J . Phys. Chem. 1989, 93, 3304-3306
3304
Discussion Low in the flame the temperature is too low for significant rates of formation of polycyclic aromatic hydrocarbons from acetylene, molecular hydrogen, or hydrogen atoms, even though the formation reactions are thermodynamically spontaneous. Higher in the flame appreciable amounts of polycyclic aromatic hydrocarbons are formed, but they go through maxima because the temperatures and partial pressures of reactants that form these species become less favorable higher in the flame. The fact that the polycyclics go through a maximum is a good indication that they are at equilibrium in the neighborhood of the maximum. Calculations based on mechanism 1 predict the heights of zero net rate of formation of CloHBand C14H10 within experimental error. According to mechanism 2, the conditions are not thermodynamically unfavorable in the region where the polycyclics begin to decrease.
This indicates that the superabundance of hydrogen atoms is not a part of the driving force for the synthesis of higher polycyclic aromatic hydrocarbons in this particular flame. These calculations are for one series of polycyclic aromatic hydrocarbons, the benzene series. This is the series with the highest ratio of hydrogen to carbon. Therefore, it will tend to predominate at equilibrium at high hydrogen partial pressures. Within this series low hydrogen partial pressures tend to favor polymerization. Acknowledgment. This research was supported by a grant from Basic Energy Sciences of the Department of Energy (Grant DE-GF02-85ER13454). I am indebted to Prof. William R. Smith for helpful discussions. Registry No. C6H6,71-43-2; acetylene, 74-86-2; hydrogen, 1238513-6.
A New Electronegativity Scale for the Correlation of Heats of Formation. 3. Bond Dissociation Energy of X-R Bonds and the Heat of Formation of the Isopropyl Radical Yu-Ran Luo and Sidney W. Benson* Donald P . and Katherine B. Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park, Los Angeles, California 90089- 1661 (Received: August 17, 1988)
Linear relations between ADH"(X-CH3/X-R) and V, have been found, where ADH"(X-CH,/X-R) DHo(X-CH3) DH"(X-R), R = CH3,(CH3),, ( m = 1 or 3), and V, is the unshielded core potential. The heat of formation of isopropyl radical in which m = 2 is estimated to be 20.0 f 0.5 kcal mol-'. The average deviation from observed bond dissociation energy (BDE(X-R)) of the estimated ones for 16 bonds is only 0.3 kcal with the maximum deviation 0.9 kcal. Three types of orders of BDE values of R-X bonds have been discovered which vary as the electronegativity of X, V,, changes.
Introduction The BDE (bond dissociation energy) of a chemical bond X-R is defined as the enthalpy change in the fission reaction: X-R * X + R (1) The standard state is 1 atm pressure, ideal gas at 25 "C. DH"(X-R) = AHI"298 E BDE(X-R)
= AfH"(X)
+ AfH"(R) - AfHO(RX)
(2)
TABLE I: Values of ADHo(X-CH3/X-R), kcal mol-'
F OH CI NH2
Br SH
I
For the reaction CH3 + RX R + CH3X (3) the reaction enthalpy change or the difference in BDE of R-X and CH3-X is given by -AH3 = ADHo(X-CH3/X-R) E DHO(X-CH3) - DHo(X-R)
= AAfHo(RX/CH3X)
+ AAfH"(CH,/R)
(4)
where AAfHo(RX/CH3X) = A,H"(RX) - AfH"(CH3X) (5) AAfH"(CH,/R) = AfH"(CH3) - AfHo(R) (6) Linear relations between AAfHo(RX/CH3X) and V,, where R = CH3-,(CH3), [ m = 1, 2 , or 31, and Vx,the unshielded core potential which forms the basis for a new electronegativity scale, have been described in previous There should thus be linear relations between ADHo(X-CH3/X-R) and V, because AA$f"(CH3/R) is independent of the nature of X. These relations will be discussed and used to derive a heat of formation of the isopropyl radical. (1) Luo, Y . R.; Benson, S. W. J . Phys. Chem. 1988, 92, 5 2 5 5 . (2) Luo, Y . R.; Benson, S.W. J . Am. Chem. SOC.,in press.
