J . Phys. Chem. 1990, 94, 3803-3806 calculated at equilibrium for both phases at any given temperature; however, in order to calculate the values for Qs of two phases, one more equation is needed. It is not clear how to obtain this equation, here.
Discussion ESCM has been applied to solve the nearest-neighbor problems exactly. The calculation that is presented in section I is valid when f # 0.5, however. Remember that f = 0.5 corresponds to the critical density (see ref 9). It may be because of the possibility of the phase-transition phenomenon that the straightforward method (section I) cannot be applied for the case wheref= 0.5; for that, it has been handled specifically in section 11. There are a few main points that may be deduced from our results. On the one hand, in the absence of interaction energy (or at very high temperatures), the equilibrium state corresponds to the random distribution of atoms on sites. This point may be seen in Table I1 (for the 1D model) when W = 0 and in Table VI (for the 2D model) when U = 0. In these cases, W = 0 and U = 0, the probability for any given ij pair,fij, is
fi
where fi and are the fraction of i and j atoms in the lattice, respectively, and the lattice has complete disordered configurations. On the other hand, when the interaction energy is very high (or at very low temperatures), fAA - f , f A B 0, a n d & , 1 -f, and the lattice has a complete ordered configuration; such types of behavior are expected. Another point is related to those thermodynamic properties of the lattice that are the first derivatives of the free energy, namely, the configurational energy and entropy (and volume in the 3D model). The configurational entropies are plotted against the interaction energy in Figure 1, for the 1D model, and Figure 2 , for the 2D case, for some values off (for the cases wheref # 0.5). The configurational energy is also plotted in Figure 3 for the square lattice. These figures do not show any step (discon-+
-
3803
tinuity) at all. Such a result is expected, by the fact that the interaction energy between the nearest-neighbors does not govern any first-order phase transition, except when f = 0.5. The configurational heat capacity is given by eq 38 and is plotted against the reduced temperature in Figure 4, for the one-dimensional model, when f = 0.5. The heat capacity goes through a limited maximum, continuously at about kT/Jtl= 0.25. Therefore, the nearest-neighbor interaction does not govern any first-order phase-transition phenomenon in the I D model, at all. If there was any phase transition in this case, the heat capacity function would have gone through a step at the maximum or at some other points. Similar curves have been presented by the other exact calculated methods (for instance see ref 9). For the 2D model (square lattice), however, different ordering behavior has been observed whenf= 0.5. The ordering behavior of the lattice can be related to the value of P4, in such a way that a larger value for P4 corresponds to more ordering in the lattice. The probability P4 is plotted against Z in Figure 5. This figure shows that at high temperatures there is only one value for P4 of the lattice; however, when the temperature is decreased, the curve splits into two curves ( F and G ) roughly at Z = 0.41. Therefore, at this splitting point the system begins to become as two phases, C (more ordered phase) and F (more disordered phase). This point corresponds to the critical temperature, the exact value of Z , = 2'/* - 1 = 0.414 has been obtained by the other exact calculation^.^ The system coexists at the equilibrium between two phases until the temperature becomes so low as to give Z = exp(t/kT) = 0.233. Therefore, the system has two phases in equilibrium when 0.233 Q 2 < 0.41. If the temperature becomes very low, in such a way that Z < 0.233, the lattice will exist as a one-phase system, which seems to be logical. Although ESCM has been used here for the one-dimensional and two-dimensional models (of square lattice), as the special cases, it is applicable to other 2D and 3D models as well; for instance, in a simple cubic lattice, a nonsolid site along with its six nearest-neighbor solid sites should be considered the basic unit.
Thermodynamic Properties of Benzyl Radicals: Enthalpy of Formation from Toluene, Benzyl Iodide, and Dibenzyl Dissociation Equilibria H. Hippler and J. Troe* Institut f u r Physikalische Chemie der Universitat Gottingen, Tammannstrasse 6, 0-3400 Gottingen. West Germany (Received: April 20, 1989; In Final Form: November 9, 1989)
Measurements of the dissociation and reverse recombination rates of toluene, benzyl iodide, and dibenzyl in shock waves have provided a direct access to the dissociation equilibria. A third-law analysis of these data is made, providing a new value = 210.5 f 4 kJ mol-' which is higher than that given by earlier evaluations. of the enthalpy of formation of benzyl of On the basis of this value, thermodynamic properties of benzyl are tabulated over the range 0-3000 K. Revised values of the bond energies of toluene, benzyl iodide, dibenzyl, and ethylbenzeneof = 378.4, 190.0,277.2, and 328.8 kJ mol-', respectively, are also given.
