3356
TERRY S. CARLTON AND ALANB. HARKER
with pH measurements and equilibrium constant estimations encountered by other workers.1° I n the studies in the intermediate pH range this creates a problem in assessing the contributions of reactions 1and 2. The agreement between the results from this work and that from oxygen-18 exchange data a t 25OZ1points to a negligible isotope effect between oxygen-15 and oxygen-18 in reaction 1, and shows that the use of relationship ka = k1/3 used to calculate kl is in fact valid. The studies of reaction 2 are further evidence of the lower rates as opposed to those of Himmelblau and Babb. Due to the lower exchange in the available time, these values are not as accurate as those of kl. The values obtained experimentally, however, show remarkable agreement with values calculated from published values of ka and K . These also show the
constancy of the activation energy of reaction 2 up to 55". This study has shown the feasibility of chemical kinetic studies with a very short-lived radioisotope. Oxygen-15 and 10-min half-lived nitrogen-13 are the only radioactive isotopes of the elements oxygen and nitrogen, and this study points to the potential of these iaotopes in chemical kinetic studies.
Acknowledgments. The authors thank Dr. M. M. Ter-Pogossian for his interest in this work, Professor Teresa J. Welch for very helpful discussions, and Mr. E. E. Hood. and Mr. L. Troutt for their assistance. (21) This work gives k~ = 3.848 X 10-2 sec-1 at 25' while Poulton and Baldwin (ref 10) obtained a value of 3.64 X 10-2 sec-1 at an ionic strength of 0.6 and showed that the rate constant increased with decreasing ionic strength.
Kinetics of the Reaction of Hydrogen Iodide with Tetrafluoroethylene by Terry S. Carlton and Alan B. Harker Department of Chemistry,Oberlin College, Oberlin, Ohw 440'74 (Received April 8,1969)
The reaction between gaseous hydrogen iodide and tetrafluoroethylene is first order in both reactants between 176 and 222'. 1,1,2,2-Tetrafluoroethaneand iodine are the major products and l-iodo-1,1,2,2-tetrafluoroethane is the minor product. The presence of added iodine reverses the relative importance of the products but does not affect the rate constant. The activation energy for tetrafluoroethylene consumption is 20.5 4 0.4 kcal/mol and A = 1.1 x lo*l./(mol sec). Unlike reactions between hydrogen iodide and alkenes, the principal rate-determining step is transfer of a hydrogen atom from hydrogen iodide to tetrafluoroethylene. The C-H bond dissociation energy of the CHF,CF, radical is shown to be at least 49 kcal/mol, which is 10 kcal/mol greater than the corresponding bond energy of the ethyl radical. Introduction Hydrogen iodide reacts with alkenes in the gas phase to produce alkyl iodides and alkanes.' Likewise the reaction between hydrogen iodide and 1,l-difluoroethylene produces 1,1-difluoro-1-iodoethaneand 1,ldifluoroethane.2 Methyl groups have a pronounced effect on the activation energyll but the activation energy for the reaction with 1,1-difluoroethylene is only slightly less than that for the reaction with ethylene itself. The CH2group is present in both ethylene and 1,l-difluoroethylene, and the present investigation of the reaction between hydrogen iodide and tetrafluoroethylene was undertaken to determine whether complete substitution of fluorine for hydrogen would have a The Journal of Physical Chemistry
larger effect on activation energy and mechanism than did partial Substitution. Experimental Section Experimental details are those of ref 2, with the following exceptions. Tetrafluoroethylene (Peninsular Chemresearch) was purified by gas chromatography at -79" on a column whose liquid phase was 1,1.,3,5,7,8hexachlorododecafluorooctane. l-Iodo-1,1,2,2-tetrafluoroethane and 1,1,2,2-tetrafluoroethanewere syn(1) P. 8. Nangia and @. W. Benson, J. Chem. Phys., 41, 530 (1964), and references cited therein. (2) T. S. Carlton, A. B. Harker, W. K. Natale, R. E. Needham, R. L. Christensen, and J. L. Ellenson, J . Amer. Chem. SOC.,91,556 (1969).
3357
KINETICS OF HI REACTION WITH C Z F ~ ~~~~
Table I : Kinetic .Data for Reactions between Hydrogen Iodide and Tetrafluoroethylene" Run no.
Temp, OC
Time, min
1 2 3b 4c 5d 6 7 8 9 10 11 12 13* 14 15 16' 17 18 19' 20 21 22 23
222.3 222.3 222.3 222.3 222.2 212.1 212.0 202.4 202.3 195.3 193.7 185.5 185.4 184.5 184.5 175 9 175.9 175.9 175.9 165.2 165.2 165.2 165.2
13.3 12.5 14.3 17.6 33.0 22.3 22.2 32.3 30.2 30.3 28 31.1 29.6 30 30 29.5 29.5 22 34.5 21 21 35 21
I
---
.
