3040
C. A. GOYAND H. 0. PRITCHARD
portance cannot be determined on the basis of sedimentation velocity data alone. Considering the available information from a strictly empirical standpoint, at least one important conclusion may be drawn. The degree to which the behavior of a particular protein deviates from that predicted by eq. l a in a given salt can be measured. It cannot be assumed, however, that the same protein in another salt or another protein in the same salt will be abnormal to the same degree. The density correction required to extract, for example, the molecular weight of a given protein from sedimentation data obtained in a con-
centrated solution of a particular salt will, in general, be unique for that combination of protein and salt. In view of the increasingly common use of two-component solvents for studies of proteins, a search for a pattern in the behavior of known systems would clearly be in order. In the meantime, the interpretation of experiments of this kind must be approached with some caution.
Acknowledgments. The authors wish to thank Dr. Charles R. Willms for his help with the sedimentation equilibrium experiment and Mr. Booker T. Dabney for his able technical assistance.
Kinetics and Thermodynamics of the Reaction between Iodine and Methane and the Heat of Formation of Methyl Iodide
by C. A. Goy and H. 0. Pritchard Chemistry Department, University of Manchester, Manchester 18,England
+
(Received March 83,1966)
+
The equilibrium CH4 I 2 e CHJ H I has been studied in the gas phase over the tem= 12.67 i perature range 585748°K. The heat of this reaction is calculated to be 0.05 kcal./mole, leading to a heat of formation of gaseous methyl iodide AHf0298 = 3.40 kcal./mole. The equilibrium is established via the reaction I CH4+ H I CH3,which has a rate constant k = 1016.0exp[(-35.0 f l.l)lOaRT]cc. mole-' sec.-l over the temperature range 548-618°K.
+
The reaction between H I and CHaIhas been studied by Flowers and Benson' over the range of temperature 533-589°K. They propose a kinetic scheme involving the reactions
Iz
I
+ I equilibrium constant = K , ki I + CHd + CH3 12
kz
ka
CH,
+ HI If CH* + I
+
librium at somewhat higher temperatures over periods ranging from 3 days to a few hours (depending on temperature) by heating together IZand CH,. Also, over a restricted temperature range, we have been able to determine the Arrhenius parameters of the ratedetermining step k4.
Experimental All experiments were carried out by sealing up known quantities of CHI and I 2 in a 300-ml. Pyrex flask. The
kr
We have found that it is possible to establish this equiThe Journal of Physical Chemistry
(1) M. C. Flowers and 8.W. Benson, J. Chem. Phys., 38, 882 (1963).
KINETICS AND
THERMODYNAMICS O F THE
REACTION
whole flask, up to and including the break-seal, was heated in an electric furnace. The temperature, which was constant to & l oover the volume of the vessel, was determined using a thermocouple calibrated at the melting point of lead (600.5"K.). Each experiment was terminated by breaking the seal and pumping the hot gases into a liquid nitrogen trap containing solid ICN. (This converts the H I quantitatively2 into HCN, which is less likely to be lost by reaction with tap grease or metal parts of the gas chromatograph, and which, incidentally, is easier to resolve from CH31 with simple column packings.) The fraction containing the CHJ and the HCN was collected from this trap and analyzed using a gas chromatograph with thermistor detectors. Almost any column packing is satisfactory. In the kinetic runs, reaction was never taken more than 10% of the way toward equilibrium, and, to minimize the error in timing due to heating up the flask, the following modified procedure was adopted. The flask containing the reactants was brought t o temperature equilibrium in a subsidiary furnace at 550°K. and then moved into the reaction furnace. The reaction was terminated in the normal way. Experiments using a dummy flask containing unshielded thermocouples suggest that the uncertainty in the reaction time is about A 2 min., which is negligible compared with the reaction times used (3-55 hr.). Equilibrium Measurements. Two series of experiments were performed. The first series (A) of 10 runs was carried out at or about 630°K. using wide variations in Izand CHI concentrations (over a factor of 20 in each case), in order t o establish that the equilibrium really was of the form CH4
+
I2
CH3I
+ HI
The concentrations of both CHd and H I (i.e., HCN) produced were checked, but the calculated equilibrium constants are based on CHJ formation as being the more reliable. A second series (B) of 9 runs was then carried out over the range of temperature 585-748"K., a typical run having initially about 2.5 cm. pressure of CH4 and about 025 g. of Iz. The results of these in experiments are 1' and a leastmsquares plot of log K , vs. 1/RT has a slope of 12.67 f 0.20 kcal./mole, with an intercept of 0.759.
The Heat of Formation of Methyl Iodide determinations Of the heat of formation of CH3I have been discwed in detail by Hartley, Pritchard, and Skinner3 and by Carson, and but it has so far not proved 'Ossible to select a very precise value for this quantity.