0022-3654/89/2093-3304$01.50/0
CHg H
9.915
8.11
-1.4 f -0.5 f 0.9 f 0.4 f 1.1 f
7.04 6.67 6.13 5.77 5.25 5.19 2.70
0.6 0.7
-1.4 f 0.5
0.6
1.7 2.0 4.4 4.4 4.9 10.8
0.8 0.6 1.8 f 0.8 1.7 f 0.6 4.5 f 0.6
1 . 1 f 0.8 f 0.5
f 0.7 f 0.5 f 1.0 f 0.5 f 0.5
TABLE II: Values of the Intercepts and Slopes for Eq 7 I,,,/ kcal mol-' S,/kcal A mol-' est est ADH" (CH,/R) exptl (eq 7) exptl (eq 7) R = CH,-,(CH,), m=l,CH,CH2 m = 2, (CH3),CH m = 3, (CH3),C
7.6f0.3 17.0 f 0.3
7.6 12.9 17.0
-1.14f0.04 -1.14 (-1.84 f 0.04)" -1.83 -2.30 f 0.04 -2.31
See Table IV in ref 1 .
Linear Relation between ADHo(X-CH3/X-R) and V , The data on heats of formation for CH,, C2HS,and t-C4H, radicals are known with good accuracy. We have AfHo(CH,) = 35.1 i 0.1 kcal mol-i,3-5 AfHo(C2Hs)= 28.4 f 0 . 4 : ~ 28.6 ~ f (3) Baghal-Vayjme, M. H.; Colussi, A. J.; Benson, S . W. Int. J . Chem. Kinet. 1979, 1 1 , 147. (4) Heneghan, S . P.; Knoot, P. A,; Benson, S. W. Inr. J . Chem. Kiner. 1981, 13, 677. ( 5 ) Dobis, 0.;Benson, S. W. I n f . J . Chem. Kinet. 1987, 19, 691.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 3305
Bond Dissociation Energy of X-R Bonds
TABLE 111: DHo(X-R), kcal mol-' X AfHo(X)' F (1 8.98) OH
R -,(ArHo(R)) CH3 C2HS i-C3H7 (35.1 f O,l)* (28.4 f 0.4)' (20.0 f
92.7 f 0.2
(9.4) 83.7 f 0.3
(28.99)
NHZ
84.9 f 1.2
(44.3 & 1.1)
Br
70.3 f 0.4
(26.74)
SH
74.6 f 0.6
(34.0 f 05'.)
I
57.1 f 0.4
(25.52)
CH,
90.2 f 0.2
(35.1 f O . l ) b
H
105.0 f 0.2
(52. IO)
and V,.
