A NEWISODIELECTRIC METHOD FOR MEASUREMENT OF DIPOLEMOMENT
pounds based on previously determined or estimated vibrational constants are in error. (7) Only limited experimental data are available for the vibrational constants of group 11-a halides. Any method of entrapolating force constants from one compound to another is of dubious reliability until such procedures can be checked against more extensive experimentally derived frequencies. Future
3217
matrix isolation studies on the alkaline earth halides should be extended to the far-infrared region to encompass the bending frequencies. In addition, wavelength measurements accurate to at least 0.1 cm-1 should be made so that advantage can be taken of isotope shifts in order to calculate bond angles. Acknowledgment. The author wishes to thank the Army Office of Research for supporting this research.
A New Isodielectric Method for Measurement of Dipole Moment in SolutionlV2
by R. Thomas Myers and Viola M. L. Sun Department of Chemistry, Kent State University, Kent, Ohio 4.4840
(Received March 8, 1966)
The compound whose dipole moment is to be measured is dissolved in a solvent such that the dielectric constant does not change on addition of this solute. Application of the Kirkwood-Onsager equation to this process at constant dielectric constant yields an equation connecting the physical properties of the solvent and solution (dielectric constant and densities) with the molar polarization of the solute. The dipole moment of the solute in the solution can then be calculated, using the correlation parameter of the solvent and then the moment calculated for the gas phase by use of the Onsager relation. The solvent consists of mixtures of dioxane and ethylene carbonate, with a dielectric constant variable over a wide range and constant molecular weight. That mixture for which the dielectric constant is constant on adding the solute is determined by interpolation. The method is more accurate and more straightforward than the usual procedure, in which a solvent of low dielectric constant is used, and the data are extrapolated to infinite dilution. Physical properties of the dioxane-ethylene carbonate system are also included (density, dielectric constant, and refractive index).
Introduction The customary procedures for determination of dipole moment involve the measurement of dielectric constant of dilute solutions of the polar substance to be measured in a nonpolar solvent. Some procedure is used to extrapolate the data back to zero concentration. This is frequently an extrapolation of the molar polarization of the solute to zero concentration.a At infinite dilution the Debye equation is assumed to apply, and the dipole moment is calculated by the use of this equation. There are fundamental flaws in this and similar procedures. The first is that a linear extrapolation is used
for data which are not strictly linear. The second is that the Debye equation applies to the gaseous state, and not actually to liquid solutions. The third is that a solution of a strongly polar substance in a nonpolar solvent is expected, by its very nature, not to be ideal. It follows that dipole moments measured in solution (1) Supported in part by the Directorate of Chemical Sciences of the Air Force Office of Scientific Research, Contract AF 49(638)-641. (2) Based in part on material submitted for the Master’s thesis of V. M. L. Sun. ( 3 ) See, e.g., C. P. Smyth in “Technique of Organic Chemistry,” A. Weissberger, Ed., Vol. I, 2nd ed, Interscience Publishers, Inc., New York, N. Y., 1949.
Volume 70, Number 10
October 1966
R. THOMAS MYERSAND VIOLAM. L. SUN
3218
frequently differ markedly from data obtained on gaseous molecules. The method proposed here is designed to obviate all of these objections. A linear interpolation of data is used, which is expected to be linear; the Kirkwood-Onsager equation for dielectric constants of liquids is used, and the polar solute is dissolved in a solvent of equal polarity, thus assuring more ideal behavior. As expected, there is better agreement between results in the liquid and gaseous state. A crucial part of this new approach was the choice of a solvent whose dielectric constant may be varied to match the molar polarization of solutes. The solvent consists of mixtures of dioxane and cyclic ethylene carbonate, with variation of dielectric constant from 2.3 to about 60. These two compounds have the added advantage of having molecular weights which differ by only 0.06%, so that the molecular weight of mixtures is always constant.
