T H E
J O U R N A L
OF
PHYSICAL CHEMISTRY
Registered i n U.S. Patent Ofice @ Copyright, 1971, by the Amerimn Chemical Society
VOLUME 75, NUMBER 10 MAY 13, 1971
J. Phys. Chem. 1971.75:1333-1338. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 08/31/15. For personal use only.
A Comparison of RRK and RRKM Theories for Thermal Unimolecular Processes1 by David M. Golden,* Rikhhard K. Solly, and Sidney
W.Benson
Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park, California 94086 (Received December 14, 1970) Publication coats borne completely by The Journal of Physical Chemistry
It is shown that in prescribed temperature regions the Kassel integral of RRK theory gives values of k / k , in good agreement with values computed from RRKM theory for a number of widely different thermal unimolecular processes. The parameter s is uniquely defined as C,ib(T)/R.
Introduction The application of transition state theory to gas phase chemical kinetics, combined with rapidly increasing experiences with various types of chemical reactions, has progressed to the point where the activation parameters, and thus the rates, for many elementary chemical reactions can be estimated fairly accurately. This state of affairs is very useful to the chemist who may be trying to understand the mechanism of a chemical process consisting of many such elementary reactions. Often some of these elementary processes are unimolecular, or the reverse (Le.> radical combination), and as such can be pressure dependent. It is useful to be able to predict simply the degree of such dependence. This kind of prediction has often been made by using the Rice-Ramsperger-Kassel (RRK) theory incorporating a n estimated empirical parameter, s, the “number of effective oscillators.’’ Bensona has suggested s = Cvib/R.
Recent publication^^"^^ have claimed, based on the more accurate modification of RRK theory by Marcus (RRKM), that s was too complicated a function of the complexity of the species, the frequency pattern, and the temperature to be estimated in any simple way. It was suggested that only application of RRKM theory is appropriate. Lamenting both the fact that simple use of tables of the “Kassel integral” would not suffice to predict lc/k,, and the necessity of using the costly (in both
time and money) procedure involved with use of R R K M theory, it was decided to compare RRKM and RRK (s E Cvib/R) for a number of different thermal unimolecular processes. Table IQ E
S
Model no.
H
H
H
H H
H L
1 2
H
L L
H H L L 0
Parameter
A
,-
H L L L L
7
L
3 4 5 6
H
7
L
8
L
H
The definitions of H and L might be
H 2 L I
Log A
E
S
15.5 13.5
50 20
25 15
(1) This work was supported in part by Contract NAS 7-472, with the National Aeronautics and Space Administration, Ames Research Center, Moffett Field, Calif. (2) L. S. Kassel, “Kinetics of Homogeneous Gas Reactions,” Reinhold, New York, N . Y., 1932. (3) 6 . W. Benson, “Thermochemical Kinetics,” Wiley, New York, N . Y., 1968. (4) (a) D. W. Placzek, B . 8. Rabinovitch, G. Z. Whitten, and E. Tschuikow-Roux, J . Chem. Phys., 43, 4071 (1965); (b) E.Tschuikow-Roux, J . Phys. Chem, 7 3 , 3891 (1969).
1333
D. M. GOLDEN, R. K. SOLLY,AND S. W. BENSON
13b4
Experimental Section Procedure. a. RRKM. The procedures of Rabin-
complexes were calculated with the use of a program kindly Provided by L. H. Scharpen of Hewlettl'mhrd COrP. Frequency assignments for reacting molecules were taken from the literature where available. Otherwise, frequencies were assigned by analogy. Hindered rotors were treated as torsions. The
ovitch and coworkers6 have been followed. The program, used with a CDC 6400 computer, was kindly supplied by Professor Rabinovitch. Moments of inertia products for reacting molecules and activated Table 11: Calculated Falloff Data ( k / k , ( T ) ) for Models 1-8