and 9.9 f 0.3'' kcal mol-'. The differences of BDE, ADHo(XCH,/X-R), can be calculated by use of eq 4. They have been listed in Table I. In Table I, X = F, O H , CI, NH2, Br, SH, I, CH,, and H. As shown in Figure 1, there are good linear relations between ADHO (X-CH3/X-C2HS), ADHo(X-CH3/X-t-C4H9), and V,. The values of intercepts and slopes for these lines are in Table 11. According to eq 4, the slope of the linear relation between ADHo(X-CH,/X-R) vs V, and AAfHo(RX/CH3X) vs V, are same. The slope is given by
+ 0.21m)
(7)
Thus, the slope of the linear relation between ADHo(X-CH3/ X-i-C3H7) vs V, can be estimated, although AfHo(i-C3H7)has been not yet determined accurately. The estimated slope is -1.83 kcal 8, mol-' (see Table 11). For estimating the unknown value of the intercept of the linear relation between ADHo(X-CH3/X-i-C3H7) vs V,, reproducing both experimental intercepts and slopes and estimating ADHO(X-CH,/X-R), we can use the empirical equation
ADHo(X-CH3/X-CH3-,(CH3),)
=m
+ 0.36m - V, 0.67 + 0.21m
6.33
For the 16 bonds involving C2H5-X and t-C4H9-X, in Table I, the average deviation of estimated ADHo(X-CH3/X-RJ is 0.3 kcal mol-' with the maximum deviation 0.9 kcal mol-I. The two bonds with maximum deviation are C2H5-NH2 and t-C4H9-Br. As pointed out in ref 1, heats of formation of these two compounds have not yet been determined with better than f l kcal accuracy. Estimated BDE Values Using eq 8, we can estimate values of BDE(X-R) because DHo(H-CH,) has been determined with high precision. This is DHo(X-R) = DHo(X-CHJ - m
+ 0.36m - V, 0.67 + 0.21m
(115.3)
(115.8) 94.0 f 0.4 (94.3) 82.5 f 0.5 (82.8) 83.1 f 1.1 (83.2) 68.2 f 0.5 (67.3) 70.1 f 0.7 (70.8) 52.6 f 0.8 (52.1) 85.2 f 0.4 (85.1) 94.1 f 0.4 (94.1)
(94.6) (83.7) (84.2) (68.6) (72.3) (53.8) (86.8) (97.0)
TABLE IV: AfHo(i-C3H7),kcal mol-' AfH" (I'-C3H7) 19.2 f 1.0 18.2 f 1.0 22.3 f 0.6 21.0 f 0.7 20.0 19.0 f 0.5 2.0 f 0.5
methods radical buffer review shock tube equilibrium review pyrolysis empirical relations
ref 14, 15 16 17, 18 19 20
21 this work
TABLE V: Place of Maximum and Minimum DHo(X-R) and the Classes CH3 C2H5 i-C3H7 f-C4H9 classes OH CI
min C min < min >max
NH2
max
F
> Br max > SH max > I max > CH3 max > H max >
< >max++ >
> > > > > >
> > > > > > >
min min min min min min min
reverse irregular irregular regular regular regular regular regular regular
Some DHo(X-R) values are listed in Table 111. Two values are listed for each bond except X-CH3 and X-i-C3H7. The data on AfHo(i-C3H7)are still in controversy. We will discuss the data later. The first values of each bond in Table 111 are the observed ones, and the second are estimated in this work. The values based on eq 2 are called "observed". The estimated ones are in parentheses. As can be seen from Table 111, the estimated BDEs are in agreement with observed ones to within the experimental uncertainties. The average deviation for all 16 bonds for C2H5-X and t-C4H9-X is only f0.3 kcal with a maximum deviation of 0.9 kcal.
6.33
(9)
( 6 ) Pacey. P. D.; Wilmalasena, J. H. J . Phys. Chem. 1984, 88, 5657. (7) Brouard, M.; Lightfoot, P. D.; Pilling, M. .I. J . Phys. Chem. 1986, 90, 4456. (8) Parmar, S. S.; Benson, S. W. Kinetics and Thermochemistry of the
Reaction: CI + C2H6* C2H5+ HCI, unpublished. (9) Parmar, S. S.; Benson, S. W. Kinetics and Thermochemistry of the Reaction: C2D6 CI e C,D5 + DCI, the Heat of Formation of the C2DS and C2H5 Radicals. J . Am. Chem. SOC.,in press. ( I O ) Benson, S. W. J . Chem. SOC.,Faraday Trans. 2 1987, 83, 791. ( I I ) Muller-Markgraf, W.; Rossi, M. J.; Golden, D. M. Presented at the 5th Informal Symposium on Kinetic and Photochemical Processes in the Atmosphere, UCLA, Los Angeles, March 24, 1988.
