NOTES
3336
mately 10% of an electron in excess of neutrality on each fluorine atom. It is gratifying that it was possible to compute the observed dipole moment with a charge distribution so close to the one preferred by the force constant arguments. The lone-pair model is the only one that has been put forth that correctly accounts for the bend-bend interaction force constant found for KF3. Certainly other effects, and in particular orbital-following effects, contribute to the potential energy. Using R, = 0.6 and R, = 3.0 gives B = +O.l in King’s2 eq 9. This would imply P,, = f0.7 and Frat = *0.7. These are larger force constants than those preferred by the analysis above, but assuming contributions to the potential energy of up to a half by orbital-following effects permits accounting for the observed force constants, in particular, different values for P,, and P,,‘. Attempting to estimate this quantitatively is unrewarding since it corresponds to fitting ten parameters to five pieces of data. We may also note that i t seems
possible to account for the force constants assuming a bent-bond model.27 This work implies that the charge on the fluorine atoms is appreciably less than other estimates. Fitting the dipole moment using one-electron theory requires assuming that a little less than two electrons reside in the lone pair or equivalently assuming the lone pair is richer in s character than required by the orthogonality relation.
Acknowledgment. This research was supported by the Air Force Office of Scientific Research under Contract AF49(638)-1135. We are also grateful for the assistance and cooperation of the Rocketdyne Research Department and to A h . Dee Braniion for typing the manuscript . (26) This is much less satisfactory than using a great number of similar molecules or isotopic data. However, it must suffice in this case since the first do not exist and the isotopic shifts for nitrogen are so small as to provide no additional information. (27) E. c. Curtis, to be published.
NOTES
Estimated Activation Energies for the Four-Center Addition Reaction of
H2, HX, and X2 to Acetylenes by Sidney W. Benson and Gilbert R. Haugen Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park, California (Received March 2.9, 1366)
In this note, we describe the application of an electrostatic model. to predict the activation energy of the four-center addition reactions of acetylenes, AA* -C=C-+ -CA=CA*-. The transition state is considered an intimate semi ion pair with an equivalent charge separation of f‘/z formal charge. The energy of activation can be equated to the electrostatic energy of interaction of point dipoles.’
+
E&
{
e2 r 2 A A * = - -
8
~ A A *
+--
r2BB* ~ B B *
Table I Bond ruptureda
CH=CH CHaC=CH CH3C-CCHa
TOAA*~
1.21 1.21 1.21
UAA*
5.12 8.02 10.9
Bond formedd
C-H
C-I C-Br C-C1 C-F
TOAB~
1.07 2.09 1.89 1.72 1.33
a The triple bonds in the acetylenes are assumed to be fiveelectron bonds in the transition state. We have equated this transition-state bond length with the carbon-carbon distance of 5/2 bond order (1.25 A): L. Pauling, “Nature of the Chemical Bond,” Cornel1University Press, Ithaca, N. Y., 1960. Groundstate bond lengths were obtained from L. E. Sutton, “Table of Interatomic Distances,” Special Publication No. 11, The Chemical Society, London, 1958. c ~ A A *represents the ground-state longitudinal polarizability of the molecule (see ref 1 for details Transition-state bond lengths = T O 1.0 A. and sources).
+
The distances rAA*, ?+BB*,and re are the transition state bond lengths A-A*, B-B*, and the average of the equi(1) 9. W. Benson and G. R. Haugen, J . Am. Chem. SOC.,87, 4036 (1965).
