MAURICEM. KREEVOY AND HERBERT B. SCHER
3814
benzoic acid radical, was not the same as that of methanol radical, so all of the above reactions (1 to 5 ) must contribute to the apparent decay. In these experiments, the poor signal-to-noise ratio gives rise to an ambiguity in the decay pattern; therefore, no definite mechanism could be proposed using the present technique.
Acknowledgment. The author is grateful to Professor H. S. Mason for his encouragement and worthwhile discussions. Mr. Gunther Weiss' kindness in making the mixing cell and other apparatus is also appreciated. This study was supported by grants from the American Cancer Society and the United States Public Health Service.
The Diffusion Coefficient of Atomic Mercury in Isooctane
by Maurice M. Kreevoy" and Herbert B.' Scherlb School of Che??%istry, University of Minnesota, Minneapolis, Minneeota
(Received May 14, 1966)
The diffusion coefficient for atomic mercury in isooctane solution, 1.6 X cm.2 set.-', has been determined at 20" with an uncertainty of about 10% by experiments in which the mercury is removed from solution by a gold-plated rotating brass disk. When combined with other available information, this value strengthens the conclusion that the surface reaction of iodine with metallic mercury is impeded by nontransport (ie., chemical) factors.
In a previous papert2it was suggested that the rate of reaction of molecular iodine in isooctane solution with metallic mercury is principally controlled by the rate of a chemical reaction, rather than by the rate of the transport process. A key factor in this conclusion was the observation that the rate constant for reprecipitation of dissolved atomic mercury was larger by a factor of about 3 than that for reaction of iodine. The validity of this argument rests on the assumption that the diffusion coefficient of iodine, D12, in this solvent, is not much smaller than that of atomic mercury, D H ~ ~The . latter has now been measured and the former reliably estimated from closely related data. In fact, D I J D Hwould ~ ~ seem to be about 1.8, lending strong support to the original argument. Levicha14 has solved the dynamic diffusion equation for the case of a circular disk rotating about a perpendicular axis under conditions of nonturbulent flow. The results is shown in eq. 1, where IC is the apparent D'/Sw'/2 k=(1) 1.61 2 ~ ' ' ~ The Journal of Physical Chemietry
(transport-controlled) rate constant, D is the diffusion coefficient, w is the angular velocity of the disk (in rotations per unit time), and v is the kinematic viscosity of the solvent. If some substrate can be removed, irreversibly, at such a disk, at a rate substantially larger than the diffusion rate, then its diffusion coefficient can be evaluated if the rate constant for its disappearance from solution is m e a s ~ r e d . ~ It has been known for some time that mercury is appreciably soluble in isooctane and that it exists as the free atoms in solution.6 The present paper shows
(1) (a) Alfred P. Sloan Foundation Fellow, 1960-1964; (b) Esso Research and Engineering Fellow, 1963-1964. (2) P. Warrick, Jr., E. M. Wewerka, and M. M. Kreevoy, J . Am. Chem. Soc., 85, 1909 (1963). (3) V. G.Levich, Acta Physicochim. URSS, 17, 257 (1942). (4) V. G.Levich, Rues. J . Phys. Chem., 18,335 (1944). (5) A. C. Riddiford in "Advances in Electrochemistry and Electrochemical Engineering," Vol. 41, P. Delahay and C. W. Tobias, Ed., Interscience Publishers, Inc., New York, N . Y., forthcoming. (6) H. H. Reichardt and K. F. Bonhoeffer, 2. Eleldrochem., 36, 753 (1930).
DIFFUSION COEFFICIENT OF ATOMIC MERCURY IN ISOOCTANE
that it reacts with gold-plated brass with the required speed and irreversibility.