+
(113.7) 94.0 f 0.5 (94.3) 84.2 k 0.5 (84.1) 84.0 f 1.4 (84.9) 69.9 f 0.6 (69.7) 73.5 f 0.7 (73.6) 55.7 f 0.6 (55.5) 88.5 f 0.5 (88.5) 100.5 f 0.5 (100.5)
"From ref 12. bFrom ref 3-5. 'From ref 6-9. dEstimated in this paper. eFrom ref 11. /From ref 13.
0.4,8 and 28.3 f 0.4 kcal ~ O I - Iand , ~ AfHo(t-C4H9)= 9.5 f 0S1O
S, = -m/(0.67
t-CqH9 (9.9 f 0.3)e
110.0
CI
Figure 1. Relation between ADHO(X-CH,/X-R)
*
(12) Kerr, J. A. Handbook of Chemistry and Physics, 68th ed.; CRC Press: Boca Raton, FL, 1987-8; pp F-177, 181. (13) Shum, L. G. S.; Benson, S. W. I n f . J . Chem. Kinet. 1985, 17, 749. (14) Castelheno, A. L.; Griller, D. J . Am. Chem. SOC.1982, 104, 3655. (15) Griller, D.; Wagner, D. D. M. Reu. Chem. Infermed. 1986, 7 , 31. (16) McMillen, D. F.; Golden, D. M. Annu. Reu. Phys. Chem. 1982, 33, 493. (17) Tsang, W. J . Am. Chem. Sot. 1985, 107, 2872. (18) Tsang, W. I n f . J . Chem. Kinef. 1978, 10, 821. ( 1 9) Russell, J. J.; Seetula, J. A,; Gutman, D. Presented at the Symposium
on the Chemistry and Photophysics of Energetic Species, USC, Los Angeles, CA, September IO, 1987. (20) Von E. Doering, W. Proc. Nafl. Acad. Sci. U.S.A. 1981, 78, 5279. (21) Baldwin, R. R.; Drewery, G. R.; Walker, R. W. J . Chem. Sac., Faraday Trans. I 1984, 80, 2827.
J. Phys. Chem. 1989, 93, 3306-3308
3306 Discussion
The heat of formation of isopropyl radical has been determined and discussed recently by a few groups (see Table IV). Using the data both of the estimated intercept of ADH"(X-CH3/Xi-C3H7)vs V, (in Table 11) from interpolation and the observed intercept of AAfHo(i-C,H7X/CH3X) in ref 1 , we can estimate AfHo(i-C3H7)= 20.0 f 0.5 kcal mol-'. The value is from AfHo(i-C3H7)= AfH"(CH3) - 12.9 (10.3) - 2.2 (f0.3) = 20.0 f 0.5 kcal mol-'
and DH"(H0-CH3)
> DHo(X-C2Hs) > DHo(X-i-C3H7) > DH"(X-t-CdH9)
where X = H, CH3, I, S H , Br, and NH2.
< DHo(HO-C2H5) < DHo(HO-i-C3H7)
> DH"(HO-t-C,Hg)
3. Reverse order DH"(F-CH,)
As shown in Table IV, the estimated value is very close to the average one from these groups. In Table V, we compare bond strengths in the RX series. We find three categories as we go from Me to Et to i-Pr to t-Bu for R: 1. Regular order DHo(X-CH3)
2. Irregular order DHO(C1-CH,) < DHO(C1-C2H5) > DHO(C1-i-C3H7) > DH"( Cl-t-CdH,)
< DHo(F-C2H5) < DHo(F-i-C3H7) < DHO(F-t-C,Hg)
The data in Table I11 show that the place of maximum bond strength DHo(X-R) is changeable, as shown in Table V, and varies with electronegativity of X. Acknowledgment. This work has been supported by a grant from the National Science Foundation (CHE-87 14647). Registry No. F, 14762-94-8; O H , 3352-57-6; C1, 22537-15-1; N H 2 , 13770-40-6; Br, 10097-32-2; S H , 13940-21-1; I , 14362-44-8; CH3, 2229-07-4; H , 12385-1 3-6; CHgCHz, 2025-56-1.