1. Introduction
There is considerable interest in the precise enthalpy of formation of benzyl radicals since "there is probably no other single radical upon which so many bond energy values depend".l A variety of methods have been employed to derive this quantity. Among these are studies of iodination kinetics,'-" comparative (1) McMillen, D. F.; Golden, D. M. Annu. Reu. Phys. Chem. 1982, 33,
493. (2) Rossi, M.; Golden, D. M. J . Am. Chem. SOC.1979, 101, 1230. (3) Golden, D. M.; Benson, S. W. Chem. Reu. 1969, 69, 125.
0022-3654/90/2094-3803$02.50/0
single-pulse shock tube dissociation experiment^,^ and the ion cyclotron resonance bracketing technique.6 Over the years the has moved up from3 188 f 4 to4" 201 f 9 kJ value of AHfo298 mol-I. The applied methods have their merits but also their problems. Recent activities in this field (see, e.g., refs 7-14 and (4) Walsh, R.; Golden, D. M.; Benson, S.W. J . Am. Chem. Soc. 1966,88, 650. ( 5 ) Tsang, W. I n t . J . Chem. Kinet. 1969, I , 245; Ibid. 1978, 10, 41. (6) DeFrees, D. J.; Mclver, R. T.; Hehre, W. J. J . Am. Chem. SOC.1980, 102, 3334.
0 1990 American Chemical Society
3804 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 other work cited therein) have led to considerable revisions of the enthalpies of formation of many radicals such that a check of the benzyl value appears necessary as well. We have encountered the present problem in a series of shock tube dissociation studies of benzyl-containing molecules. In particular, high-temperature dissociation studies of toluene using various detection techniques and implying calculated values of equilibrium constants have led to widely differing conclusions about rate coefficient data. On the basis of our most recent experiment^'^ we now believe that we can attribute at least a part of these discrepancies to inadequate values of the equilibrium constant K,, for the toluene dissociation: toluene e benzyl
+H
(1)
We have, therefore, performedI5 a direct measurement of K,, by independently measuring toluene dissociation and the reverse recombination rate coefficients, kdiSI,and respectively, under conditions where mechanistic complications were as small as possible. In the present article we evaluate these results with respect to of benzyl. Besides toluene dissociation, we recently have also measured16 dissociation and recombination rate coefficients for the reactions
k,,
benzyl iodide
benzyl
+I
K practically coincide. At temperatures near 1500 K there is also good agreement with the recent ARASshock tube measurements from ref 18 ( k , = 1015.6 exp(-374 kJ mol-I/RT) s-l at 2 bar and
1300-1 800 K; possibility of some falloff effects lowering the apparent activation energy) such that k l appears well established now. The disagreement with the recent results on k , from ref 19 can be explained by problems with the rate coefficient and pathway of benzyl dissociation and with reaction -1; see the discussion in ref 15. The uncertainty in the absolute value of k l is estimated to be less than a factor of 1.5 and in the apparent activation energy less than about 20 kJ mol-]. The recombination benzyl H toluene (-1) was measured independently in ref 15 over the range 1300-1600 K with the result (falloff effects of about a factor of 0.80)
+
k-, = (2.0
* 2benzyl
(3)
These results can also be evaluated with respect to AHf0298 for benzyl although the heats of formation for benzyl iodide and dibenzyl appear slightly less well-known than for toluene. Compared to some of the earlier studies, the present work has the advantage that forward and reverse reactions were measured directly under the same conditions. Therefore, no assumptions about temperature coefficients of radical recombinations or activated complex models had to be made in order to specify the equilibrium constants. 2. Experimental Values of Equilibrium Constants 2.1. Toluene Benzyl H . Our recent shock tube measurements of the toluene dissociation rate constant in the highpressure limit of the unimolecular reaction led to an experimental value ofi5 exp(-(360 f 20) kJ mol-’/RT)