Experimental Section A brass cylinder -1.5 cm. in diameter was machined so that the part projecting into the solution was trumpet-shaped and the upper part could be attached to a shaft. The entire surface of the piece, with the exception of the bottom, was coated with a thin layer of Kel-F polymer by dipping it into an appropriate dispersion (3M commercial product), wiping the bottom clean, air drying, and then baking in a vacuum oven for 2 hr. a t 240’. The bottom surface was then electroplated with about 3 X cm. of gold.’ After electroplating, the gold surface was washed with distilled water, dried, and finally rinsed with isooctane. To perform an experiment, the gold-plated brass piece was immersed up to an appropriate level in 150 ml. of isooctane, previously saturated with atomic mercury. The solution was contained in a 250-ml. round-bottom flask. The disk was coupled to a synchronous motor through a gear train and a rod and rotated a t a known speed. Periodically, 15-ml. samples were withdrawn and analyzed spectrophotometrically for mercury (in a cell with a 5-cm. path length). After the analysis (requiring about 3 min.) the sample was returned to the reaction flask. During the period when the sample was out of the reaction flask, the motor and the timer (which were on the same circuit) were stopped. It was shown experimentally that almost no change in Hg“ concentration takes place, even over long time periods, when the motor is stopped. After each experiment, the diameter of the goldplated disk was measured with a micrometer caliper, and the mercury-contaminated gold plate was sanded off on a lathe. The brass was then polished and replated. (It was remeasured each time because its diameter changed with sanding and polishing.) To verify the applicability of the Levich equation to the present mechanical and geometric situation, the apparatus was also used to measure the diffusion constant of triiodide ion. These experiments were carried out in exactly the same way except that the brass disk was not gold plated and an aqueous solution, 4.0 M in potassium iodide, 0.04 M in triiodide, and 0.005 M in sulfuric acid, was used in the place of the mercury in isooctane. A nitrogen atmosphere was maintained over the solution during the experiment by continuous purging. Samples (1-ml.) were withdrawn periodically and titrated for iodine with thiosulfate. These conditions are chemically identical with those used by Bircumshaw and Riddiford to verify the Levich equation. a
3815
Results Good first-order kinetics were observed for the disappearance of triiodide ion, as previously reported by Bircumshaw and Riddiford. A rate law taking into account the minor diminution in volume during the course of the experiment was used.g At 2.00 rev. set.-' it gave a rate constant of 2.52 X lod3 cm. set.-'. The uncertainty in this value, deduced from the deviation of points from the rate law, is - f l % , but other experience with rate constants measured in this way suggests that their usual reproducibility, in fact, is in the neighborhood of f5-10%. The rate constant calculated from the Levich equation is 2.77 X cm. set.-', taking 1.27 X sec.-l as D,lo and 0.581 centistokes as v.ll The agreement with experiment is moderately satisfactory. If the diffusion coefficient had been calculated from the observed rate constant, it would have been 15% lower than the reported value.lO When the gold-plated disk was rotated in a saturated solution of mercury in isooctane (such a solution is 4 X M in atomic mercury initially2), 70-90% of the mercury is removed over a period of time. If the disk is reused without cleaning, more mercury is removed, although not as much as that removed initially, and with repeated reuse the disk finally will take up no more mercury. The reaction is not reversible, for neither partially nor completely “saturated” disks will release mercury to fresh isooctane. In each experiment with a freshly prepared disk, the disappearance of mercury followed a first-order rate law12 for a t least one half-life, and sometimes two. Figure 1 shows a typical plot of log A (the absorbance at 257 mp) as a function of time. Such plots were used to evaluate k by means of eq. 2 .
k=-
2.303 t-
lo
Ao log A,
Eight rate constants were obtained in this way, all at 20.0’, with stirring rates varying from 30 to 180 r.p.m. A plot of log k against log w is acceptably linear with a “best” slope of 0.44 f 0.06,13as determined by (7) L. Weisberg and A. K. Graham, “Modern Electroplating,” A. G. Gary, Ed., John Wiley and Sons, Inc., New York, N. Y., 1953, Chapter 9. (8) L. L. Bircumshaw and A. C. Riddiford, J. Chem. Soc., 698 (1952). (9) R. 9. Bradley, Trans. Faraday SOC.,34, 278 (1938). (10) G. Edgar and 5. H. Diggs, J. A m . Chem. SOC.,38, 253 (1916). (11) L. L. Bircumshaw and A. A. Riddiford, J . Chem. Soc., 1490 (1951). (12) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, Inc., New York, N. Y., 1961, Chapter 3. (13) The uncertainty is the 50% confidence limit.
