167
~ Q M M ~ J N I C TO ~ ~THE I O ~EDITOR ~
it]erative procedure, on the SDS 940 computer. The density constants a,@, and 6 were taken from ref 6. The vapor presswe constants for the Antoine equation, A , -LE, and 6 , were taken from NBS Bulletin 510.’ The results of this procedure, for a gas to liquid molar volume ratio of 335.0, are shown in Table I. As can be Table I Compound
n-Cz n-6.2 82-G
n-cs n-Cs 12-C7
n-c* n-69
?&-@lo
n-G n-Gz n-G
T ,OK
As, eu
w(os1cd)
0
180.7 224.4 261.4 294.8 325.6 352.3 376.5 398.3 418.8 437.8 456.0 472 0 488.1 502.1 515.9 529.9 562.8 266.9 346.1 348.1 332.5 333.9 340.1 334.6 362.1 359.4
19.05 19.85 20.32 21.14 21.52 22.40 22.72 23.48 23.88 24.46 24.76 25.37 25.75 26.21 26.52 26.95 27.96 20.61 21.83 21.82 21.33 21.60 21.33 21.11 21.38 20.99
0.0815 0.147 0.189 0.255 0.285 0.358 0,383 0.445 0.478 0.525 0.550 0.598 0,630 0.667 0.693 0.728 0.81 0.212 0.311 0,310 0.271 0.293 0.271 0,253 0,275 0.243
0.105 0.152 0,201 0.298 0.290 0.352 0.398 0.441 0.586 0.530 0.553 0.593 0.626 0.650 0.704 0.763 0.710 0.195 0.327 0.314 0.300 0.307 0.284 0.260 0.275 0.244
I
n-614
n-CE n-c26 n-617
n-czo Neopentane 3-Methylhexane %Ethylpen tane 2,ZDimethylpentane 2,4-Dirnethylpentane 3,BDimethylpentane 2,2,3-Trirnethylbutane E thylcyclopentane Methylcy clohexane
seen, a linear relationship does exist between the empirically derived acentric factor, u, and the entropy (AsVAP - 18.00) required to vaporize a nonspherically symmetrical molecule. For spherically symmetrical atoms or molecules both (AsVAP - 18.00) and o approach zero. From these results, it appears that 88331,
-*
A5O33jj
(12.7)~
in a value for of -0.057. From eq 6, a value of 0.057 is equivalent to 0.7 eu. This is in excellent agreement with the value (18.65-18.00) eu found experimentally. Thus for these measurements, represents the entropy of vaporization of the carbon atom core, for whichw = 0. For those data points which vary considerably from the linear relationship, it appears that the w values are inconsistent rather than As. For example, n-CloHzz has an acentric factor that is significantly greater than either n-CgHzoor n-C11H2., whereas A s values increase in a continuous fashion. For polar and associated molecules, there i s essentially no correlation between the acentric factor and As335. The reason for this is inherent in the initial assumptions. The intermolecular potential for polar molecules cannot be approximated by a simple twoparameter equation, since two parameter potential functions ignore dipole-dipole interactions. Thus any suitable intermolecular potential (such as the Stochmeyer potential function) involves an additional term and is no longer of the same general form as ey 4 . I n conclusion, it does appear that the acentric factor, for normal fluids, is a direct measure of the deviation of the entropy of vaporization from the spherically symmetrical molecule. Acknowledgment. I would like to acknowledge the help of R. Moore in conceiving this study and D. Lebaw for his assistance in programming. (6) E. W. Washburn, Ed., “International Critical Tables,” McGrawHill Book Co., New York, N. Y., 1926. (7) Rossini, et al., “Selected Values of Properties of Hydrocarbons and Related Compouiids,” American Petroleum Institute Research Project 44, Thermodynamic Research Center, Texas A & M University, College Station, Texas. (8) R. C . Reid and T. K. Sherwood, “The Properties of Gases and Liquids,” McGraw-Hill Book Co., New York, N. Y., 1966, p 571. (9) R. C. Weasl,, Ed., “Handbook of Chemistry and Physics,” Chemical Rubber Publishing Co., Cleveland, Ohio, 1969, p D-145.
