NOTES
3684 H P O (ice)
+ H2180(water) H2180 (ice)
+ H2160 (water)
Two sources of error are possible in the method employed: (1) nonequilibrium ice formation at positions close to the coil and (2) the trapping of liquid during crystal growth. I n both cases these errors would operate in the direction making the ice isotopically too light. I n the first case, the initially formed ice grows
Samuel Epstein of the California Institute of Technology for making his laboratory available to carry out this research.
A Measurement of the Heterogeneous Rate Constant for the Thiocyanate-Catalyzed Polarographic Reduction of Trivalent Gallium' by E. D. Moorhead and G. M. Frame, I1
Table I: Isotopic Compositions" of Water and Ice Samples and Fractionation Factors
a
School of Chemistry, Rutgers-The State University, New Brunswick, New Jersey (Received May $3,1968)
Sample
8(180)
6(D)
a('B0)
a@)
Water (1) Ice (1) Water (2) Ice (2)
2.4 5.3 1.5 4.6
-33.4 -16.2 -41.7 -23.0
1.0029
1.0178
1.0031
1.0195
Deviations from working standards in parts per thousand
of the l*O:laO and D:H ratios in the standards.
so quickly that it is probably not fractionated with respect to the liquid watera9 I n the second case, the ice is, of course, contaminated by isotopically lighter liquid water which subsequently freezes and is indistinguishable from equilibrium ice. The effect of these errors would be to make the measured fractionation factors smaller than the equilibrium values. The isotopic compositions of the ice and water from the present experiments varied with time in the expected manner, and the fractionation factors for the two sets of data are in good agreement. The second sampling is considered to more closely represent equilibrium conditions, because the nonequilibrium effects discussed above would decrease with distance from the coil. It cannot be proved that equilibrium was attained under the conditions of these experiments. However, the measured fractionation factor of 1.0195 for the hydrogen isotopes is in excellent agreement with the equilibrium value calculated by Weston from the best thermodynamic data. It is assumed that if the hydrogen isotopes were taken up by the ice in equilibrium with the water, then the oxygen isotopes were also. Except for a brief mention of preliminary results of experiments by Craig,13 these are the first measurements which identify the direction and magnitude of the fractionation ' of oxygen isotopes on the freezing of water.14 Acknowledgments. The author thanks Professor (13) H.Craig and L. I. Gordon, Conference on Stable Isotopes in Oceanographic Studies and Paleotemperatures, Spoleto, Italy, 1965. (14) Publication authorized by the director, U. S. Geological Survey. California Institute of Technology Contribution No. 1536. The Journal of Physical Chemistry
A most unusual feature of aquo trivalent gallium when compared with chemically similar, highly solvated polyvalent metal cations, e.g., trivalent indium, is the fact that its apparent rate of electroreduction at the dropping mercury electrode (dme) is accelerated or catalyzed in seemingly exclusive fashion by the presence of isoelectronic thiocyanate2 or azidea anions in solutions containing high concentrations of an inert salt (NaC104). The response of the SCN-catalyzed reduction process to systematic variation in a number of solution parameters was recently reportedU2 In both that work and in preceding studies of gallium electr~chemistry,~ the qualitative description of reduction rates made meaningful comparisons with other systems impossible and emphasized the need for a numerical estimate of the apparent standard heterogeneous charge-transfer rate constant, k ' , , ~ , ,for Ga(II1) reduction to the amalgam. The object of this note therefore is to report on a determination of k ' s , ~ aobtained by application of established techniques of ac polarographyP The rate parameters reported here refer to the reduction of Ga(II1) at the dme from acidified (pH adjusted to 1.0 with HC104) 6.0 M NaC104, catalyzed either by 0.05 or by 0.1 iM NaSCN, as this medium has been most recently discussed.2 As a preliminary check on our measurement procedures, an independent determination of the Cd(I1) charge-transfer rate was made, and the results of that work are also reported here. Experimental Section A jacketed, all-glass Metrohm three-electrode po(1) This work was supported by grants from the National Science Foundation (GP7255), The Research Corp., The Alfred P. Sloan Foundation, and the Research Council of Rutgers-The State University. (2) E. D. Moorhead and G. M. Frame, 11, Anal. Chem., 40, 280 (1968). (3) E.D.Moorhead and G. M. Frame, 11, J . Electroanal. Chem., 18, 197 (1968). (4) E. D. Moorhead, J . Amer. Chem. SOC.,87, 2508 (1965), and references cited therein. (5) For a recent review of ac polarography, see D. E. Smith, "Electroanalytical Chemistry-A Series of Advances," A. J. Bard, Ed., Marcel Dekker, New York, N. Y., 1966, Chapter 1.