Volume 69, Number I1 November 1966
MAURICE M. KREEVOY AND HERBERT B. SCHER
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3 9
d-
4
.
02 2 t
-
N g 1
0
.
1
.
1
200 TIME
.
1
.
1
400 (MIN.)
.
coo
Figure 1. The log of the optical density at 257 mp, A, as a function of time in a typical rotated disk experiment.
the method of least squares. The average deviation of points from this line is the equivalent of about an 11% error in k, which is not inconsistent with the estimated experimental imprecision. This average deviation does not grow appreciably worse if the slope is arbitrarily given the theoreticalat‘ value of 0.5, and in that cme2set.-'. This value case D at 20° is 1.62 X would seem to be uncertain by -lo%, as judged either by the agreement in the triiodide case or by the deviation of points in the logarithmic plot of k vs. w.
Discussion It is well known that mercury vapor (atomic) readily amalgamates gold. It is not surprising that atomic mercury in solution should do the same. The obedience to the w‘/’law indicates that it does. If the mercury were not absorbed on every encounter, k would tend to become independent of w at higher w , and no such trend is observed. The diffusion coefficientobtained for atomic mercury may be compared with that of carbon tetrachloride in isooctane at 2 5 O , 2.57 X cm.2 sec.-’.l4 Presumably this would be a little lower at 20°, but still
The Journal of Physicd Chembtry
larger than D H ~ It . is somewhat unexpected that HgO should have a smaller diffusion coe5cient than CCL, as they are about the same size. The vapor phase radius of atomic mercury is 3 1%.,16 about the same &s the hard-sphere radius for carbon tetrachloride estimated from its molecular volume. The difference may not be as large as it seems, since DI,- obtained in this apparatus was also somewhat low, but a value of D H in~ excess of that for CCla seems very definitely excluded. For both HgO and CClr the StokesEinstein D is 1.1 X cm.2sec.-l at 20° if one makes the usual assumption that the first layer of solvent “sticks” to the substrate and 1.7 X 10-5 cm.2 sec.-1 if it does not.’& The diffusion coefficient of iodine does not seem to be known in isooctane, but in a number of hydrocarbon solvents at temperatures around 20’ it displays a Walden product around 5 X 10-10.14917 Combining this with the viscosity of isooctane at 20’ (0.502 X poise1*) a value of 2.9 X cmS2set.-' is obwould seem to be tained. Thus the ratio DI*/DH@ about 1.8. It may be a little smaller than this but seems, surely, greater than 1.0, and approximately temperature independent. If the Drr is equal to or larger than D H ~it@can be quite unambiguously concluded that a transport controlled reaction of I2would have to be at least &s fast as any reaction of HgO in the same mechanical system.1g Since the rate of the heterogeneous conversion of Iz in isooctane solution is slower than the rate of HgO reprecipitation, the former reaction must be significantly impeded by nontransport ( i e . , “chemical”) factors. ~
~~
(14) 8. B. Tuwiler, “Diffusion and Membrane Technology,” Reinhold Publishing Corp., New York, N. Y., 1962, p. 372. The value actually given by Tuwiler is smaller than this by a power of ten but comparison of Tuwiler’s values with others’ reveals a typographical error. (15) J. Jeans, “An Introduction to the Kinetic Theory of Gases,” Cambridge at the University Press, 1948, p. 183. (16) (a) See ref. 16, p. 56; (b) H. Eyring, D. Henderson, B. J. Stover, and E. M. Eyring, “Statistical Mechanics and Dynamics,” John Wiley and Sons, Inc., New York, N.Y., 1964, p. 463. (17) P. Chang and C. R. Wilke, J . Phys. Chem., 59,592 (1955). (18) R. R. Driesback, “Physical Properties of Chemical Compounds. 11,” American Chemical Society, Washington, D. C., 1959, p. 47. (19) L. L. Bircumshaw and A. C. Riddiford, Quart. Rar. (London), 6, 157 (1952).