J. Phys. Chem. 1971.75:1333-1338. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 08/31/15. For personal use only.
Pb
108 10' 10-1 10-3 km
--k/km(300)--MC
-lc/km(600)M
K ( s = 7)d
1 . 0 (-1) 9.9 (-1) 8.1 (-1) 2 . 8 (-1) 2.4 x
1.0 0.55 1.0 0.078 1.0 0,0033 9 . 3 ( - l y 0.0067 3 . 4 x 10-42
P
k/km(300) M
108 10' 10-1 10-8
km
P
-
(300) K(8 = 10)
-k/k, M
108 10' 10-1 10-8
1.0 9.9 6.9 9.6
x
8.7 X 8.7 X 8.7 X 8.7 X 10-48
-
0.96 (-1) 5.4 (-1) 0.89 (-2) 0.39 5 . 6 x 10-7
K(s
E
c -
M
7)
9 . 1 (-1) 1.1 3 . 3 (-1) 0,051 2 . 1 (-2) 0.011 4 . 3 (-4) 0.016 2.36 x 10-16
( 1200)--K ( s = 27)
r-k/lc,
K ( s = 23)
9.9 (-1) 9.4 7.9 (-1) 5 . 5 2 . 6 (-1) 1 . 3 2.6 (-2) 1.4 2 . 1 x 10-2
(600)
M
lo-' 10-8 10-lo 10-12
M
0.97 7.0 2.3 0.30
-k/k, K ( s = 2)
1.0 0.84 0.20 8 . 5 X 10-8 6.78
---k/km(90O)-
K ( s = 16)
k/k,(QOO)--K ( s = 10)
M
8 . 7 (-1) 8.1 3 . 5 (-1) 2.9 4.0 (-2) 3 . 9 1.8 (-3) 2 . 3 1 . 9 x 10s
----k/k~(1200)-IM K ( s = 13)
6.0 (-1) 1 . 9 9.0 (-2) 1 . 5 3.0 (-3) 5 . 2 4.7 (-5) 1.1 2.19 x 10-4
2.9 (-1) 1.4 2 . 2 (-2) t . 0 5 . 2 (-4) 3 . 4 7 . 0 (-6) 7 . 3 6.95 X' 10'
3. LHH PhCO 4 Ph. CO log e], = 14.6 28.6/0
+
-
-
---k/k, M
9.7 5.4 6.5 2.0
M
6.9 9.5 3.0 4.5
(-1) 9.4 (-1) 4.4 (-2) 5.8 (-3) 2.9 1 . 4 X 106
(1ZOO)--K ( s = 27)
---k/km
----k/km(90O)-
(600) K ( s = 19)
K ( s = 24)
(-1) 9.4 (-2) 9.7 (-3) 3.7 (-5) 7.1 4 . 3 x 107
4. LHL CHgNHNH2 4 NHa CHz=NH log k, = 13.2 63.9/0
M
2.9 (-1) 2.9 1.3 1 . 2 (-2) 2.1 1.9 (-4) 2.4 2.1 (-6) 2 . 3 x 109
+
-
P
108 10' 10-1 10-8 km
(600)-
~-k/k,(300)M K ( s = 4)
-k/km
----k/km(9O0)-
1.0 0.87 1.0 0.18 9.8 (-1) 0.056 4.2 (-2) 0.0076 8 . 7 x 10-27
1.0 0.99 9.9 (-1) 8.0 7.3 (-1) 2.2 1.1 (-1) 0.16 3.5 x 10-7
K ( s = 9)
M
M
K ( s = 13)
1.0 9 . 0 (-1) 3.2 (-1) 2 . 0 (-2) 1.2
0.99 7.6 2.0 1.6
--M
k/k,( 1200)-K ( s = 15)
9 . 8 (-1) 9 . 7 6.4 (-1) 5.5 9.9 (-2) 8 . 2 3 . 4 (-3) 4 . 1 2 . 3 X 10%
5. HLH tert-Bu0 + (CHs)zCO CHs log k, = 15.5 is.s/e
-
P
108
101 10-1 10-8 km
--k/k,(300)M
8.0 1.5 3.3 3.4
K ( s = 9)
(-1) 4.6 (-1) 0.49 (-3) 1.8 (-5) 3 . 5 2.2 x 108
The Journal of Physical Chemimtry, Vol. 76,No. 10,2971
---k/k,(600)M
1.5 4.4 5..5 5.6
+
-k/km(90O)-
K ( s = 18)
1.5 (-1) 6.2 (-3) (-5) 12 (-7) 17 2 . 1 x 109
M
K ( s = 23)
1.6 1.5 (-2) 2 . 0 (-4) 2 . 3 2.1 (-6) 2.5 2 . 1 (-8) 2.6 2 . 3 X 10l1
---k/km(l20O)M K ( s = 27)
2.2 (-3) 2.1 2.3 (-5) 2.1 2.4 (-7) 2.2 2.4 (-9) 2.2 2.5 X 10l2
1335
COMPARISON OF R R K AND RRKM THEORIES Table I1 (Continued)