s-l
(4)
over the range of temperatures 1200-1 500 K where falloff effects are still small (factor 0.85) and secondary reactions were absent. Earlier measurements in a flow system gavel’
k , = 1014,8 exp(-356 kJ mol-’/RT)
X
l O I 4 cm3 mol-,
SKI
s-I
(5)
over the range 913-1 143 K. There were some heterogeneous contributions at the low-temperature end but these were accounted for. The two rate expressions (4)and (5) over the range 900-1 500 (7) Tsang. W. In!. J . Chem. Kinet. 1978, I O , 821; J . Am. Chem. Soc. 1985,
(6)
Since this value agrees with earlier measurements at room temperature,2w22it appears safe to assume a temperature-independent value of k-, for the range 900-1500 K. From eqs 4 and 6 we, therefore, derive an experimental value of the equilibrium constant for toluene dissociation of
K,, = k , / k _ , = 5 exp(-(360 f 20) kJ mol-’/RT) mol (7) over the range 900-1500 K with an uncertainty of about a factor of 1.5 in the absolute value. This value of K,, is smaller by a factor of about 3-6 than the values calculated before and used in earlier shock wave studies of the dissociation of toluene (see discussion in ref 23). This discrepancy is explained by the use of the previously derived small value of the heat formation of benzyl; see below. Kinetic measurement^^,^ of the rates of the forward and reverse reactions
I
+ toluene e benzyl + HI
(8)
after corrections in order to account for isotope effects and temperature dependences, near 1000 K have led to an equilibrium constant of
+
k, =
* 0.5)
-
(2)
and dibenzyl
Hippler and Troe
K,, = 25.7 exp(-75.7 kJ mol-I/RT)
(9)
The combination of Kc8 with the tabulated24equilibrium constant for the equilibrium HI =.= H + I of 10 exp(-297.7 kJ mol-I/RT) mol cm-3 near 1000 K leads to an expression of Kcl = 257 X exp(-373.4 kJ mol-’/RT) mol ~ m - The ~ . corresponding value of KcI(1000 K) = 8 X 10-l8 mol is about a factor of 10 larger than our present result of Kcl(lOOO K) = 7.9 X mol cm-) from eq 7. This discrepancy appears to be far outside the uncertainties of the conversion between the benzyl DI and benzyl + HI rate constants kT8in ref 2. However, the conversion of the I toluene rate constant k8 from their measurement near 500 K to a temperature of 1000 K may be very uncertain. By analogy to the H + toluene reaction,15 there may be a strongly non-Arrhenius type temperature dependence, caused by preferential addition at low temperatures and dissociation of the I-toluene adduct at higher temperatures. The ambiguity of relating measurements of the rate constants k8 and k-8 made at quite different temperatures, thus, appears to be the reasons for the discrepancies
+
+
107. 2872.
( 8 ) Castelhano, A. L.; Griller, D. J . Am. Chem. SOC.1982, 104, 3655. (9) Holmes, J. L.; Lossing, F. P.; Maccoll, A. J . Am. Chem. SOC.1988, 110, 7339. (10) Holmes, J. L.; Lossing, F. P. J . Am. Chem. SOC.1988, 110, 7343. ( I I ) Muller-Markgraf, W.; Rossi, M. J.; Golden, D. M. J . Am. Chem. Soc. 1989, I l l , 956. (12) Parmar, S. S . ; Benson, S. W. J . Am. Chem. SOC.1989, 111, 57. (13) Brouard, M.; Lightfoot, P. D.; Pilling, M. J. Phys. Chem. 1986, 90,
445. (14) Russell, J. J.; Seetula, J . A.; Gutman, D. J . Am. Chem. Soc. 1988, 110, 3092. ( I 5) Hippler, H.; Reihs, C.; Troe, J . 2. Phys. Chem. (Munich), in press. (16) Muller-Markgraf, W.; Troe. J. J . Phys. Chem. 1988, 92, 4899. (17) Price,S. J . Can. J . Chem. 1962, 40, 1310.