Theoretical Development The Kirkwood-Onsager equation4
P =
(E
- 1)(2e 9E
+ 1) M
4rN
gp2
3
3kT
-=----(y+-=
d
Pa
+ 47rNgp2 ___ = P a + Pp 9kT
The JOUTTZU~ of Physical Chemistry
+
It will be noted that the left side of the above equation contains quantities pertaining only to the solute and the right side contains only experimentally determined quantities. By use of eq 1 we can calculate the value of the dipole moment of the solute, provided that g is known. The dipole moment of t'he molecule in solution is calculated from the gas value by t,he Onsager equation.' (em
P = PO
+ 2)(2E + 1) 3(2e
+
(4
em)
It was stated previously that a linear interpolation of data is used to obtain figures to be used in the calculations. (For details see the Experimental Section.) This graph for interpolation can be shown to be linear. For the solvent mixture PI =
(E1
- 1)(2€l + 1)Mi
-
9Eidi
(1)
is applicable to liquids since it takes into account the hindrance of rotation due to neighboring molecules. The correlation parameter g shows this hindering effect. However, the evaluation of g requires a knowledge of the structure of a liquid, which in general is not available. Consequently, the Kirkwood-Onsager equation per se is not in general a valid way to calculate dipole moments when applied to pure liquids. Osters has concluded, for polar solutes in nonpolar solvents, that the correlation parameter of the solute is a smooth function of mole fraction of solute and approaches the value 1 in dilute solutions.6 We shall use such graphs of correlation parameter in the computation of dipole moments. We choose a solvent of such dielectric constant that there is no change in the dielectric constant on adding the solute. We assume that the molar polarizations of solvent and solute are additive. For the solvent
For the solution
In these equations the subscripts 1, 2, and 12 refer to solvent, solute, and solution, respectively, and X is the mole fraction. Substituting (2) into (3), remembering that MI, = X I M I XZM2and rearranging, yields
Pel
- 1 - (l/El>lM1 2ElM1 -9di
9di
or P I
Plz a
(6)
el, if e is fairly large. Likewise for the solution, e2. However, we have assumed molar polariza-
0:
tions to be additive, so
AP = Pi2 - Pi = XlPi
+ XZpz - P1 =
+
Pl(X1 - 1) X Z 2 (7) However, X1 and XZare constant in any series of measurements, and X2P2 is constant, so AP is a linear function of P1. It follows from the previous relations that Ae is a linear function of €1. Experimental Section The measurement of dielectric constant was made by using a General Radio Co. Type 821-A Twin-T impedance circuit and Type 1330-A bridge oscillator, and Hallicrafters' S-85 receiver as detector. The Twin-T bridge was calibrated by the General Radio Co. The dielectric constant cell followed the design of (4) J. G. Kirkwood, J . Chem. Phys., 7 , 911 (1939). (5) G.Oster, J . Am. Chem. SOC.,6 8 , 2036 (1946). (6) The true situation is somewhat different from the conclusions of Oster. This will be the subject of a separate communication. (7) L. Onsager, J . Am. Chem. Soc., 58, 1486 (1936).
A NEW ISODIELECTRIC METHODFOR MEASUREMENT OF DIPOLE MOMENT
Conner, Clark, and Smyth.s The inner surfaces of the cell were gold plated. The cell was calibrated by use of air and pure water, dichloromethane, dioxane, l-propanol, dimethylformamide, 1,2-dichloroethane, acetone, and methanol. A graph of dielectric constant against capacity of the cell was linear, with the point for water on the line. Subsequent checks on the calibration curve were made by merely measuring the capacity of the empt,y cell and that of the cell when filled with water. It was found that if the cell was left plugged into the capacity bridge connector at all times, except when in use, its capacity remained constant, within experimental error. In fact, over a period of 3 years the measured i:apacit,ance of the cell filled with water was 512.7 f 0.2 pf. Refractive index was measured with a Bausch and Lomb precision Abbe refractometer. Refractive indices of solid solutes, which cannot be measured directly by use of the refractometer, were calculated from refractive index and density of solutions. The LorenzLorentz molar refraction of the