P
--k/km(300)-
M
103 10' 10-1
10-3
J. Phys. Chem. 1971.75:1333-1338. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 08/31/15. For personal use only.
km
K
( 5 s
2)
(-1) 0.031 1 . 2 (-2) 0.0031 1 . 3 (-4) 0.0031 1 . 3 (-6) 0.0031 8.3 X l o d 2
4.6
-k M
/ k , (600)-
-k/k,(1200)-
-k/k,(QOO)-
K f e = 6)
K(s = 8)
M
1.1 1 . 5 (-1) 3.2 2 . 5 (-3) 2 . 5 (-5) 5.0 5.9 2 . 5 (-7) 4.2 X lo8
5.1 6.8 6.8 6.8
(-2) 6.1 (-4) 16 (-6) 24 (-8) 29 1.7 x 109
M
K ( s = 9)
1 . 9 (-2) 2 . 5 2.3 (-4) 4.7 2 . 3 (-6) 6.1 2 . 3 (-8) 6.9 3 . 5 x 1010
7. LLH %-hexyl-+sec-hexyl log k, = 10.0 i3.5/e
-
P
7--
M
108 10' 10-1 10-3
1.0 1.0 9.7 4.1
km
k/k,(300)K ( s = 12)
1.0 9.8 4.9 2.6
1.0 1.0 8.4 2.5
(-1) (-1) 1.3
.---k/km(600)M
---k/k,(
-k/k,(900)-
K ( s = 25)
M
1.0 (-1) 9.7 (-1) 4 . 7 (-2) 3.1 1.3 X lo6
k/km(33)
1.0 1.0 8.3 (-1) 8.2 9 . 1 (-2) 9.2 1.3 (-3) 1.4 5 . 8 X 10e
M
9.9 5.4 1.7 1.9
1200)K(e = 39)
(-1) 9.9 (-1) 5 . 4 (-2) 1.7 1.8 (-4) 3.8 X 107
8. LLL
cyclobutane + butadiene 32.i/e log k, = 12.8
-
P
--k/km(300)-
M
103 10' 10-1 10-8 km
K(e
I .o 9 . 9 (-1) 61 (-2) 180 (-4) 1 . 5 x lo-"
=:
4)
0.72 0.83 0.19 0.23
---k/ka(600)-M K ( s = 11)
1.0 8.6 2.0 3.9
k/km (900)K ( s = 15)
7 -
---k/km(l
M
M
(-1) 9.5 (-1) 4.2 4.2 (-2) 4.1 6.2 (-4) 14 9 . 7 x 104
0.98 (-1) 6.3 (-1) 1.1 (-3) 5.8 1.2 x 10'
9.8 5.3
200)K(s = 18)
8.5 9.0 (-1) 2 . 4 (-1) 2 . 0 9.2 8 . 6 (-3) 1.1 (-4) 1.8 8 . 4 X lo8
'
a At ()!' = 9OO"X, units sec-1, e = 2.3 R T kcal/mol. Torr. k/lc,(T) as computed from RRKM theory. k/k,(T) as computed from RRK theory (s E-ZZ C,ib(T)/R). e ( - 1) signifies multiplication by 10-1 for entries in both columns M and K .
frequencies of the activated complex were assigned by appropriate adjustments in those of the reacting species as described in the Appendix. The total entropy of the reacting species was computed, and frequencies were assigned with an eye toward agreement with known values. The entropy of the activated complex was adjusted to yield known or expected A factors [log A = log (ekT,/h) (A&*/ 2.3 R ) 1. T , = mean temperature in experiment. b. RRK. A program for evaluating the Kassel integral for given values of B E/RT (E = Arrhenius activation energy),6" D = log ( A / w ) (u = collision frequency), and s was obtained from Dr. G. Emanuel of the Aerospace Corp.'Ib This program was modified to accept exactly the same input data as the RRKM program (ie., frequencies, moments of inertia, collision diameters, etc.), from which it computed values of B and D, as defined above, and s = C,ib/R. Thus, regardless of the reality of the models, thay are identical. c. Test Species. I n order to cover the widest possible range of model systems, we envisaged the eight possibilities for high ( H ) and low (L) values of kinetic
+
parameters, shown in Table I. As will be seen, not all the models chosen are perfect examples of models 1-8, but, although it was not necessary, a preference for working with real reactions was expressed.
