABLE VIII: Enthalpies of Solution of Trifluoroacetates compd heptyP heptyl hexyl hexyl
n 2 4 2 2
W+I, M 0.002 0.000 0.002 0.000
AH^,^
AHhyd? cal/mol -8074 f 76 -7682 f 76 -7984 f 50 -7941 f 53 -7838 f 52
compd 2-hexanol 3-hexanol 2-heptanol 3-heptanol 4- heptanol
+
kcal/mol -93.68 f 0.21 -93.29 f 0.21 -99.65 f 0.16 -99.61 f 0.16 -99.50 f 0.16
-
QForthe reaction 1-hexene H20 hexanol or the corresponding the AH, of 1-hexene or 1-heptene and reaction of 1-heptene. AHf of liquid water (-68.315 kcal/mo14).
TABLE VII: Enthalpies of Reaction of Heptanols compd 2-heptanol 3-heptanol 4-heptanol
TABLE I X Enthalpies of Hydration and Formation of Hexanols and Heptanols
AH,, cal/mol -694 f 4 -665 f 11 -850 f 60 -829 f 20
a An
equilibrium mixture of the possible trifluoroacetate was used to prevent any heat due to equilibration in the calorimeter.
of trifluoroacetic acid were determined in the reaction solvent, both with and without trifluoromethanesulfonic acid. The results of these measurements are given in Table VIII. The data may now be combined as previously described' to give the enthalpies of hydration and enthalpies of formation of the alcohols (Table IX). In examining the heats of solution of the n-heptyl trifluoroacetates there appeared to some small (100 cal) deviations from the data for the n-hexyl compounds. We had expected the two series to give rather similar results. Thus, we have also reinvestigated the enthalpies of solution of the n-hexyl esters giving the data in Table VIII. The results are slightly different than those previously reported, and corrected values for the enthalpies of formation of the hexanols are given in Table IX. The enthalpies of formation of the 2-, 3-, and 4-heptanols are not known, and the values obtained in this investigation depend on the accuracy of the enthalpy of formation of 1-heptene. Although we had no reason to doubt the reported value for the latter, we wished to see if our results were consistent with the data for other alcohols. It is known that constant methylene increments to AHf are normally found with increasing chain length.' This correlation for the 2-alkanols is shown in Table X. Our data, and the previous data for the C, to C, compounds are in good agreement, with a methylene increment which is the same as that found for the 2-methylalkanes, Thus, we are confident that our values for the hexanols and heptanols are correct. It is not readily possible to check the AHf for the 1-alkanols by reaction calorimetry, and therefore the correlation with chain length also was examined for these compounds (Table X). It can be seen that the data for 1-hexanol and I-heptanol do not agree well with (7) Franklin, J. L. Ind. Eng. Chem. 1949, 41, 1070.
TABLE X Enthalpies of Formation of Liquid Alcohols and Alkanes AH,(obsd) : kcal/mol
compd
AHf(calcd), kcal/mol
1-Hydroxyalkanes -66.42 f 0.08 -72.51 f 0.30 -78.29 f 0.13 -84.27 f 0.17 -90.65 f 0.24 -95.29 f 0.20 -102.30 zk 0.26
ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol
-66.43 -72.40 -78.37 -84.34 -90.31 -96.28 -102.26
diff, kcal/mol 0.01 -0.1 1 0.08 0.07 -0.34 1.01 -0.04
methylene increment = 5.97 kcal/mol n-Alkanes -35.38 f 0.16 -41.49 f 0.17 -47.46 f 0.18 -53.59 f 0.22 -59.78 f 0.25
n-butane n-pentane n-hexane n-heptane n-octane
-35.36 -41.45 -47.54 -53.63 -59.12
-0.02 -0.04 0.08 0.04 -0.06
methylene increment = 6.09 kcal/mol 2-Hydroxyalkanes -76.02 f 0.12 -87.87 f 0.23 -87.74 f 0.18 -93.68 f 0.21 -99.65 f 0.16
2-propanol 2-butanol 2-pentanol 2-hexanol 2-heptanol
-75.98 -81.89 -87.79 -93.70 -99.61
-0.04 0.02 0.05 0.02 -0.04
methylene increment = 5.91 kcal/mol 2-methylpropane 2-methylbutane 2-methylpentane 2-methylhexane 2-methylheptane
2-Methylalkanes -37.02 f 0.13 -42.88 f 0.17 -48.91 f 0.24 -54.85 f 0.27 -60.95 f 0.36
-36.96 -42.93 -48.92 -54.91 -60.89
-0.06 0.06 0.01 0.06 -0.06
methylene increment = 5.98 kcal/mol OData were taken from ref 4 or the present work (2-hexanol, 2-heptanol).