solution was calculated and assumed to be the sum of solvent and solute, respectively. The density for solute was calculated on the assumption that molar volumes are also additive. The result is the refractive index for a hypothetical pure liquid solute at 25’. The validity of this procedure is shown in Table I. Small errors in refractive index have little effect on calculations using eq 5. Temperature was maintained at 25 f 0.03’. A 10-cc hypodermic syringe was used for transferring samples in order to protect them from moisture of the air. It was especially useful for filling the pycnometer. All materials (except ethylene carbonate) were of reagent or spectroscopic grade from Eastman or hfatheson Coleman and Bell. The ethylene carbonate was recrystallized by cooling to -15’ at least three times from a 1.05:1 by volume mixture of chloroform and carbon tetrachloride. (A typical crystallization used 210 ml of chloroform, 200 ml of carbon tetrachloride, and 200 ml of ethylene carbonate.) I n order to prevent condensation of moisture on the cold crystals, an atmosphere of very low humidity was maintained in the Buchner funnel until the crystals came to room temperature. Excess solvent clinging to the crystals was removed in a vacuum desiccator by use of a water aspirator or by evaporation in the room if the humidity was below 30%. If the conductances of the solutions of ethylene carbonate in dioxane were too high to permit measurement of dielectric constant, then it was recrystallized until a product of suitably low conductance was obtained. It appeared that absence of moisture was the most important factor. A solvent mixture was made up whose dielectric
3219
Table I: Summary of Experimental Results Obtained from Graphs of Data for Individual Compounds: 4 Mole % of Solutes d% of solvent
of soh,
n26D Of
uolute
d254
€
dt
dl2
6.38 7.28 7.78 7.00 9.95 11.72 14.20 17.75 22.75 39.25 38.5
1.0548 1.0595 1.0623 1,0572 1.0732 1.0864 1.0928 1.1089 1.1279 1.1859 1.1836
1.0611 1.0696 1.0703 1.0572 1,0808 1.0968 1.0937 1.1042 1,1161 1.1844 1.1846
1.4572 1.4368 1.4412 1.5180 1.4213 1.588“ 1 .61gb 1.5299 1.3563 1.379gc 1.5499
Calculated from molar refraction, as indicated in text. Calculated from molar refraction. Agrees fairly well with value of 1.605 interpolated from data for the supercooled liquid, taken from Beilstein. J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Elsevier Publishing Co., New York, N. Y., 1950, p 578. O
constant was expected to be near the correct value, and its dielectric constant, density, and refractive index were measured. (The dielectric constant of the solvent mixture is near that of the solute if the latter is liquid. Solid solutes require more experimentation to obtain solvent mixtures of suitable dielectric constant.) Then a fixed mole percentage (either 4 or 10%) of solute was added, and the measurements were repeated. The difference in dielectric constant, A e = e12 - el, was determined. The measurements were repeated for at least two other solvent mixtures of slightly different composition, preferably including one with Ae of opposite sign. Graphs of Ae, dl, dl2, ( T L ~ ~ Dand ) ~ , (7225~)12 against el were constructed, and the values of the variables were read off where Ae is zero. This will then fit the conditions imposed in eq 4. These graphs were always linear, provided Ae was no larger than *0.5. In practice we chose several solutes of known dipole moment (in the gaseous state) and calculated P 2 / M 2 . This was then plotted against the experimentally determined quantity on the right side of eq 4 called the e function. These compounds of known dipole moment were used to establish an empirical test of eq 4. We may assume that the correlation parameter of the solute was essentially the same as that for the ethylene carbonate in the solvent, since the structure of the solvent is to a large extent determined by the ethylene carbon(8) W. P. Conner, R. P. Clark, and C. P. Smyth, J. Am. Chem. Soc., 72, 2071 (1950).
Volume 70, Number 10 October 1966
3220
R. THOMAS MYERSAND VIOLAM. L. SUN
ate. It is not surprising then to find that the calibration curves are essentially straight lines of slope near 45O.