Results Table I1 shows the results for eight prototype reactions a t 300, 600, 900, and 1200"K, and at pressures of los, lo', lO-l, and Torr. (The values of a, the collision frequency, vary slightly from model to model as a result of slight changes in mass and collision diameter.)
Discussion The results in Table I1 show that the computed values for k / k , are very similar whether RRK or RRKM ( 5 ) B. S. Rabinovitch and D. W . Setser, Adwan. Photochem., 3 , 1
(1964). (6) (a) The usual definition of B is EoIRT where Eo is the activation energy of OOK. We prefer to use the above definition since the value of the Kassel integral at infinite pressure is k , = Ae-B. If B is EoIRT, then A cannot be the usual Arrhenius A factor defined as A k,eEIRT, but must be redefined as Ao = k m e E d R T . This use of A and E,, instead of Ao and EO,makes insignificant differences in the values of k/km. (b) G. Emanuel, Air Force Report No. SAMSOTR-69-36, Aerospace Report No. TR-0200(4240-20)-6.
-
The Journal of Physical Chemistry, Vol. 76,No. IO, 1071
D. M. GOLDEN, R. K. SOLLY,AND S. W. BENSON
1336 Table 111:" Calculated Falloff Data [k/k,(T)] for Example from Ref 3
+
1. CH4 4CHa H (Model 2 of ref 3) kw(2500) = 15.5 io7.2/e P,Torr
-
--k/k,
(1000) K(s = 5)
M
108 106 104 102 1
1 1 8.8 2.2 4.6
kW
--k/kw
M
1 0.96 (-1) 4.2 (-1) 0.29 (-3) 0.60 1 . 7 x 10-8
1 9.8 6.3 7.4 1.2
-
--k/kw(2500)-
(1500)K ( s = 8)
M
0.99 (-1) 9.2 (-1) 3.2 (-2) 2.0 (-3) 0.41 8 . 7 x 10-1
1. 8.6 2.2 1.0 1.3
-k/km(4000)-
K ( s = 8)
M
1 (-1) 8 . 3 (-1) 2.0 (-2) 1.0 (-4) 2.3 1 . 4 X 108
K(8
= 9)
9.9 (-1) 9.8 5.6 (-1) 5.3 4.9 4.7 (-2) 1.3 1.1 (-3) 2.1 1 . 2 (-5) 4 . 8 x 109
+
J. Phys. Chem. 1971.75:1333-1338. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 08/31/15. For personal use only.
2. CFaH 4 CF2 H F (Model 2 of ref 3) log kw(i400) = 14.66 - 71.99/e P,Torr
-k/km(600)-
M
108 106 104 102 1 k W
-k/kw(1000)--M K ( 8 = 7)
K(s = 5)
1 1 1 1 9 . 9 (-1) 8.0 6.7 (-1) 1 . 5 6.9 (-2) 0.52 4 . 1 x 10-12
" Nomenclature
1 1 8 . 7 (-1) 2.6 (-1) 1 . 2 (-2) 8.9 x
1 1 7.6 1.5 0.72
1800)--
,--k/k,(
2200)--
K ( s = 8)
M
K(s = 8)
-k/kw(1400)M K ( s = 8)
--k/k,( M
1 1 9.9 (-1) 9 . 8 6 . 3 (-1) 5.9 8 . 9 (-2) 7.7 2.6 (-3) 2.9 2.6 X loa
1 1 9 . 5 (-1) 9.4 4 . 1 (-1) 3 . 5 3.2 (-2) 2 . 5 7.0 (-4) 6.6 8 . 4 X 106
1 1 8 . 9 (-1) 8 . 6 2 . 5 (-1) 2.0 1.3 (-2) 0.96 2 . 3 (-4) 2.0 3 . 4 x 101
identical with Table 11.