the predicted values. Initially, they were included in the correlation, but obviously were in error, and forced the methylene increment to have a rather isw value. The data in Table X do not include these compounds in the correlation. It seems almost certain that the literature value for 1-heptanol is in error by about 1 kcal/mol, and that for 1-hexanol is in error by somewhat more that the assigned uncertainty interval. Experimental Section
Materials. 1-Heptene (Aldrich, 99%) was found to contain the 2- and 3-heptenes as the only impurities, and they were easily
3688
J . Phys. Chem. 1984, 88, 3688-3696 Calorimeter. The experiments were carried out using an automated calorimeter with a quartz thermometer as the temperature measuring probe.8 The previous design was modified by producing a 30-MHz signal from a harmonic of the IO-MHz master oscillator, and mixing it with the -28-MHz signal from the quartz thermometer. The -2-MHz signal thus produced contains all of the information and is sent to the data synchronizer and paired counters as previously described.8 It is then possible to use LSI counters, and to avoid the difficulties associated with transmitting and counting high frequencies. The computer system also was improved, and new calibration heater timing and power units were con~tructed.~ Equilibration of Trifluoroacetates. Mixtures of the trifluoroacetates which lay on opposite sides of the approximate equilibrium ratio were prepared and added to trifluoroacetic acid containing 0.25 M trifluoroacetic anhydride and 0.5 M methanesulfonic acid. The solutions were placed in N M R tubes and sealed under reduced pressure. They were placed in thermostats at the indicated temperatures (Tables I and VI) and periodically checked by N M R until the spectra were identical. In the case of the heptyl trifluoroacetates, the tubes were opened, diluted with methylene chloride, and the solution was washed with sodium bicarbonate solution until neutral. After drying over magnesium sulfate, the solutions were analyzed by GC using a 35 ft X l/s in. didecyl phthalate column at 90 OC. The response factors were determined with synthetic mixtures having compositions near that at equilibrium. With the pentyl trifluoroacetates, the product composition was determined from the 500-MHz N M R spectra. The protons adjacent to the trifluoroacetoxy group were well separated and the relative areas were determined by integration. An examination of spectra of mixtures of the two trifluoroacetates indicated groups of bands which also could be used for the analysis. The two sets of data gave comparable results.