The results of the interpolation of the graphs for individual solutes are summarized in Tables I and 11. From these data the values of the e function were calculated for each compound used as solute and are listed in Tables 111 and IV. Included also in these latter t,ables are the values of polarizations, dipole moment, etc., used in the calculations. The properties of the dioxane-ethylene carbonate solvent system are given in Table V. These values
Table IV: Calculated Values of the E Function and P2IM.2, and Data Used in the Calculation: 10 Mole Toof Solutes E
Compd
Function
PdMz
1.03 1.10 1.19 1.28 1.29 1.52 1.81 2.58 3.62 5.67 6.74 6.96
1.17 1.21 1.33 1.46 1.60 1.20 2.27 2.58 3.57 5.25 8.00 7.68
Table 11: Summary of Experimental Results Obtained from Graphs of Data for Individual Compounds: 10 Mole % ' of Solutes d% of
Compd
E
solvent, di
soln, dri
n-CeHtaBr n-C5HIlBr n-C4HgBr wcaH.~Br p-C1CaH&Ha CHeCla p-ClCeH4NOz ( C&)eCO CsH5COCHa CHsCOCHa CHaNOa CaH5NOz
5.92 6.55 7.27 8.29 6.70 9.65 11.65 13.35 17.20 22.4 37.60 38.1
1.0519 1.0536 1.0590 1.0644 1,0572 1.0718 1.0824 1.0887 1,1060 1.1244 1.1806 1.1821
1.0675 1.0749 1.0835 1.0947 1.0572 1.0920 1.1204 1.0915 1.0942 1.0988 1.1769 1.1845
Pa
39.6 33.3 30.0 24.8 39.7 18.7 41.0 60.7 37.9 17.0 15.2 35.9
of solute
nB(D
1.4572 1.4412 1.4368 1.4313 1.5180 1.4213 1.588" 1.618' 1.5299 1.3563 1.3799' 1.5499
See footnote a in Table I. 'See footnote b in Table I.
' See footnote c in Table I.
Table 111: Calculated Values of the E Function and P2/M2, and Data Used in the Calculation: 4 Mole % of Solutes
Table V: Properties of Dioxane-Ethylene Carbonate Solvent System
W t % of ethylene carbonate"
Dielectric constant
da5k
0 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
2.209 4.15 6.42 9.00 11.79 14.90 18.33 21.95 25.75 29.75 34.12 38.88
1.0282 1.0415 1.0548 1.0683 1.0820 1.0960 1.1102 1.1246 1.1392 1,1540 1.1690 1.1843
a
n25D
1.4202 1.4206 1.4210 1.4215 1.4219 1,4223 1.4226 1,4229 1.4232 1.4234 1.4236 1.4238
P
6.35 6.56 6.69 6.77 6.82 6.86 6.89 6.92 6.93 6.95 6.96
Approxb correlation psrameter, o
1.01 0.95 0.95 0.96 0.98 1.01 1.03 1.05 1.07 1.10 1.13
This is, of course, almost numerically identical with mole To.
'Approximate because the correct moment for ethylene carbonate
E
Compd
2.79 2.78 2.80 2.82 2.90 2.07 4.02 4.55 4.37 3.70 4.55 6.28
See footnote for Table 111.
a
d% of
P
2.17 2.20 2.17 2.17 2.16 1.59 2.77 3.06" 3.06 2.88 3.46 4.25
Function
PdMz
1.12 1.19 1.34 1.35 1.59 2.13 2.75 3.73 5.74 6.95 7.02
1.16 1.33 1.27 1.61 1.15 2.27 2.62 3.61 5.23 8.06 7.45
w
2.17 2.17 2.20 2.16 1.59 2.77 3.06" 3.06 2.88 3.46 4.25
P
Pa
2.80 2.80 2.86 2.91 2.07 4.02 4.56 4.38 3.69 4.55 6.29
39.6 30.0 33.3 39.7 18.7 41.0 60.7 37.9 17.0 15.2 35.9
Estimated. The measured moments for acetophenone and benzophenone in benzene are almost the same, so the moments in the gas phase are assumed to be equal.
in the gas phase is unknown. I n this calculation the moments of dioxane and ethylene carbonate were assumed to be zero and 5.25, respectively, and the molar polarizability to be 25.0 and 18.0. The index of refraction of (hypothetical) liquid ethylene carbonate was calculated from mole refraction of the solution to be 1.426, giving 2.03 for .,E (It should be noted that the value of 4.51 tabulated by McClellan is actually for vinylene carbonate.)
were obtained by plotting the data on large graph paper and drawing the best smooth curve through the points. The data obtained from the graphs were further smoothed by use of first and second differences. The calculation of the correlation parameter was by the
A KEWISODIELECTRIC METHODFOR MEASUREMENT OF DIPOLEMOMENT
3221
Table VI : Comparison of Accuracy of Dipole Moments Determined in Solution, as Compared to Moment Determined in Gas w (4 mole
Substance
PO (lit.)