(18) Braun-Unkhoff, M.; Frank, P. EEC Rep. 1986, 3N3E-0091-D(B). Just, Th. Private communication, 1989. (19) Rao, V. S.;Skinner, G.B. J . Phys. Chem. 1989, 93, 1864. (20) Ackermann, L.; Hippler, H.; Pagsberg, P.; Reihs, C.; Troe, J. J. Phys. Chem., in press. (21) Hippler, H.; Pagsberg, P.; Troe, J. To be published. (22) Bartels, M.; Edelbuttel-Einhaus, J.; Hoyermann, K. H. Twenty-Second Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, in press. (23) Muller-Markgraf, W.; Troe, J. Twenty-First Symposium (Infernotional) on Combustion; The Combustion Institute: Pittsburgh, 1986; p 81 5 . (24) JANAF Thermochemical Tables, 3rd ed.; J . Phys. Chem. ReJ Dora 1985, 14, Suppl. 1 .
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3805
Thermodynamic Properties of Benzyl Radicals between the conclusions on AH,-(benzyl) from ref 2 and the present work. 2.2. Benzyl Iodide + Benzyl I . Our shock tube studies16 on the dissociation of benzyl iodide (2) and the reverse recombination (-2) were straightforward and free from complications. They gave the results k - 1014.77 exp(-181 kJ mol-'/RT) s-I (10)
+
2 -
and
k-2 = 1013.70 cm3 mol-'
(1 1)
SKI
over the range 750-950 K with an uncertainty in the absolute value of about a factor of 1.5 and in the apparent activation energy of reaction 2 of about f 1 0 kJ mol-'. From eqs 10 and 11 one obtains the equilibrium constant
Kc2 = k 2 / k - z = 12 exp(-181 kJ mol-I/RT) mol cm-j
+ HI
(13)
was measured in ref 4 over the range 483-663 K leading to a value of
K C l 3= 3.8 exp(-43.1 kJ mol-I/RT)
(14)
Combining this value with our expression of K,, and the tabulated H I + I of 1.7 equilibrium constant for reaction of H + I2 exp( 150.9 kJ mol-'/RT) (between 700 and 900 K) leads to an expression for Kc2 of
Kc2 = 1.8 exp(-166 kJ mol-I/RT) mol cm-,
(15)
The absolute values of Kc2 from eqs 12 and 15 agree very well near 900 K; they differ by a factor of 2 near 700 K. However, these differences are well within the uncertainty of the extrapolations of eqs 7 and 14 toward lower and higher temperatures, respectively. 2.3. Dibenzyl + 2Benzyl. Shock tube studies of benzyl iodide dissociation, at temperatures where the equilibrium 2 is at the benzyl + I side but where benzyl does not yet dissociate, also provide a direct access to the benzyl recombination rate constant k-3 and the equilibrium constant Kc3. Our results from ref 16 are
k 3 = 10'4.90exp(-250 kJ mol-I/RT) s-' k-3 = 1012,70exp(-1.9 kJ mol-I/RT) cm3 mol-'
OK toluenez7
H24
73.22 216.04 229.00
b e r ~ z y I ; ~all ~-'~ vibrations b e n ~ y l ; ~hindered *-~~ 229.00 rotor; V, = 25.9 kJ mol-' b e n ~ y lhindered ; ~ ~ ~ ~229.00 ~ rotor; Vo = 66.9 kJ mol-I benzyl i ~ d i d e ~ , ~ ~ 124 107.16 dibenzyl
298.15 K 1000 K 298.15 K 1000 K 321.0 543.1 50.17 24.70 139.9 222.25 114.7 218.00 210.55 192.89 321.0 540.6 210.68
193.81
321.7
542.5
208.08
192.52
317.6
537.7
127.3 106.76 143.9
77.4 76.94 104.9
381.8
620.5 205.9 912.0
180.8 479.1
(12)
for the temperature range 750-950 K. W e are not aware of other determinations of benzyl iodide dissociation or recombination rates or the corresponding equilibrium constant. However, the equilibrium constant for the reaction
I2 + toluene + benzyl iodide
TABLE I: Thermodynamic Properties Used in the Present Work (with AH",.(benzvl) = 229 kJ mol-' from This Work) AH",,/kJ mol-l S o T / J mol-! K-I
(16) s-I
(17)
K,, = 160 exp(-248.1 kJ mol-I/RT) mol cm-3
(18)
and
over the range 900-1 500 K. Earlier dissociation studiesz5 apparently are unreliable.z6 Earlier estimates5sZ6of either k3, k-3, or Kc3 also did not arrive at the values directly measured in our work. On the basis of the enthalpy of formation of dibenzyl and the estimated entropies of dibenzyl and benzyl,26eq 18 provides an independent access to AHr of benzyl radicals.