3041
Table I: The Equilibrium CHI A[-
T,OK.
Log KT
748 732 717 708 688 620 616 607 585
- 2.9455 - 3.0267 - 3.0871
+ Iz
CH31
+ HI
- H0z08)/Tl, cal. mole-' deg.-1
(POT
3.480 3.468 3.457 3.451 3.436 3.387 3.385 3.378 3.364
- 3.1588 - 3.2595 - 3.7300 -3.7110 -3.8063 -3.9688
Av.
AHOzes, csl. mole-]
12,685 12,677 12,607 12,677 12,626 12,682 12,545 12,623 12,592 12,635
The free energy function - ( F o r - Hozgs)/Tis tabulated in the "JANAF table^"^ for the molecules CH4, Iz,and HI. The free energy function for CH31 was calculated according to the same formulas, using the vibration frequencies given by Herzberg6 and the internuclear separations given in ref. 7. It was found that the change in free energy function in the reaction was precisely linear over the temperature range 600800"K., making interpolation of A[- ( F o T - H02es)/T] at the experimental temperatures a trivial matter. Table I lists the interpolated values for each run, together with the derived value of
AHOW,
=
-RT In K ,
+ T A [ - ( F o T - H02ss)/T]
for the reaction. The result is that = 12.64 i 0.05 kcal./mole, where the limits quoted include eight of the nine results. (The results of all 19 determinations, i.e., series A and B, taken together also give 12.64 kcal./mole but with a somewhat larger spread.) In the "JANAF Tables," thermodynamic functions for diatomics are calculated including vibrational anharmonicity, but for polyatomic it is neglected. Comparing the molecules CH, and CHJ, the neglect of anharmonicity is unlikely to cancel, and the calculations shown in Table I were repeated assuming that the two lowest frequencies v 3 and v 6 (2) C. A. Goy, D. H. Shaw, and H. 0. Pritchard, J . Phys. Chem., 69, 1504 (1965). (3) K. Hartley, H. 0. Pritchard, and H. A. Skinner, Trans. Faraday Sac., 46, 1019 (1950). (4) A. S. Carson, W. Carter, and J. B. Pedley, Proc. Roy. Sac. (London), A260, 550 (1961). (5) " JANAF Interim Thermochemical Tables," Dow Chemical Co., Midland, Mich. (6) G. Herzberg, "Infrared and Raman Spectra," D. Van Nostrand Co., Inc.,New York, N. Y.,1945. (7) S. L. Miller, L. C. Aamodt, G. Dousmanis, and C. H. TOppnee, J . Chem. phys., 20,1112 (1952).
Volume 69,Number 9 September 1966
3042
C. A. GOYAND H. 0.PRITCHARD
using the same numbering as Flowers and Benson. The over-all activation energy for the formation of CH3I is 53.2 1.1 kcal./mole, and, making use of interpolated values of log K , for the dissociation Iz 21 from the “JANAF Tables,” one gets the rate constant for reaction 4, the rate-determining step. The values of k4 obtained in 14 experiments are plotted in Arrhenius form in Figure 1, and a least-squares fit to these points gives log A = 14.95 (cc. mole-’ set.-' units) and E = 35.04 i 1.1 kcal/mole. Flowers and Benson determined Arrhenius parameters for k1 and k3/kz in their kinetic experiments. According to their reaction scheme, the KT which we have determined is related to their rate constants by the expression K , = k4kz/lCakl, giving kq = exp [(-34.1 =k 1.5)103/RT] cc. mole-1 set.-', in good agreement with our direct value. We therefore confirm their conclusion that the frequency factor A4 for this reaction is higher than the conventional collision number.
*
1.60
1.70
1.65
1.75
1.80
10a/T.
Figure 1. Arrhenius plot for the CH, HI CH,. reaction I
+
+
in CHaI had values of 09, = 5 cm.-l. This is likely to be an overestimate, but the resulting correction is only 30 cal./mole, giving = 12.67 i 0.05 kcal./mole.* We therefore obtain the heat of formation of gaseous CHaI as A H f 0 2 % = 3.40 i (0.05 z) kcal./mole, where fx is the uncertainty in the heats of formation of CH4, Iz(g), and HI, as given in the “JANAF Tables.”
+
Kinetic Measurements The rate of formation of CHaI in the temperature range 548-618°K. was found to be half order in 12 and first order in CH4,consistent with the mechanism
+
Acknowledgment. We wish to thank Dr. G. Pilcher for several very helpful discussions. (8) The agreement between this value and the slope of the van’t Hoff plot is fortuitous since correction to T = 298OK. v i a the a p propriate values of HOT HOaoa leads to a resultant slope of 12.37 kcal./mole.
-