2.17 2.20 2.17 2.17 2.16 3.06* 3.06 2.88 3.46 4.25 1.62 2.77
From McClellan’s compilation, ref 11.
%I,
present method
7% dev
2.22 2.32 2.08
$2.3 $5.4 -4.1
...
...
1.97 3.20 3.18 3.08 3.26 4.20 1.91 2.73
-8.8 $4.6 +3.9 $6.9 -5.8 -1.2 $17.9 -1.4
* Estimated;
see text.
method of O ~ t e r . The ~ high value of the correlation parameter at 5 mole % is no doubt real. One of the difficulties of the present research was finding suitable solutes. These must first of all have accurately measured values for dipole moment in the gas phase and give a good range for P z / M ~ .In addition they must, not tend to form hydrogen bondslo with the solvent and should have varied shapes and sizes. One can find few compounds meeting these criteria and, therefore, giving a valid test of the method. It was necessary to use one compound (benzophenone) with estimated dipole moment. The accuracy of the procedure is demonstrated in the followingway. The values of P2/M2 for each compound were calculated, assuming that the correlation parameter for the solute was the same as that of the ethylene carbonate in the solution. Correlation parameters were interpolated from a graph of data from Table V. The moment of ethylene carbonate was assumed for this purpose to be 5.25. If this were the correct moment for ethylene carbonate then the result should be a straight line through the origin with a slope of 1. In practice, the data were fitted by the method of least squares to an equation of the form Pz/MZ = M ( t function). The values of M were 1.04 and 1.07 for 4 and 10 mole % solute, respectively. Then the experimental E function was assumed to be correct, and the corresponding value of P2/M2 was calculated, i.e., as if the point lay on the line. From this the moment in the gas phase was computed. These calculated moments are compared to literature values of moments” in the gas phase in Table VI. In the same place a comparison is also made with the average
w (10mole %), present method
2.15 2.16 2.11 2.09 1.96 3.17 3.19 3.10 3.27 4.18 1.90 2.53
% dev
-0.9 -1.8 -2.8 -3.8 -9.3 +3.6 +4.2 +7.6 -5.5 -1.6 $17.3 -8.7
fi in benzene4
1.99 2.00 1.97 1.97 1.89 2.98 2.93 2.69 3.13 3.93 1.53 2.60
% dev
-8.3 -9.1 -8.3 -9.2 -12.5 -2.6 -4.2 -6.6 -9.5 -7.5 -5.9 -6.1
moment” of the compounds as obtained in benzene solution. It can be seen that the present method gives results for dipole moment which are closer to the values in the gas phase. This is even more impressive when one realizes that the figures given for the moment in benzene solution are an average for several investigators. On examining the individual values making up any one of these averages one observes very wide deviations. This either indicates that the extrapolation is not linear, in which case different experimenters arrive at different extrapolated values, or means that errors in measurement are so high at the low concentrations used that the exact position of the straight line is in doubt. In any event the precision of measurements by different investigators is not high. On the other hand, the close agreement of moments determined by the present interpolation method with the average dipole moment is good indication of its high precision. It also appears that the method given here has nearly reached the maximum accuracy, or, in other words, averaging the results for several investigators will not give much improvement. This is clearly shown by the good agreement between the moments calculated for the 4 and 10 mole % solutions. One possible way to improve the accuracy may be to go to smaller concentrations of (9) G. Oster, J . Am. C h a . SOC.,6 8 , 2036 (1946). (10) Solutes which may form hydrogen bonds will be the subject of a separate study. Oster’s calculations show greater variability for the correlation parameter for hydrogen-bonding solutes. (11) Practically all the moments used were obtained from A. L. McClellan, “Tables of Experimental Dipole Moments,” W. H. Freeman and Co., San Francisco, Calif., 1963.