3. Thermodynamic Analysis of Equilibrium Constants With the now available direct measurements of the equilibrium constants K c I ,Kcz,and K,, from eqs 7, 12, and 18, one may derive three independent values of the enthalpy of formation of benzyl. At first we consider the toluene dissociation reaction (1). The thermodynamic properties of toluene have been elaborated recently (25) Horrex, C.: Miles, S. E. Discuss. Faraday SOC.1951, 10, 187. (26) Benson, S.W.; O'Neal, H. E. "Kinetic Data on Gas Phase Unimolecular Reaction": NSRDS-NBS21: Department of Commerce: Washington, DC, 1970.
TABLE I t Ideal Gas Thermodynamic Properties of Benzyl Radicals = 229 kJ mol-' from This Work and an Based on AH:, All-Vibrations Model of Benzyl" -(GO H O T Cpo So H0298)/T H0298 AHfO AGfo log K , f 0 0.00 0.0 -18.54 229.0 229.0 394.3 -1 4.90 100 44.56 245.3 221.1 233.0 330.0 200 72.47 285.0 215.9 246.8 -64.44 -9.00 298 74.81 321.1 0.00 210.5 263.0 -46.10 321.1 0.21 321.1 300 109.8 321.8 210.5 263.4 -45.86 400 143.1 358.1 12.89 205.8 281.7 -36.79 325.9 500 171.1 393.1 201.9 301.2 -31.46 28.66 335.8 46.94 348.2 600 194.0 426.4 198.9 321.3 -27.97 361.7 700 212.5 457.8 196.5 342.0 -25.52 67.28 800 227.9 487.2 194.8 362.9 -23.69 89.33 375.5 112.8 389.5 900 240.8 514.8 193.6 383.9 -22.28 1000 251.7 540.7 192.9 405.1 -21.16 137.4 403.3 1100 261.0 565.0 163.1 4 16.9 192.5 426.3 -20.24 1200 268.9 588.2 430.2 192.6 447.6 -19.48 189.6 1300 275.7 610.0 192.9 468.8 -18.84 216.8 443.2 244.7 1400 281.6 630.6 193.4 490.1 -18.29 455.8 1500 286.6 650.3 194.1 511.2 -17.80 273.1 468.2 1600 291.1 668.9 302.0 480.2 194.9 532.3 -17.38 1700 294.9 686.7 195.9 553.4 -17.00 33 1.3 491.8 1800 298.3 703.6 196.9 574.4 -16.67 361.0 503.0 514.1 1900 301.2 719.8 198.8 595.3 -16.37 390.9 2000 303.8 735.4 199.2 616.2 -16.09 421.2 524.8 2100 306.2 750.2 200.5 637.1 -15.85 451.7 535.1 2200 308.2 764.5 201.7 657.8 -15.62 482.4 545.2 2300 310.1 778.2 203.0 678.5 -15.41 513.3 555.0 2400 311.7 791.5 204.2 699.2 -15.22 544.4 560.5 574.0 205.5 719.7 -15.04 2500 313.2 804.2 575.0 2600 314.5 816.6 206.7 740.3 -14.87 607.0 583.1 592.0 2700 315.7 828.5 208.0 760.7 -14.72 638.5 2800 316.8 840.0 600.6 209.2 781.2 -14.57 670.2 2900 317.8 851.1 210.5 801.6 -14.44 609.1 701.9 3000 318.7 861.9 211.5 822.0 -14.31 617.3 733.7 (IT in K; c p o ,So, and -(Go - H0298)/Tin J mol-' K-I; Ho - H0298, SHr", and AGIO in kJ mol-', standard state pressure = 0.1 MPa.
in ref 27. Table I summarizes the relevant data for 0, 298.15, and 1000 K. The corresponding values for H are from ref 24. Thermodynamic data on benzyl in the past have been based on guesses, the major uncertainty probably being in the height of the barrier for internal rotation of the CH, group. On the basis of an all-vibration model, with frequencies such as given in Table I11 of ref 28, one obtains the values given in Tables I and 11. Considering a hindered rotor with a barrier in the order of 20-70 kJ mol-' changes these values only very ~ l i g h t l y . ~Table ~ . ~ ~I includes dataz9 for barriers of 26 and 67 kJ mol-'. (27) Chao, J.; Hall, K. R.; Yao, .I.-M. Thermochim. Acta 1984, 72, 323. (28) Brouwer, L. D.; Muller-Markgraf, W.; Troe, J. J . Phys. Chem. 1988, 92, 4905. (29) Skinner, G. B. Private communication, 1984. (30) Pamidimukkala, K. M.: Kern, R. D. Poster, International Conference on Chemical Kinetics, Gaithersburg, June 1985.