SHELLCHEMICAL Go. MORTON SCHRAGER PLASTICS AND RESINSTECHNICAL CENTER NEWJERSEY 08096 WOODBURY, RECEIVED AUGUST19, 1970
(6)
where Asoa36 denotes the entropy of vaporization of spherically symmetrical atoms (or molecules) as met+ sured at a gas to liquid molar volume ratio of 335.0. It was previously noted that at a gas to liquid molar volume ratio of 335.0, the entropy of vaporization of the inert gases Ar, Kr, and Xe are approximately 18.65, and have acentric factors of 0. Equation 6 would project for these elements acentric factors of 0.053. This discrepancy can be resolved by examining the neon atom. The acentric factor, a, for neon has previously been estimated to be Q U 8 Ne can, however, be determined using eq 1. Over the range 1 < p o < 10 atm, neon vapor pressure datag can be accurately fitted to the Clausins-Clapeyron equation, resulting
Concerning “Kinetics of Isopropyl Alcohol Radicals by Electron Spin Reson,ance-Flow technique^'^ Publication costs assisted by the National Research Council of Canada
Sir: I n their recent paper, James and Siciliol purport to have measured the rates of reaction of the radicals (CH&cOH (RI) and CHsCHOH6H2 (Rz) with HzOz (1)
R. E. James and F. Sicilio, J . Phys. Chem., 74, 1166 (1970). The JotiTml of Physical Chemistry, Vol. 76,No. 1I lsTl
168
COMMUNICATIONS TO TEE EDITOR
in the system aqueous Ti(II1)-HzOz-2-propanol. It is the purpose of this communication to demonstrate that the kinetic analysis and the conclusions drawn by the authors are inconsistent with their own data and with previous work in the field and to present an alternative interpretation of their observations. The kinetic analysis by the authors is based upon the following assumed mechanism Ti(I1I) %- HzOz--+ Ti(1V)
+ OH- + OH
+ R1 OH 4- 2-propanol +H2O + RZ
OH 4- 2-propanol -+H20
1
R:!
-k H2OZ-+-termination
+ HzOz
---f
termination
(1) (5)
(6)
-d [Ti(III)] -dB1 - kl[Ti(III)][H~O~l = --dt dt
________
where [R]represents the total concentration of radicals. This would give an apparent first-order decay when [HzOz]>> [Ti(III)], reducing to a second-order decay when [HzOz]= [Ti(III)], as is observed in the experimental system.' The values attributed to Jc7 and ks
(7)
't
(8)
and is dependent on the assumption (not explicitly stated) that reaction 1 is entirely complete in a time shorter than that required for the first observation of the radicals. Values of IC1 ranging from 200 to 1800 1. mol-' sec-l have been determined.2Bs Using a reasonable4 value of 1000 1. mol-' sec-l for IC1 would give a half-life of 14 nisec for reaction 1 in the systems depicted in Figures 2-6 of ref l where the initial [HzOz] (after mixing) Is 0.05 M . Thus the initiating reaction is only slightly more than half complete a t the time of the first observation (-20 msec) and is continuing at a significant rate during almost the whole of the period of oblservation ( ~ ~ msec, 7 0 or five half-lives). Thus the primary assumption, on which the remaining analysis rests, has inanifestly not been met. This invalidates the kinetic treatment used and the conclusions drawn from it. (The same invalid assumption is found in an earlier p~blication.~) T o demonstrate that the kinetic analysis and the conclusions drawn from it are inconsistent with the data, a concentration-time profile has been calculated for a system initially (after mixing) 0.005 M in Ti(III), 0.05 M in &02,and 0.25 M in 2-propanol. The rnechanism outlined above and the values of IC1 and k, advanced by the authors (1000 and 400 1. mol-' sec-', respectively) and kg. = 1.2 X lo9 1. mol-' sec-' have been used to evaluate [RI] as*a function of time after mixing. The rcsulting curve, shown in Figure 1, may be compared directly with Figure 3 of ref 1. It is immediately apparent that the rate constants and mechanism claimed b y James and Sicilio would require radical concentrations almost four orders of magnitude greater than those actually observed, and radical concentrations increasing in magnitude over the first 35 msec of reaction time, whereas this is the period of most rapid concentration decrease in the experimental system. On the other hand if, as has been previously suggested,3 the rate of reaction 1 is clearly rate-determining, the absolute magnitudes of the radical concentraThe Journal of Physicul Chemistry, Vol. 76,No. 1 1971
tions are a function of their subsequent fast reactions but the kinetics of their decrease are simply those of the initiation. Whatever the mechanism(s) of the radical termination, the pseudo-steady-state condition may be represented as
c 4 0 4
n
\
io2
x TIME
(sec)
Figure 1. Concentration-time profile for solution 0.005 A[ in Ti(III), 0.05 M in Hz02, and 0.25 M in %propanol, calculated from mechanism of ref 1: - - -, [Ti(III)]; -, [Ri].