theory is used, as long as the rate constant itself is in a measurable range. Thus, for values of k > low4sec-' (le = [(k/k,) X l e m ] ) , the values of k / k , computed by the two methods usually agree to within a factor of 2 or 3. This is more than enough accuracy to justify use of RRK, particularly for predictive purposes. Conversely, if one is using measurements of IC in the falloff
region to obtain high-pressure Arrhenius parameters, an error of a factor of 2 or 3 will lead to an error of ca. 1 kcal/mol in the activation energy for a process whose A factor is known. The only exception in Table I1 is the value for acetyl a t 3OO0K, where the value of s = 2 is probably the problem. This could lead to a generalization about
Table IV : Molecular Parameters Used 1. WC4H10-7 Molecule Complex
7 -
Frequencies, om-', and regeneracies
IAAIBIc (g cm2)s X 10180 TIri$ cm2) X 1040'
2950 (6) 2870 (4) 1460 (6) 1370 (3) 1280 (3) 1170 (2) 1030 (2) 960 (2) 820 (2) 730 (1) 431 (1) 271 (1) 210 (2) 102 (1)
2950 (6) 2870 (4) 1460 (6) 1370 (3) 1280 (3) 1180 (1) 1030 (2) 952 (1) 803 (1) 730 (1) 109 (2) 32 (2)
x
1.56 x 107 9.16 X lo2 27 2
2.01
106
TQlr
Sigma" Collision diameter,
A
2 6.0
2. Molecule
7 -
CsHe-
3. PhCOComplex Moleoule
7 -
Complex
2974 (2) 2950 (2) 2915 (2) 1469 (2) 1460 (2) 1388 (1) 1370 (1) 1190 (2) 995 (1) 822 (2) 260 (1)
2960 (6) 1436 (6) 95 (2) 66 (2)
3060 (5) 1700 (1) 1600 (3) 1483 (1) 1260 (3) 1160 (2) 1035 (3) 940 (3) 785 (3) 655 (2) 440 (3) 350 (2) 154 (1) 80 (1)
3060 (5) 1950 (1) 1600 (3) 1483 (1) 1290 (2) 1160 (2) 1035 (3) 940 (3) 785 (3) 655 (1) 440 (3) 310 (1) 175 (2) 80 (1)
x
3.28 x 105 2.92 3 6
5.83 X lo1
1.17 X lo8 3.00 X 10' 3
1.85
104
6
1
5.0
'Product of reduced moments of inertia for internal rotors (internal symmetry = "foldness" of the rotor). isomers. The Journal of Phyaical Chemiatry, Vol. 76,No. 10, 1071
1
6.0
' Product of internal
COMPARISON OF RRK
AND
values of s < 5 or 6 , but the problem really does not arise that much in molecules of chemical interest at the usual pyrolysis temperatures. I n several of the model cases presented here, the reverse reaction is susceptible to study under conditions where the unimolecular proCH3; cess is not. Data on these systems ( i e . , CH3 CzH5 CzHs)show that the RRKM formulation predicts more closely the correct pressure dependence.’ This in no way detracts from the simple notion presented here, to wit: RRK theory may be used to estimate pressure dependence of thermal unimolecular processes in the “measurable” range. I n ref 3 and 4 the authors have defined values of s in terms of the vibrational energy content, and they have shown that these values are generally lower than sk, the value of s from a best fit of the Kassel integral. However, s may also be defined as Cyib/R, and this value of s is close to sk, so much so that it serves to make s a known input parameter. The fact that Cyib/ R, a t the temperature T, is not the same as E,ib/RT is not surprising for nonclassical oscillators. It is not the intention here to prove by analytical means that Cvib/R is a better definition of s than E,ib/RT. Clearly these are the same in the classical limit. Given that Cvib/R turns out to work better as a definition for the Kassel integral, one is tempted to offer as an explanation the fact that, whereas the energy is a measure of the average number of “effective oscillators” from 0 to TOK, the heat capacity at T measures the number of oscillators a t this temperature. The examples of ref 3 have been recomputed here as
+
J. Phys. Chem. 1971.75:1333-1338. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 08/31/15. For personal use only.
+
7-4. CHsNHNH2Molecule Complex
1337
RRKM THEORIES
--6.