3806 The Journal of Physical Chemistry, Vol. 94, No. 9, I990
Hippler and Troe
Based on the calculated reaction entropy of Table I for the all-vibration model of benzyl, a third-law analysis of Kpl(1000 K) = 6.5 X bar from KcI of eq 7 leads to
certainties, particularly if the small differences between the results from refs 15 and 18 and the possibility of falloff effects are taken into consideration.
AHfO298(benZyl) = 210.5 kJ mol-'
5. Derived Thermochemical Quantities The high value of AHfo(benzyl), first, results in an increase of the C-H bond energy in toluene which increases to
(19)
This value is higher than earlier values. It is close to the upper limit of the uncertainties of the recently discussed high values of AHf. The value appears, however, in line with another recent e ~ a l u a t i o n . ~Evaluating ' the measured temperature dependence of K,, by a second-law analysis would give values that are by 22.9 kJ mol-' smaller. However, the corresponding error in the calculated reaction entropy would be inconceivably large. Therefore, the relatively uncertain temperature coefficient of the measured KcI should not be taken too seriously and the third-law analysis undoubtedly should be preferred. Estimating an uncertainty in the measured value of K,(1000 K ) of a factor of 1.5, in the calculated reaction entropy of *5 J mol-' K-I, and in the difference of AHf,Tbetween 1000 and 298 K of f0.8 kJ mol-', the value of eq 19 should have an uncertainty of about f 8 kJ mol-'. The analysis of benzyl iodide and dibenzyl dissociation equilibria appears slightly less reliable, since the enthalpies of formation of these molecules are presumably slightly less well-known than the value for toluene. One may base the determination of the enthalpy of formation of benzyl iodide on the most recent measurements of Kc13 in ref 4. (In this work, earlier determinations were also discussed with respect to internal consistency). Using the derived AHfo298 = ( 1 27.3 f 12) kJ mol-' for benzyl iodide and Acpo = 6.7 J mol-' K-' for reaction 13, for benzyl iodide one calculates AHyOlooo= 77.4 kJ mol-' and Solooo = 620.5 J mol-' K-I. With IMM = 126 J mol-' K-' the corresponding reaction entropy of So and the value of Kp2(1000 K) from eq 12. the third-law analysis gives AHfo298(benzyl)= 210.3 kJ mol-'
(20)
Likewise, using AHf0298 = 143.9 kJ mol-' and = 479.1 J = 5.2 J mol-' K-I for the mol-' K-' for dibenzyl, as well as reaction 3 from ref 26, for dibenzyfone calculates AHfoIOOO = 104.9 kJ mol-' and SolOOO = 912.0 J mol-' K-'. With the corresponding reaction entropy ASolMM = 169.2 J mol-' K-' and the value of Kp3(1000 K ) from eq 18, the third-law analysis gives AHfo298(benzyl)= 210.6 kJ mol-'
(21)
The agreement between these three independent AHf0298determinations for benzyl is remarkable. Nevertheless, in all three cases similar uncertainties of the estimated entropies remain. These enter the dibenzyl calculation to a larger extent since two benzyl radicals are involved. However, even there no particular deviation is visible. Our final result then is given by the three values of eqs 19-21. i.e.. AH?298(benzyl) = 210.5 f 4 kJ mol-'
(22)
which corresponds to AHfoo(benzyl) = 229.0 f 4 kJ mol-'
(23)
4. Thermodynamic Data of Benzyl Because of its importance for a variety of applications, in Table 11 we give thermodynamic data of benzyl radicals that are consistent with the present "high" value of the enthalpy of formation. On the basis of this table and the corresponding tables for toluene in ref 27 and H in ref 24, one derives an expression for KCIbetween 900 and 1500 K of the form K,, = 66 exp(-382 kJ mol-'/RT) mol
(24)
The temperature coefficient slightly differs from that of eq 7; however, the absolute values near 1000 K obviously agree since they served for the determination of AH?(benzyl). The differences in the temperature coefficients are within the experimental un(31) Tsang, W. Private communication, 1989.