Final
Initial &mol--
------#mol
HI
CZFI
CaHFiI
CzHzF4
36.9 35.8 39.0 34.3 74.2 58.0 46.7 65.3 115.4 65.4 81.6 94.5 88.8 90.1 94.9 133.9 146.2 135.3 146.5 193.1 200.8 204.6 192.9
19.1 37.8 29.5 0.0 0.0 52.5 44.6 57.0 48.0 94.8 72.1 93.0 85.8 91.3 90.2 137.4 131.7 136.5 0.0 145.6 140.7 184.8 174.3
0.03 0.04 0.76 1.93 4.00 0.45 0.29 0.55 0.60 0.69 0.34 0.44 2.49 0.41 0.37 3.00 1.04 0.47 6.0 0.45 0.57 0.75 0.15
0.53 0.91 0.11 0.01 0.20 2.06 1.63 2.48 3.40 2.46 2.12 2.50 2.04 2.13 2.21 0.86 2.91 2.04 0.1 2.53 1.87 3.82 1.76
Rate constants, ----l./(mol sea)----IC (0s 1) IC'
0.113 0,108 0.100
0.107 0.103 0.0127
0.0727 0.0694 0 0425 0.0475 0.0328 0.029 0.0177 0.0201 0.0198 0.0193 0.0135 0.0133 0.0117
0.0596 0.0589 0.0348 0.0404 0.0256 0,025 0.0151 0.0173 0.0166 0.0165 0.00302 0.0098 0.0095
0.0095 0.0077 0 0056 0.0043
0.0081 0.0059 0.0047 0.0040
... ...
...
...
I
...
...
I
Reaction vessel 94.4 ml in runs 7, 8, 12, 22, and 23, and 110.6 ml in all others. Surface-to-volume ratio three to four times larger in 2.31 pmol CFHzCFHI and 1/z pmol IZpresent initially. d 4.26 pmol C H F Z C F ~ I the 94.4-m1 vessel. b 5 x 10 pmol Izpresent initially. and pmol Izpresent initially. e 2.16 pmol CHFzCFzIpresent initially. Increase in amount of CHFzCFzI was used in calculating k 6.34 pmol CHFzCFzIand 8/z pmol IZpresent initially. and k'. f 6 X 10 pmolIZpresent initially.
thesized by the reaction of gaseous hydrogen iodide with unchromatographed tetrafluoroethylene a t room temperature. After preliminary fractionation the products were purified by gas chromatography. 1,1,2,2Tetrafluoroiodoethane was identified by its proton nmr splitting pattern3 and by a molecular-weight determination, accurate to within 2%, by means of a gasdensity type gas chromatography detector. 1,1,2,2Tetrafluoroethane was identified by its infrared spect r ~ m . Iodine ~ (Baker and Adamson) was ACS reagent grade. Quantities of reactant iodine were determined by weighing or by filling the reaction vessel with iodine vapor that was in equilibrium with solid iodine a t a known temperature. Reaction temperatures were maintained constant to k0.1". Reaction mixtures were separated a t - 130" into volatile and nonvolatile fractions, each of which was analyzed with a separate gas chromatography column a t room temperature. Elution times were 7 min for 1,1,2,2-tetrafluoroiodoethane on the Halocarbon 11-21 column and 15 min for 1,172,2-tetrafluoroethane on the dimethylsulfolane column.
Results
- 1.0
-0 -
-1.3
VI
i?
5 - -1.6 .-c -t -t-
-1.9
ISI
3
-2.2
2.02
2.08
2.14
2.20
2.26
103h deg-'. Figure 1. Arrhenius plot for k (eq 1).
sions were limited to small percentages, and the sum of the rates of 1,1,2,2-tetrafluoroiodoethane and 1,1,2,2tetrafluoroethane production was proportional to the product of the average concentration of hydrogen iodide and the average concentration of tetrafluoroethylene. This second-order rate law was observed regardless of whether additional iodine or 1,1,2,2-tetrafluoroiodoethane was present from the start of the reaction. Kinetic results appear in Table I and Figure 1. The
The only products of the reaction of hydrogen iodide (3) Observed nmr parameters at 60 MHz: d = 6.26 ppm relative to with tetrafluoroethylene were 1,1,2,2-tetrafluoroethane1 tetramethylsilane; JHZFI= 2.6 Ha; JHZFZ = 54.7 H E . 1,1,2,2-tetrafluoroiodoethane1 and iodine. Conver(4) R. Klaboe and J. R. Nielsen, J . Chem. Phya., 32,899 (1960). ,
Votume 73,Number IO
October 1969
3358
TERRY S. CARLTON AND ALANB. HARKER
rate constant k was calculated from eq 1, in which the subscript i indicates initial concentration, f indicates final concentration, and t is the reaction duration. The expressions in parentheses are simply the average concentrations of the reactants.