The Journul of Physical Chemistry
NOTES
3337
Table I1 Reaction' AA* BB* products
+
-
Etcta,"lCd,'
EAA*~
EBB*^
Eintb
E',
0°K
E,,tcglcd,',c
298OK
EaCt"bad,'
298'K
AE',~ 298OK
a-1 H F + C H i C H CH& i CHO CHaC i CH' CH& i CCHa
75.4
12.7 8.09 8.09 5.95
9.64
25.2
53.3 48.7 48.7 46.6
52.1 47.5 52.5 45.4
a-2
37.0
12.7 8.09 8.09 5.95
9.50
2.63
37.6 33.0 33.0 30.9
36.4 31.8 36.8 29.7
-24.0' -20.2' -20.23 -17.Q2
32.2
12.7 8.09 8.09 5.95
9.35
1.06
34.5 29.9 29.9 27.8
33.3 28.7 33.7 26.6
-26.23 -24.2' -24.28 -20.92
25.5
12.7 8.09 8.09 5.95
9.44
0.16
28.6 24.0 24.0 21.9
27.4 22.8 27.8 20.7
38.5
12.7 8.09 5.95
10.0
0.00
41.2 36.6 34.5
40.0 35.4 33.3
81.5
12.7 8.09 5.95
11.3
0.00
82.9 78.3 76.2
81.7 77.1 75.0
36.0
12.7 8.09 5.95
9.89
0.00
38.8 34.2 32.1
37.6 33.0 30.9
-48.28 -46.6' -43.92
31.0
12.7 8.09 5.95
9.52
0.00
34.2 29.6 27.5
33.0 28.4 26.4
-36.18 -33.2' -30.42
22.6
12.7 8.09 5.95
9.21
0.00
26.1 21.5 19.4
24.9 20.3 18.2
+ + + HCl + CH CH + CHIC i CHe j
+ CHaC i CHI + CHaC CCHa HBr + CH CH + CHaC i CHe + CHaC i CH' + CHaC i CCHa HI + C H i C H + CHaCiCH' + CHIC i CH' + CHaC i CCHa HH + C H i C H + CHaCiCH + CHaCiCCHa FZ+ CH i CH + CHaC i CH + CHaC i CCHa Clz + CH i CH + CHsC i CH + CHaC i CCH, Brf + CH i CH + CHaCiCH + CHaC i CCHa IO + CH i CH + CHaC i CH + CHaC i CCHa j
a-3
a-4
a-5
a-6
a-7
a-8
a-9
j
L25 f lg 8 3 5 f 3'
-41.1' -38.g4 -36.04
' re, the distance between the dipole centers (in Angstroms) is a-1, 2.20; a-2, 2.39; a-3, 2.47; a-4, 2.55; a-5, 2.07; a-6, 2.32; a-7, 2.66; a-8, 2.80; 1-9, 2.96. (See ref 1 for details.) 'See ref 1. Etherma1 is - 1.2 kcal/mole for all the reactions tabulated in this table. Standard heat of reaction a t 298°K. aE" (298°K) was calculated from the following tables of thermodynamic properties: (1) National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1950; (2) bond additivity properties, S. W. Benson, "The Foundations of Chemical Kinetics," McGraw-Hill Book Co., New York, N. Y., 1960; (3) group additivity properties, S. W. Benson and J. H. Buss, J . Chem. Phys., 29, 546 (1958); (4) American Petroleum Institute, Research Project 44 (1953). "Anti-Markovnikov" addition; Ep,i,t charge is +5.0 kcal/mole (see ref 1). "Markovnikov" addition; Epointcharge is zero (see ref 1). J. E. Douglas, B. S. Rabinovitch, and F. S. Looney ( J . Chem. Phys., 23,315 (1955)) noted the absence of HZand DZin their investigation of the cis-trans isomerization of CHD=CHD a t 820°K. This implies that the molecular rate is less than or equal to 10% of the observed isomerization rate. This requires a lower limit of 25 kcal/mole for the activation energy of the hydrogenation reaction (the molecular rate was assumed to have the form 1013-E/e). The investigation by K. Kuratani and S. 13. Bauer (J.Am. Chem. SOC.,87. 150 (1965)) of the rate of exchange of CZHZand DZ (a future publication will describe a possible chain mechanism for t h i exchange) Szwarc ( J . Chem. Phys., 17, 284 (1948)) investigated the also places a lower limit of 25 kcal/mole on the hydrogenation reaction. pyrolysis of CHsCH=CH2 a t a mean temperature of 1050'K. The unobserved molecular rate cannot be greater than 10% of the observed rate of pyrolysis. A reasonable rate for the molecular dehydrogenation would be 1013.0-EEn/e,consequently establishing a lower limit for Em of 77 kcal/mole and a lower limit for hydrogenation of 35 kcal/mole.