-
+
benzyl H) = 378.4 kJ mol-' (25) AHo2,,(toluene or Moo = 37 1.8 kJ mol-' and Doo(C,H5CH2-H) = 3 1 080 cm-I. Second, the increase of AHyO(benzy1) results in a decrease of its resonance energy3 from 54 to 33 kJ mol-'. The agreement between the AHfo values for benzyl, such as derived from the toluene, benzyl iodide, and dibenzyl dissociation equilibria, also confirms the accuracy of the enthalpies of formation of benzyl iodide from ref 4 and of dibenzyl from ref 26. These values formed the basis of the benzyl iodide and dibenzyl entries in Table I. Accordingly the C-I bond energy in benzyl iodide is characterized by
-
AHo298(benZyl iodide benzyl + I) = 190.0 kJ mol-' (26) whereas the C-C bond energy in dibenzyl corresponds to
-
AH0298(dibenzyl 2benzyl) = 277.2 kJ mol-' (27) The present results for benzyl influence the value of the C-C bond energy in ethylbenzene which follows as AHo2,,(ethy1benzene
benzyl
+ methyl)
= 328 kJ mol-'
(based oni4 /1Hf0298(CH3) = 148 kJ mol-' and ~'iHf~298(ethylbenzene) from refs 32 and 33). Note Added in Proof. In a recent reevaluation of a variety of rate data related to the toluene e benzyl + H equilibrium, W. Tsang3' has arrived at quite similar conclusions about the equilibrium constant Kcl. He calculated the corresponding log Kp,f values of -45.40 (298.16 K), -21.20 (1000 K), and -17.95 (1500 K ) in close agreement with the present values of -46.10 (298.16 K), -21.16 (1000 K), and -17.80 (1500 K). However, as a consequence of a somewhat different set of benzyl vibrational frequencies (about 10% higher values for the low-frequency modes), different entropies and enthalpies of formation were obtained corresponding to a different partitioning of AGyO into enthalpy and entropy contributions. (Tsang's values: So = 315.6 (298.16 K). 533.2 (1000 K), and 642.6 (1500 K) J mol-' K-I; this work: So = 321.1 (298.16 K), 540.7 (1000 K), and 650.3 (1500 K) J mol-' K-I. Tsang's values: AHf' = 205.12 (298.16 K), 186.30 (1000 K), and 187.26 (1500 K) kJ mol-'; this work: AH? = 210.6 (298.16 K), 192.9 (1000 K), and 194.1 (1500 K) kJ mol-'.) Tsang's frequency set involved more extensive estimations in contrast to the present set based mostly on spectroscopic measurements (see references cited in ref 28). There is some further uncertainty related to the hindered rotor of benzyl with the related uncertainties illustrated in Table I. As a consequence of the existing ambiguities of the benzyl frequencies and hindered rotor properties, the question of the heat of formation and entropy of benzyl remains somewhat uncertain, whereas the present work agrees well with Tsang's conclusions about the equilibrium constant KCIand the AGfO value of benzyl in the relevant temperature range 1000-1500 K.
Acknowledgment. We are grateful to G. B. Skinner for communication of his thermodynamic table for benzyl radicals. We are also grateful to W. Tsang for communicating the results of his recent analysis of benzyl reactions. Discussions with D. M. Golden, D. F. McMillen, and S. Stein are acknowledged. Financial support of this work by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 93 "Photochemie mit Lasern") is acknowledged. Registry No. Benzyl, 21 54-56-5; toluene, 108-88-3; benzyl iodide, 620-05-3; dibenzyl, 103-29-7; ethylbenzene, 100-41-4. (32) Stull, D. R.; Westrum, E. F.; Sinke, G . C. The Chemical Thermodynamics of Organic Compounds; Wiley: New York, 1969. (33) Miller, A.; Scott, D. W. J . Chem. Phys. 1978, 68. 1317.