k = { [C2HFdI]r
+ [CdW"]r ]/ i t ( [Hili
- ' / z [ C ~ H F ~I ] ~[CZHZRI~) X ([C~F4j'i - '/2 [ G H F J I f - '/2 [CdU"lf) ]
Discussion Two possible mechanisms for the reaction merit consideration. Mechanism A consists of reactions 2-5, with reaction 2 as the rate-determining step.
+ H I *CHFzCFz + I CHFzCF2 + CHFzCFJ + I CHF2CFz + H I +CHFZCHFZ + I 21 + i\iI I2 + &I 1 2 ---+
(2) (3) (4)
(5)
Mechanism B consists of reactions 3-7, with reactions 6 and 7 as slow steps.
+ HI CHFzCFJ CHF2CFzI + I +CHF2CF2 + CzF4
---t
(6) I2
(7)
A mechanism analogous to B was the principal one in reactions of hydrogen iodide with alkenes.' In the reaction with 1,l-difluoroethylene a B-type mechanism was the only one for 1,l-difluoro-l-iodoethane formation, though possibly not the only one for 1,l-difluoroethane formation.2 However, mechanism A is the more important one in the reaction with tetrafluoroethylene, since runs 4,5, 13, and 19 demonstrate that reaction 7 is too slow for 1,1,2,2-tetrafluoroiodoethane to have been the precursor of more than a small fraction of the tetrafluoroethane in runs without added iodine. Although mechanism A is responsible for most of the tetrafluoroethylene consumption and for almost all of the tetrafluoroethane production, it is possible that mechanism B is partly responsible for production of 1,1,2,2-tetrafluoroiodoethane. I n runs 3 and 16 the initial iodine concentration was more than ten times greater than the final iodine concentration for any other run. The much larger C H F r CF21:CHF2CHF2ratios observed in these two runs are in accord with mechanism A, though not incompatible with mechanism B. Runs 3 and 16 also demonstrate that reactions 8-10 are insignificant in the temperature range of this investigation CzF4
+ I +CFzICF2
The Journal of Physkal Chemistry
(8)
(9)
I2
(10)
+
If reactions 8-10 are insignificant, k equals ICz kq, which is independent of concentrations, in agreement with experiment. If reactions 8-10 were significant, the presence of iodine would increase k by an amount
(hd[ I 2 I/& (1)
The rate constant k' was calculated from a modification of eq 1 in which only the concentration of 1,1,2,2tetrafluoroethane appeared in the numerator.
C2F4
+ +CF2ICFz + I CFzICFz + H I +CHFzCFzI + I C2F4
+
[I2I)/ [HIlaverage
Such an increase is not observed in runs 3 and 16. The normal k values for runs 3 and 16 also demonstrate that the overall reaction rate is not increased by iodine catalysis. The rate constants for runs in the reaction vessel with the larger surface-to-volume ratio tended to be slightly low, but above 175" the discrepancy was small, suggesting that surface effects were of little or no importance. Rate constants a t 165" were not used in calculating Arrhenius parameters because of irreproducibility. I n reactions with 1,l-difluoroethylene the low-temperature limit for reproducible results was about 200" . 2 The Arrhenius parameters from a least-squares analysis of the k values are E = 20.5 f 0.4 kcal/mol and A = 1.1 X lo8 l./(mol sec) (log A = 8.06 0.19). Uncertainties are standard deviations. An Arrhenius plot of k' values showed about the same scatter as Figure 1, except that the presence of extra iodine resulted in very low values of k' for runs 3 and 16. Leastsquares analysis of the other k' values gave E' = 22.1 & 0.5 kcal/mol and A' = 5.8 X lo8I./(molsec) (log A' = 8.76 f 0.23). If 1,1,2,2-tetrafluoroiodoethanewere formed only by mechanism A, E would be the activation energy for reaction 2, whereas if it were formed only by mechanism B, E' would be a better measure of the activation energy for reaction 2. In either case the minor importance of mechanism B for the overall reaction allows one to place an upper limit of 22.6 kcal/mol on the activation energy for reaction 2. Since the activation energy of reaction 2 is no less than its endothermicity, 22.6 kcal/mol is also the upper limit for AE (or A H ) of reaction 2. The 25" bond-dissociation energy of hydrogen iodide is 71.4 kcal/mol.6 Therefore the lower limit for the C-H bond dissociation energy of CHF2CF2 at 25" is 49 kcal/mol. By comparison, AEzssis 38 to 39 kcal/mol for the reactione-8 CHaCH2 ----t CH2CHz
+H
(11)
The striking effect of fluorine substitution in strengthening the C-H bond in these radicals is not predicted by (5) T. L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed, Butterworth and Co. Ltd., London, 1968. (6) L.F.Loucks and K. J. Laidler, Can. J. Chem., 45, 2795 (1967). (7) D.B. Hartley and S. W. Benson, J . Chem. Phys., 39, 132(1963). (8) "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500,U. 8. Government Printingoffice, Washington, D. C., 1950.
