J. Phys. Chem. 1993,97, 5791-5792
Comment on "Hydrogen Transfer between Anthracene Structures" Donald M. Camaioni,' James A. Franz
S.Tom Autrey,
and
Pacific Northwest Laboratory,? P.O. Box 999, Richland, Washington 99352 Received: January 19, 1993; In Final Form: March 17, 1993 In 1986Billmers,Griffith, and Stein (BGS) published a papert in thisjournal on hydrogen transfer between anthracene structures. They reported on the mechanism, kinetics, and activation parameters for transfer of mew hydrogens from 9,lO-dihydroanthracene (AnH,) to 2-ethylanthracene (EAn) in the temperature range 250-400 OC. AnH,
+ EAn
-
An
+ EAnH,
(1) The purpose of this Comment is to point out that a comprehensive kinetic analysis leads to a more conventional explanation of the observed kinetic behavior. This result needs to be recognized because the BGS explanation has been taken as precedent for a nonconventional radical reaction believed to be of central importance to coal liquefaction BGS reported that the kinetics of this reaction follows simple, second-order kinetics (rate 0: [AnH2][EAn]); they also provided supporting evidence to show that the reaction proceeds via free radicals but is not a chain reaction. Accordingly, they assigned the rate-controlling step and associated activation parameters to the molecular disproportionation (MD) reaction (eq 2). Also, they found that thesecond-orderrateconstant at 350 'Cdecreased with added An (see BGS Figure 2). To explain this behavior, they invoked the unprecedented transfer of a @-hydrogenfrom 2-ethyl-9-hydroanthryl radical (EAnH') to An (eq 3). AnH,
+ EAn
EAnH'
-
+ An
AnH'
-
+ EAnH'
(2)
+ AnH'
(3)
EAn
Equation 1 is an isergonic reaction, and therefore, its reverse reaction must be taken into account explicitly. The rate law for a reversible reaction 1 is given by eq 4, which shows clearly that d[EAnH,]/dt = k([EAn] [AnH,]
- [EAnH,][An]J
(4)
[An] retards the formation of EAnH,. The kinetic behavior of this system is analogous to that for isotopic exchange systems and yields to the same mathematical treatment.6 The integrated rate law is In (1 -A = -k(C,
+ CB)t
(5) where!= [EAnH2],/[EAnH2], or the yield of EAnH2 at time f based on the equilibrium concentration of EAnH2, CA= [EAn] [An] and CB= [EAnHz] + [AnH,]. Thevalue for [EAnH,], is given by eq 6, where CE= [EAn] [EAnH2]. Because CA, CB, and CEare determinable from initial conditions, k can be calculated with knowledge of [EAnH,] at any time, t.
+
+
(6) [EAnH,], = C&/(CA + CB) BGS's data7 for 350 OC were analyzed using this rate law. Figure 1of this paper confirms the appropriatenessof the analysis. In spite of considerable scatter in the data, the figure shows that the observed rate constants obtained from the integrated rate ~~~
+
Operated by Battelle Memorial Institute for US.Department of Energy
under Contract DE-AC06-76RLO 1830.
0022-365419312097-5791SO4.0010
5791
equation (eq 9) correlate well with (CA+ CB). The slope of the least-squares fit line yields k = (4.5 f 1) X 10-4 M-1 s-1.899 The important difference between our analysis and that of BGS is in the way in which the dependence on added [An] is explained. BGS observed that the yield of EAnH2 at 15 min decreasedas the initial ratio of [An]/ [AnH,] increased (see BGS Figure2). Interestingly,the k obtained by the equilibriumkinetic analysis increases with added An (see Figure l), but [EAnHz], decreases with added An (see eq 6). Therefore, the [EAnH,] at any time during the reaction also is decreased with added An. This behavior explains why BGS's simple second-order kinetic analysis yielded rate constants that decreased with added An. Figure 2 shows that eqs 5 and 6 reproduce well the observed decrease in production of EAnH2 at 15-min reaction times. The rate law (4) can be derived from a radical mechanism that includes reaction 2, its reverse reaction-radical disproportionation (RD)-and reactions 7-9. This simplest of radical EAnH,
+ An F? EAnH' + AnH'
(7)
+ EAn F? 2AnH'
(8)
+ An e 2AnH'
(9)
EAnH, AnH,
mechanismsleads to a definition of the rate constant for molecular disproportionation to be twice the observed rate constant: k = ' / z k ~ ~However, . as discussed by BGS, if 8-H transfer or H-abstraction reactions (10) competewith termination reactions, then k may approach the value for kMD. EAnH'
+ AnH,
e EAnH,
+ AnH'
(10) To better understand how such competitions would manifest themselves on the kinetic behavior, we derived the steady-state rate law for mechanisms that include either H abstraction or 8-H transfer. The rate laws are similar to eqs 4 and 5 with k given by the equation
where kH is the rate constant for H abstraction (klo) or 8-H transfer (k3) and F is CA/CBwhen kH is k3 or CB/CAwhen kH is klo. This equation allows fork to havevalues that range I / ~ ~ M D 5 k 5 kMD dependingon thevalueof kH/(kMD/kRD)'/*cOmpared to PI2. The values for P / 2varied from (CA/CB)'/~ = 0.2 to (Ce/CA)I/2 > 5 in the BGS study. If values for kMD and kRD are assumed to be 5 X 10-4 and lo8 M-I s-I, then kH must be >20 M-1 s-1 for reaction 3 or 10 to affect the observed rate constant significantly. If either k3 or klo is competitive, then its effect is to cause the value of k to change by