Molecule
tsrt-Bu0Complex
2980 (6) 2900 (3) 1465 (6) 1350 (4) 1220 (2) 1106 (2) 1013 (3) 919 (1) 748 (1) 450 (8) 350 (2) 250 (3)
well. The RRKM calculations agree fairly well with those tabulated therein; the small differences probably being due to the fact that the collision diameters used in this work are probably slightly different than those in ref 3. Table I11 illustrates the fact that even in the cases originally used to substantiate the claim of complexity of s, the RRK method is adequate for predicting k / k , as long as k 5’10-4. It is, therefore, concluded that use of RRK theory through the readily available tabulated values of the Kassel integraleb is justified for thermally activated systems in most practical cases. The value of s Cvib/R can be obtained from tabulated or estimated2 heat capacities by subtracting the contribution of translation and rotation, viz. C,
2900 (3) 1714 (1) 1400 (3) 1109 (1) 900 (2) 512 (1) 150 (1)
=
Cyib
S E -
R
=
Cp - 4R =--Cp - 8 R 2
It is certainly no harder to estimate A factors than to estimate the geometry and frequency assignment for the activated complex which is required by RRKM theory.
Appendix Standard Parameters and Frequencies. The actual molecular structure parameters and frequencies used as input for the computations are shown in Table IV.
2900 (3) 1900 (1) 1400 (3) 450 (2) 256 (1)
---7. Moleoule
n-hexylComplex
2940 (7) 2920 (12) 2870 (6) 2200 (1) 1460 (7) 1462 (7) 1360 (4) 1376 (2) 1303 (3) 1270 (8) 1250 (3) 1040 (3) 1160 (2) 940 (5) 1040 (4) 890 (2) 890 (3) 800 (3) 760 (3) 575 (2) 474 (1) 420 (2) 336 (2) 300 (2) 212 (2) 212 (1) 132 (2) 94 (1) 61 (1) 1.97 X IO6 7.06 X 156 5.60 X lo6 1.20 X loT 7.99 X lo4 3.25 X lo5 2.95 X IOT 2.42 X lo7 5.15 3.34 3 3 0.5 0.5 3 1 1 1 1 1 4.0 5.0 5.0 6.0 3300 (2) 3000 (2) 2800 (2) 1500 (4) 1250 (3) 1050 (3) 850 (2) 447 (1) 315 (1) 257 (1)
3293 (3) 2890 (2) 2250 (2) 1600 (1) 1350 (2) 1140 (5) 821 (2) 700 (2) 300 (1)
rotation symmetry numbers.
Sigma = u/n, where
u
C,
Cvib = C v - [(3/dRltrans - [(‘/z)R]rot
7-6. CHsCOMolecule Complex
2980 (6) 2900 (3) 1465 (6) 1350 (4) 1220 (2) 1106 (1) 1013 (2) 919 (1) 530 (2) 450 (1) 350 (2) 225 (2) 200 (2)
-R
cyclobutenMolecule Complex
7 - 8 .
3080 (2) 2950 (4) 1566 (1) 1430 (2) 1250 (4) 1090 (3) 986 (1) 840 (4) 640 (2) 325 (1)
3300 (6) 1320 (12) 660 (5)