THECRITICALCONSTANTS OF CONFORMAL MIXTURES
3359
simple Hiickel molecular orbital calculations, in which the C-F bond integral leads to a larger localization energy for tetrafluoroethylene than for ethylene.
donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Assistance was also received from the National Science Foundation through its Undergraduate Research Participation Program.
Acknowledgments. Acknowledgment is made to the
The Critical Constants of Conformal Mixtures
by Aleksander Kreglewski and Webster B. Kay Department of Chemical Engineering, The Ohw State University, Columbus, Ohw 43,910
(Received April 4, 1Q63)
The range of validity of the theory of conformal solutions was tested by the evaluation of critical temperatures To and pressures Po of a wide variety of binary systems for which data on the critical state were available. Additionally, critical temperatures and pressures of the following binary systems were determined : five systems of propane with 12-alkanes (C, to CB),n-hexane with diethylamine or 2-butanone, and the diethylamine 2-butanone system. The total pair potentials (aji)and the force constants per equivalent surface (eij) were expressed by means of the general principle of corresponding states. For mixtures of two inert liquids, elj is equal to the harmonic mean of eiz and e j j . The agreement of calculated and experimental To and Pcis very satisfactory for mixtures composed of molecules that differ in both size and shape over a wide range. The equations for the critical and the pseudocritical constants of mixtures do not involve any empirical constants. The calculations are simple and require only a knowledgeof the properties of the pure components.
+
Introduction Application of the theory of conformal solutions' requires a knowledge of a general principle of corresponding states. It is fortuitous that the classical principle is valid for small molecules such as Ar, Kr, CO, CHI, and NO,but fails completely for large molecules. Thus, a lack of agreement with experimental data for mixtures of larger molecules of different sizes does not mean that the above theory is wrong. The theory and the classical principle were applied previously2 for evaluation of the pseudocriticaltemperature TZcand pressure PZc,critical constants Tc and Pc, and the excess Gibbs energy of mixing GE by using a crude combining rule for the force constant €12 of interaction between the two components, 1 and 2, of the mixture. The calculations, though partly successful, disclosed the following principal errors. (i) The required value of the constant in the relation for (To- TZc)was 2.2 instead of the theoretical value, 9/16, resulting from the van der Waals equation. (ii) The parameter A,, determining the deviations from an ideal solution, was in general a function of composition and could be determined only a t a limiting concentration, whereas it should be a constant for a given system a t any composition. Prausnitz and Chueh,* by starting with different assumptions than those in the present work, concluded that the TOand
Vc curves are functions of surface fractions and that in this case A, is nearly independent of composition. (iii) The force constants of the pure fluids, given previously,2are much too small and do not reflect the total pair potentials but correspond rather to interactions between small segments of the molecules. This error is partly due to the questionable combining rule used for their evaluation and partly to the use of the classical principle of corresponding states valid a t most for interactions between small molecules (segments). All of these discrepancies are completely eliminated by introducing the following assumptions. (A) The minimum values of total pair potentials ai,between two molecules in relation to that of a reference substance aooare4'5
til= all - =
Tlc(V1*)1/8 T,' (Vz*)"' a22 2 2 - z - = coo Tooc(Voo*)'/8; - uo0 Tooc(Voo*)l~s
and
(1) H.C. Longuet-Higgins, Proc. Roy. Soc., A205,247 (1951). (2) A. Kreglewski, J. Phys. Chem., 71, 2860 (1967); 72, 2280 (1968). (3) P.L.Chueh and J. M. Prausnitz, A.I.Ch. E. J., 13,1107 (1967). (4) A.Kreglewski, J. Phys. Chem., 72,1897 (1968). (5) A.Kreglewski, ibid., 73,608(1969). Volume Y3, Number 10 OctobeP 1363