separated by gas chromatography using a Carbowax column at 70 OC. The trans-2- and -3-heptenes (Chemical Samples Co., 99.8%, 99.9%) were found to contain insignificant amounts of the other isomers. cis-2-Heptene (Chemical Samples Co., 96%) had as its major impurity the 1-isomer, and it was removed by gas chromatography. cis-3-Heptene (Chemical Samples Co., 98%) was found to contain only the other 2- and 3-heptenes. A partial separation was effected by gas chromatography. Analysis was performed with a 25 ft. X l/s in. 10% XF-1150 analytical column. The purified cis-heptenes contained less than 1% of the other isomers, and the enthalpies of reaction are so close that even a 1% impurity would cause less than a 0.1% error in the measured enthalpy. Some of the compounds were obtained in 1-mL ampoules sealed under nitrogen. When freshly opened, the samples were used directly. Later, the contents were purified by gas chromatography to eliminate possible autoxidation products. No difference in enthalpy of reaction was observed. 1-Pentene and trans-2-pentene (Chemical Samples Co., 99.9%, 99.9%) were found to contain negligible amounts of impurities. cis-2-Pentene was obtained from two sources (Chemical Samples Co., 98%; Fluka, 99%) and was found to have several impurities. The second sample contained four impurities, two of which, 1pentene and trans-2-pentene, were present in less than 0.05%. Pentane (0.25 f 0.05%) was a third impurity. The fourth and largest impurity (0.66 f 0.12%) was shown by GC/MS to be an isomeric pentene. It was shown not to be 2-methyl-2-butene by its retention time, and therefore it is presumably 3-methyl-1-butene or 2-methyl-1-butene. The enthalpy of reaction of these compounds will be close to that of cis-2-pentene, and the impurity should cause less than 0.08% error in the observed enthalpy. The experimental result was corrected for the pentane impurity. 2-Heptanol (Chemical Samples Co., 99%) and 4-heptanol (Chemical Samples Co., 99%) were dried by heating to reflux over calcium hydride overnight and then distilling under nitrogen, collecting a center fraction. 3-Heptanol (Chemical Sample Co., 99%) was found by IR to contain a small amount of ketone, and therefore it was treated with a small amount of sodium borohydride until the spectrum showed that the carbonyl band had disappeared. It was then treated as described above. The reaction solvent was prepared as previously described.'
Acknowledgment. This investigation was supported by the Office of Basis Energy Sciences, Department of Energy. (8) Wiberg, K. B.;Squires, R. R. J . Chem. Thermodyn. 1979, 11, 773. (9) The details of the modified calorimetric system may be found in the Ph.D. Thesis of Eric Martin.
Muonium Formation in Vapors Donald J. Arseneau, David M. Garner, Masayoshi Senba, and Donald G. Fleming*+ Department of Chemistry and TRIUMF, University of British Columbia, Vancouver, B.C., Canada, V6T 1Y6 (Received: February 13, 1984)
The fractions of positive muons thermalizing in vapors either as the polarized muonium atom (fM)or in diamagnetic environments cfD) have been measured in water, methanol, hexane, cyclohexane, the chlorinated methanes, and tetramethylsilane, in the pressure range from -0.1 to -2.5 atm. There is a marked difference in every case in comparison with the corresponding fractions (PMand PD) measured in condensed media, with -80% of incident muons forming polarized muonium in the vapor phase compared to -20% in the corresponding condensed phases. CCI4 appears somewhat anomalous in that it shows an unusually small muonium fraction in the vapor (fo fM = 0.5)and an unusually large diamagnetic fraction in the liquid (PD= 1.0). The vapor-phase results can be understood in terms of a charge-exchange/hot atom (ion) model, providing also a likely explanation for observed pressure-dependentfD's in hexane, cyclohexane, and tetramethylsilane at low (C0.5 atm) pressures in terms of termolecular processes, in analogy with some hot tritium studies. The present vapor-phase results indicate that hot atom reactions cannot account for more than about 30% of the much larger diamagnetic fractions seen in condensed phases, strongly suggesting therefore that radiation-induced spur effects play a dominant role in determining thermal muon fractions in condensed media.
-
Introduction Since the earliest experiments in which a spin-polarized beam of positive muons (b+) were stopped in matter, attempts have been made to account for the polarization of the thermalized muon
'1983-1984 John Simon Guggenheim Fellow. 0022-3654/84/2088-3688$01.50/0
ensemble. In 1958, Swanson found that the ensemble polarization depended on the chemical identity of the stopping target.' In the 1960%it was recognized that the chemistry of muonium (Mu fi+e-) played an important role in determining the thermalized (1) R.A. Swanson, Phys. Reu., 112, 580 (1958).
0 1984 American Chemical Society