5.68 X 10’ 5.68 X 106
2
2 4.0
is the symmetry number for external rotation and n is the number of optical
The Journal of Phyeical Chembtry, Val. 76, No. 10, 1971
J. Phys. Chem. 1971.75:1333-1338. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 08/31/15. For personal use only.
1338
L. L. BURTON, S. SHERER,AND E. R. VANARTSDALEN
Some of these frequencies are averages from the careful vibrational assignment. Sources are: Model 1, nand complex (ref 8) ; Model 2, CzHs and complex (ref 7) ; Model 3, PhCO and complex (ref 9) ; R/Iodel4, CH3NHNH2(ref 10) and the complex from this work using the four-center transition state of Benson (ref 2); Model 5 , tert-Bu0 this work, using tert-BuOH as a model (ref 11) and complex (this work, reducing the four deformations destined to become external rotations of products to SO%, changing the CH3 torsion to a free rotation and using the C-C stretch as the reaction coordinate.) ; RiIodel 6, acetyl (this work, using acetaldehyde as a model) (ref 12), and complex (this work, reducing the three deformations destined to become external rotations of products to 50%) changing the CH3torsion to a free rotation and using the C-C stretch as the reaction coordinate; Model 7, n-hexyl and complex were assigned in this work, the n-hexyl from simple
modifications to the assignment for n-hexane (ref 13), and the complex using methyl-cyclopentane as a basis (ref 14) ; Model 8, cyclobutene and complex (ref 15). (7) E. V. Waage and B. S. Rabinovitch, Int. J.Chem. Kinet., in press. (8) G. Z. Whitten and B. 8. Rabinovitch, J . Phys. Chem., 69, 4348 (1965). (9) R. K. Solly and 8. W. Benson, J . Amer. Chem. Soc., in press.
(10) J. R. Durig, W. C. Harris, and D. W. Wertz, J. Chem. Phys., 50, 1449 (1969).
(11) E. J. Beynon and J. J. McKetta, J . Phys. Chem., 67, 2761 (1963). (12) (a) J. C. Evans and H. J. Bernstein. Can. J. Chem.. 34. 1083 (1956); (b) K. S. Pitzer and W. Weltner, J. Amer. Chem'. SOL, 71, 2842 (1949). (13) J. H. Schachtschneider and R. G. Snyder, Spectrochim. Acta, 19, 117 (1963). (14) D. W. Scott, W. T. Berg, and J. P. McCullough, J . Phys. Chem., 64, 906 (1960). 62, 895 (15) C. 5. Elliott and H. M. Frey, Trans. Faraday SOC., (1966).
Proton Magnetic Resonance Spectra of Molten Alkali Metal Acetate Solutions of Polyhydric Alcohols and Phenols by Louis L. Burton, S. Sherer, and E. R. VanArtsdalen* Department of Chemistry, University of Alabama, University, Alabama 564.86
(Received January 6 , 1971)
Publication costs assisted by the University of Alabama
Molten sodium-cesium-rubidium acetate eutectic has been demonstrated to be a suitable fused salt solven$ for study of solutions of polyhydric alcohols and phenols between 100 and 150'. Results of nmr investigations are reported which demonstrate strong solute-solvent interaction in these solutions. A pronounced downfield shift of OH is interpreted as indicating hydrogen bonding and exchange. Aromatic diols and triols show stronger interaction than the polyhydric alcohols. Phloroglucinol in acetate melt between 130 and 150' shows but a single, sharp peak somewhat downfield from the customary C-H peaks, indicating rapid exchange of all hydrogens. Considerable research has been directed toward heterogeneous reactions in fused sa1ts.l While simple molten salts have advantageous properties, such as thermal stability, low vapor pressure, wide liquid ranges, and high conductivity, their use as solvents for homogeneous organic studies has been limited by their generally high melting points and frequently poor solubility characteristics. Several recent studies have investigated reactions of organic compounds in molten salt solvents, such as quaternary alkylammonium salts2J and alkali metal thiocyanates4and acetates.6 Phenols, polyhydric alcohols, and some amino compounds were found to be soluble in molten alkali metal The Journal of Physical Chemistry, Vol. 76, No. IO, 1071
acetates at 190 to 240°.6b Although molten alkali metal nitrates and thiocyanates have been reported to be neutral to phenolic indicator^,^"^^ the phenols and (1) (2) (3) 87, (4)
W. Sundermeyer, Angew. Chem., Int. Ed. End., 4, 222 (1965). J. E. Gordon, J . Amer. Chem. SOC.,86, 4492 (1964). (a) J. E. Gordon, ibid., 87, 1499 (1965); (b) J. E. Gordon, ibid., 4347 (1965).
(a) T. I. Crowell and P. Hillery, J. Org. Chem., 30, 1339 (1965); (b) P. Hillery, Ph.D. Thesis, University of Virginia, Charlottesville, Va., 1968; (c) K. Stewart, M.S. Thesis, University of Virginia, Charlottesville, Va., 1968. (5) (a) L. L. Burton and T. I. Crowell, J. Amer. Chem. Soc., 90, 5940 (1968); (b) L. L. Burton, Ph.D. Thesis, University of Virginia, Charlottesville, Va., 1968.