Volume 70.Number 10 October 1066
3222
T. S. CARLTON, J. R. STEEPER,AND R. L. CHRISTENSEN
--
solute; however, there is the limitation in the ability to measure accurately the change in dielectric constant. The advantages of the method are : dipole moments are obtained which are more nearly equal to values obtained on the gaseous compound; extreme accuracy is not needed for dielectric constants; the data are treated in a simple and straightforward way (in par-
ticular an interpolation is used instead of an extrapolation) ; and, apparently, high precision of measured dipole moment. Possible disadvantages are: insufficient solubility of compound being measured, and reaction of compound with solvent (e.g., if it is a strong Lewis acid or can hydrogen bond with solvent). These can be obviated in many cases by changing the solvent system
Rates of Hydrogen Abstraction from Methanol by CF, Radicals
by Terry S. Carlton, J. Rodger Steeper, and Ronald L. Christensen Department of Chemistry, Obedin College, Oberlin, Ohio 4.4074
(Receieed March 21, 196‘6)
Hexafluoroazomethane was photolyzed in the presence of gaseous CHaOH plus CD30D, CH3OD plus CDSOD, CH, plus CD30D, and CD3OH. From the relative rates of formation of CF3H and CF3D, rate constants and Arrhenius parameters were determined for abstraction by CF3 radicals of the hydroxyl and alkyl hydrogens in CH3OH. The activation energy for abstraction of each kind of hydrogen is 8.3 kcal/mole. The preexponential factor for alkyl hydrogen abstraction is 10 times the factor for hydroxyl hydrogen. The results are compared with those for abstraction from CH30H by CH3 and CD3 radicals. A dipolar model is used to explain trends in the relative activation energies for abstractions by CH3 and CF3.
Introduction Arrhenius parameters have been reported for a large number of reactions in which CH3 abstracts hydrogen atoms from substrate molecules’ and for a smaller number of reactions in which CF3 abstracts hydrogen.2 None of the CF3 reactions involved hydrogen abstraction from a functional group. This paper reports the Arrhenius parameters for abstraction by CF3 of the hydroxyl and alkyl hydrogens of methanol and compares these parameters with those for the corresponding abstractions by CH,. Experimental Section The CH30H (Baker and Adamson reagent grade) was dried by passing the vapor through Drierite and purified by bulb-to-bulb distillations. The CD30D, CD30H’ and hexafluoroazomethane Sharp and Dohme) were used without further puriThe Journal of Physical Chemistry
fication. Xmr showed that 0.3% of the methyl hydrogen in CD30D and CD30H was protium, as was 0.4% of the hydroxyl hydrogen in CD30D and 0.3% in CH30D. CF3H and CH, (Matheson) were used without further purification, since the infrared spectra revealed no impurities. 3 , 4 CF3D was synthesized from CF3H by shaking the latter with two successive por(1) See, for example: (a) A. F. Trotman-Dickenson, “Gas Kinetics,” Butterworth and Co. Ltd., London, 1955, p 199; (b) S. W. Benson and W. B. DeMore, Ann. Rea. Phys. Chem., 16, 397 (1965). (2) See, for example: (a) H. Carmichael and H. S. Johnston, J . Chem. Phys., 41, 1975 (1964); (b) G. 0. Pritchard, H. 0. Pritchard, H. I. Schiff, and A. F. Trotman-Dickenson, Trans. Faraday SOC., 52, 849 (1956); (c) W. G. Alcock and E. Whittle, ibid., 61, 244 (1965); (d) W. G . Alcock and E. Whittle, ibid., 62, 134 (1966). (3) (a) E. K. Plyler and W. S.Benedict, J . Res. Natl. Bur. Std., 47, 202 (1951); (b) H. D. Rix, J . Chem. Phys., 21, 1077 (1953). (4) American Petroleum Institute, Research Project 44, Infrared Absorption Spectrogram NO. 528, 1946.