A New Electronegativity Scale for the Correlation of Heats of Formation. 4. The Values of Group Parameters Yu-Ran Luo and Sidney W. Benson* Donald P. and Katherine B. Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park, Los Angeles, California 90089- 1661 (Received: August 31, 1988)
It has been found that the values of group parameters that are used in the Benson-Buss group additivity method for estimating heats of formation can be estimated AfHo[C-(C),(X)(H),-,] = 0.9 + ( m - 1)(10.08 - 1 . h ) - [m/(0.67 + 0.21m)3Vx where m = 1-3 for primary, secondary, and tertiary carbon atoms, respectively, and Vx is the unshielded core potential of X. The validity of the above equation has also been found to extend to silicon with use of some recently measured thermochemistry for silicon-containing compounds.
1. Introduction The group additivity scheme'-7 has been found to be one of the most useful for estimating heats of formation of organic compounds since it was proposed 30 years ago. The determination of values, however, of the group parameters has so far been limited to being derived from data on heats of formation. it has been an important goal for some time to find alternative methods to predict or estimate the values of group parameters. Because of the relative paucity of experimental data on AfHo from which group values are derived, an alternative predictive scheme could be of great value in extending group additivity. In particular, the field of organometallic chemistry, now so vital in semiconductor and superconductivity research, could benefit enormously from a good predictive scheme. ( 1 ) Buss, J. H.; Benson, S. W. J . Chem. Phys. 1958, 29, 546.
(2) Cruikshank, F. R.; Golden, D. M.; Haugen, G. R.; ONeal, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R.; Benson, S. W. Chem. Rev. 1969, 69, 279. (3) Eigenmann, H. K.; Golden, D. M.; Benson, S. W. J . Phys. Chem. 1973, 77, 1687. (4) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. (5) Benson, S. W. Chem. Rev. 1978, 78, 23. (6) Benson, S. W. In Thermochemistry and its Application to Chemical Biochemical Systems; Ribeiro da Silva, M. A . V., Ed.; Reidel: Dordrecht, The Netherlands, 1984; p 769. (7) Reid, R . C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977.
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The existence of simple, accurate, linear relations between AAfHo(RX/CH3X), AA$P (CH3X/HX), or ADHO (X-R/XCH3) and Vx,the unshielded core potentials of the atom in X attached to C or to H (in HX), have been described in the previous papers.8-'0 We have shown, for example, that AAfHo(RX/CH3X)
AfHo(RX) - AfHO(CH3X) = [0.9 - 1.5m(m - I)] m
= a,
+ bmV,
0.67
+ 0.21m vx
(8) Luo, Y.-R.; Benson, S. W. A New Electronegativity Scale for the Correlation of Heats of Formation. 1. Alkyl Derivatives. J. Phys. Chem. 1988, 92, 5255. (9) Luo, Y.-R.; Benson, S. W. A New Electronegativity Scale for the Correlation of Heats of Formation. 2. The Differences in Heats of Formation between Hydrogen and Methyl Derivatives. J. Am. Chem. SOC.,in press. (IO) Luo, Y.-R.; Benson, S. W. A New Electronegativity Scale for the Correlation of Heats of Formation. 3. Bond Dissociation Energy of X-R Bonds. J . Phys. Chem., preceding paper in this issue. (1 1) Benson, S. W.; Francis, J. T.; Tsotsis, T. T. Some Relations between the Heats of Formation of Metal Alkyls, Metal Hydrides, and the Electronegativities of the Metals. J . Phys. Chem. 1988, 92, 4515. (12) Pilcher, G.; Skinner, H . A. In The Chemistry of the Metal-Carbon Bond; Hartley, F. R., Patai, S., Eds.; Wiley: New York, 1982; p 43. (13) Yuan, H. C. Acta Chim. Sin. 1964,30, 341. (14) Doncaster, A. M.; Walsh, R. J. Chem. SOC.,Faraday Trans. 2 1986, 82. 701.
0 1989 American Chemical Society