thus bear no necessary relationship to these reactions but are, in fact, a measure of ICl. More particularly, if it is assumed that the radical termination is by bimolecular reaction, it has been shown3 that the secondorder rate constant calculated from the peroxidedependent first-order decay constants is simply h / 2 . The average of the sum of the second-order rate constants so calculated in Table I of ref 1 is -850 1. mol-' sec-l, which is in good agreement with the value of 1000 1. mol-' sec-' advanced for ICl. Moreover, substitution of a reasonable value of 4 X lou 1. mol-' sec-' for 2 k b i m o ~ e c u ~ a r 6predicts total radical concentrations (2) B. Chance, J . Franklin Inst.. 229, 737 (1940). (3) R. E. Florin, F. Sioilio, and L. A . Wall, J . Phys. Chsm., 72, 3154 (1g68). .
I
(4) E. L. ~~~i~ and F, sicilio, &id., 73, 2590 (1969). (5) c. E. Burchill and I. S. Ginns, C ~ ZJ .. Chem., 48, 1232 (1970).
COMMUNICATIONS TO TBE EDITOR
169
within an order of magnitude of those displayed in Figures 2 and 3 of ref 1. Thus the assumption of a rate-controlling initiating step and bimolecular radical termination is more consistent with the experimental observations than the mechanism proposed by James and Sicilio. One d a c u l t y with this alternative mechanism would appear to be the observed relative concentrations of KI and R2. The Iraction of R, formed initially by OH attack on 2-propanol has been reported to be 0.10 or less.' More recent determinations of this fraction from the radiation-induced6 and photo-induced8 oxidation of 2-propanol by HzOh give values of 0.14 or somewhat greater. Whatever the precise value, the initial reaction of OH with 2-propanol gives R1 as the major species, whereas the concentrations of R1 and Rz observed by esr as intermediates are nearly equal and, in some instances, [&] > [RI](see Figures 2 and 3 of ref 1). While a quantitative treatment would be difficult these observations may be qualitatively reconciled by recognizing that the concentrations observed in the esr experiment are steady-state values maintained in a dynamie system. If termination is by nonselective bimolecular reactions this would tend to equalize the concentrations of the radicals to some to extent although it would be unlikely to reduce [R1] less than [Rz]. This concentration inversion can, however, be explained by the different reactivities of R1 and Rz toward HLh. It has been demonstrated' that Rz is much less effective than RI as a reducing agent and it has been proposedg that Rzreacts much more slowly with H202than RI. The kinetics of the radiation-induced oxidation of 2-propanol by H20zin aqueous solution have been explained6 on the basis that only RI reacts with N[& in the chain propagating step ( 7 4 while Rzdoes not react in this manner. The OH pro-
RI -t B2O2
=+ -
acetone
+ HzO + OH
becomes greater than that of RI only after the reaction is partly complete and the rate of initiation has thus decreased. The occurrence of the chain reaction involving reaction 7a has been discounted by James and Sicilio, in part on the basis of the titration experiments described in Table I11 of ref 1. However, the conditions used in these experiments were such that, in the majority of cases, Ti(II1) and H2OZwere present in the ratio required by the stoichiometry of reaction 1 thus leaving little or no H202 as oxidant for the chain reaction. Under these conditions it is not surprising that only a small yield of acetone was obtained. Finally, the authors have attempted to account for their anomalous values of k7, iCs> and k g , and for the claimed lack of reactivity