'
'
Volume 70, Number 10 October 1966
3338
NOTES
librium distances (see eq 2 ) A-B and A*-B*, respectively.
CYOAA* and CYOBB* are the longitudinal molar polarizations in the ground state. CYAA* and ~ B B *represent a characteristic average for the longitudinal molar polarization between the ground and the transition states. ~ O A A * is the ground-state dipole moment. Values of the parameters and the predicted activation energies are tabulated in Tables I and 11,respectively. The activation energy for the molecular addition to acetylenes (AA* -C=C+ -CA=CA*-) is about 1.5 kcal/mole smaller than that for the corresponding olefin.' Accordingly, the chemistry of the acetylenes must be very similar to that observed for the olefins. In particular, the ground state of the acetylenes and the olefins ought to contain an identical fraction of "ionic" character. The comparison of the predicted and observed activation energies is unfortunately impeded by the lack of experimental rate parameters for the molecular addition. Nevertheless, the kinetic studies on the hydrogenation of acetylenes and the dehydrogenation of olefins permit lower limits to be established for the molecular addition of hydrogen to acetylenes. These are all in good agreement with the predicted values. In ref 1, the trends in the molecular parameters of the addition reactions of the olefins were adequately calculated with the electrostatic model. Drawing an analog between the olefin arid the acetylene systems places an error limit of =k2 kcal/mole on the calculated activation energies presented in this note. Acknowledgment. This work was supported in part by Grant No. AP 00353 from the Division of Air Polution, Public Health Service, of the U. S. Department of Health, Education, and Welfare.
theoretically, using the model of rigid charged spheres in an electrostatic and hydrodynamic continuum. The principal result of the paper mentioned above was to establish that retention of the full Boltzmann factor without approximation leads directly to a term in the conductance equation, which is due to ionic association. I n this note we want to discuss a new conductance formula given by the authors in other papers2 and to compare it with the Fuoss-Onsager and Bjerrum theories. Our recalculation is based on the following equations for the current j and the binary distribution function F,b
n
+
+
vab'),
+
=
The Journal of Physical Chemistry
+ApZ
In
p
+ +Ap2QE'(b)
xab; x 2 = 8ane2/DkT
+ R2)e21-'
A = R1RzDkT[3ao(R1 QO
I n a recent paper by Fuoss and Onsager,' the conductance of symmetrical electrolytes was investigated
+
Vab =
p =
On the Conductance of Symmetrical Electrolytes
Institute of TheoreticaZ Physics, University of Rostock, Rostock, East Germany (Received March 83,1966)
/
ebE kT (b/br) In F a b (b/br)(V,b if 1" < a; V a b ' = eaeb/Dr, V n b ' = 0 if r > a, r = xa - xb, 17 is the viscosity, D is the dielectric constant, R, is the friction constant, a is the contact distance, and n, is the concentration. These equations were derived by means of statistical consideration~.~The distribution functions and the conductance were calculated up to all powers in the Bjerrum parameter b = e2/DkTa. With respect to the concentration, all of the terms of powers higher than n and n log n, respectively, were neglected. For the conductance of symmetrical electrolytes (e2 = -el), the explicit calculation gives the formula2 where Kb'
&p2QRe1(b) - Ap -
by W. Ebeling, W. D. Kraeft, and D. Kremp
,
~~
= (nle12/R1)
+ (n2ez2/Rd
~
(1) R. M. Fuoss and L. Onsager, J . Phys. Chem., 66, 1722 (1962); 67, 621, 628 (1963); 6 8 , 1 (1964); R. M . Fuoss, L. Onsager, and J. F. Skinner, ibid., 69, 2581 (1965). (2) D. Kremp, t o be published (part I ) ; D. Kremp, W. D. Kraeft,
W. Ebeling, to be published (part 11). (3) D. Kremp, Ann. Physik, in press; W. Ebeling, Z . Physik. Chem.
(Leipaig), 224, 321 (1963); 225, 15 (1964).