of the OH from reaction 7a by suggesting that the radicals are complexed to Ti(1V) and hence unreactive. They present no experimental evidence to support such a suggestion and, in fact, the esr spectra of the organic radicals are identical with those observed in a system with no metal ions,'" whereas the formation of such a complex might reasonably be expected to modify the spectrum of the radical. To determine the effect of Ti(1V) on the free-radical chain reaction of HzOzand 2-propanol a series of deaerated aqueous solutions 0.5 M in 2-propanol and 0.05 M in HzOzwas 7-irradiated to initiate reaction. As demonstrated in Table I, the addition of 0.005 M Ti(IV)
Table I : G values for the Radiation-Induced Oxidation of 2-Propanol by HzOS in Deaerated Aqueous Solution" Conditions
Neutral solution 0.02 M HzS04 0.02 M HzSOa,0,005 M Ti(1V)
(7a)
duced in reaction 7a may then react with 2-propanol to give either R1 or Rz. If there is a significant chain reaction this sequence can readily give rise to concentrations of Rz greater than R1. (It is a corollary of the mechanism proposed for the radiation-induced oxidation of 2-propanol by HzOzthat, a t the dose rates employed, the steady-state concentration of Rzis much greater than that of R1.) It should be noted particularly that this effect would depend upon the chain length. At high rates of initiation the kinetic chain length would be short and this effect would be small but would increase in significance with reduced rate of initiation. Comparing Figures 2 and 3 of ref 1 it may he seen that in Figure 2, which represents the smaller initial concentration of Ti(II1) (and hence a lower rate of initiation a t any particular time), [Rz]is greater than [RI] at all observable times. I n Figure 3, where the rate of initiation is greater, the concentration of Rz
x
G(acetone1
54.8 f 2 . 0 55.6 11 2 . 0 48.7 A: 2 . 0
[2-propanol] = 0 . 5 M , [HzOZ]= 0.05 M, dose rate 1019eV 1.-l see-'.
=
1.35
introduced only a small, and possibly no significant, inhibition of the chain reaction-certainly far less than that implied by James and Sicilio. It is suggested, therefore, that there are no anomalous rate constants or novel radical complexes in the system aqueous Ti (111)-Hz02-2-propanol, providing [2-pro(6) M. Simic, Y. Neta, and E. Hayon, 1.Phys. Chem., 73, 3794 (1969). (7) G. E. Adams and R. L. Willson, Trans. Faraday Soc., 6 5 , 2981 (1969). (8) C. E. Burchill and P. G. Huminicki, unpublished results. (9) R. 0. C. Norman and P. R. West, J . Chem. Soc. B , 389 (1969). (10) R. Livingston and H. Zeldes, J . A m e r . Chem. Soc., 88, 4333 (1966).
T h e Journal of Physical Chemistrg, 5'01. 76,X o . 1 , 2971
COMMJNICATIONS TO THE EDITOR
170 panol] is sufficiently large to preclude attack on HzOzby OH. The time dependence of the total radical con-
-
centration i s conistent with reaction 1 being clearly rate determining, with 4 1000 1. mol-' sec-l, and with radical termination occurring by bimolecular procesBes with iiortnal velocity constants. The time dependence (or concentration dependence) of the relative concentrations of RI and R2may be explained can the basis of their differing reactivities toward HzOz,with only Rr undergoing the chain propagating reaction.
The J o t w a l of Ph,wkal Chemktry, VoL Y& No. I , 19Yl
Acknowledgment. Research support during the period of preparation of this communication was provided by the National Research Council of Canada. The useful comments by the referees are gratefully acknowledged. DEPARTMENT OF CHEMISTRY UNIVERSITY OF MANITOBA WINNIPEG19, CANADA RECEIVED AUGUST26, 1970
C.E. BURCHILL