NOTES
3685
Table I : Heterogeneous Rate Constants and Associated Parameters for Ga(111) and Cd(I1) in Various Supporting Electrolytes Eleotroaotive species 1 . 0 mM 1. O mM 1. O m M 1.O mM
Cd(I1) Cd(I1) Cd(I1) Ga(II1)
1 . 0 m M Ga(II1:)
1.O m M Ga(II1) 1 . 0 mM Ga(II1)
Supporting electrolyte 1 . 0 M NaClO4 1 . 0 M NaC104
0 . 5 M HzS04 0.05 M NaSCN 6 . 0 M NaC104 0.05 M NaSCN 6 . 0 M NaClO4 0 . 1 0 M NaSCN 6 . 0 M NaC104 0 . 1 0 M NaSCN 6 . 0 M NaC104
El/'
us.
nhe,
Rt,
106D,
--k's,
om seo-l------
V
Temp, OC
ohmsa
om2 sec-1
This work*
Lit.
-0.336 -0.335 -0.347 -0.538
2 5 . 0 +k 0 . 5 25.0 f0 . 5 24.0 =IC0 . 5 2 4 . 0 10 . 5
66.0 60.0 46.0
0 . 3 3 f0 . 0 3 0.34 + 0.03 0 . 1 7 10 . 0 2 0.017fO0.O02
0.34 0.34 0.14
50.0
8.57' 8.57' 7.54' 4.63
-0.546
24.0 f0.5
57.5
4.63
0.015 =k 0.002
...
-0.546
30.00f0.05
45.0
4.63
0.026 f 0.003
-0.543
30.0Oi=O0.05
46.0
4.63
0.027f0.003
...
I
.
.
..,
* The dominant uncertainty in k', comes a Average of a t least eight measurements with a typical average deviation of 1 2 . 5 ohms. from the f 2 . 5 - o h m deviation in Rt which was observed by experiment to cause'about a 1 1 0 % change in k f S . See ref 10.
largraphic cell along with conventional instrumentation based on operational amplifiers (G. A. Philbrick Inc.) was used to obtain basic polarographic data. A saturated NaC1-Ag-AgC1 electrode (Eo = 0.198 V vs. normal hydrogen electrode (nhe) at 25') was employed as reference, and this was isolated from the test compartment by a saturated NaN03-agar bridge and fritted glass disks; a junction potential of 0.021 V was determined from measurement of the half-wave potential (Ell2)for the reduction of Tl(1) from 0.1 M NaN08.6 Precautions and corrective procedures followed in obtaining the current-voltage data as well as the quality of reagents used have recently been described.2 Peripheral instrumentation primarily used was manufactured by Hewlett-Packard and included a Model 3300 function generator, a Model 52331, electronic counter, and a Model 5211BR 100-kHz voltageto-frequency converter (both used in tandem for precise voltage measurement), a Model 302A wave analyzer (frequency locked for signal selection), and a Moseley 2D-2 X-Y recorder for presentation of current-voltage data. The electronic counter was used for the precise measurement of the period of the applied alternating current signals. Phase angles between applied ac voltage (AE = 5.0 mV, root-mean-square) and extracted polarographic ac current were measured by coincidence to a precision of h1.0' by application of the appropriately calibrated sweep-time delay feature of a Tektronix 565 dual-beam oscilloscope. This was accomplished after the inherent phase-angle shift of the measuring circuits alone had been nulled out by an electronic phase shifter' using a resistive dummy cell. Nonetheless, replacement of the cell with a resistancecapacitance combination of known phase-angle shift revealed a constant -2.0' systematic error in the measured angle at all frequencies, and this was taken into account in over-all correction of the data. Uncompensated total cell resistance, Rt (which included a 32-ohm capillary resistance),
was obtained from capacitive current (&)-phase angle (c$~) measurements8 on the supporting electrolyte alone. Repetitive solution of the complex trigonometric equations6 required for vectorial correction of effects due to capacitive current flow and uncompensated I-R drop was carrried out using an IBM 7040 computer. This correction procedure differs from that employed by Frischmann and Timnickgby additionally correcting io to obtain the slightly different value of capacitive current flowing in the presence of faradaic current. For each determination of k', the cotangent of the corrected faradaic phase angle (cot 4) was plotted against the square root of angular frequency (ul/') for 11-17 data points taken over the frequency range 50400 Hz. As there was some scatter (roughly within the limit A@ = *l.O") among these points, a second computer program was used to provide a least-squares fit of the data to the best straight line intersecting cot C$ = 1.0 and to calculate its slope.- The heterogeneous rate constant k', was calculated from this slope, obtained at El/,,using the equationlo
where D = D O I - ~ D R(DO ~ and DR equal the diffusion coefficients of the oxidized and reduced (amalgam) species, respectively) and a is the transfer coefficient. (6) I. M. Kolthoff and J. J. Lingane, "Polarography," 2nd ed, Interscience Publishers, New York, N. Y., 1952,p 250. (7) D. E. Smith, Ph.D. Thesis, Columbia University, 1961. (8) Rt was calculated from Rt = (AB/&) cos & (see ref 9). Because cos & approaches aero as & approaches 90°, Rt was determined only from data taken from frequencies between 400 and 800 Hz, where Rt is less sensitive to errors in &. As the precision of the calculated rate constant is extremely sensitive to the value chosen for Rt, this parameter enters into our calculations as the average of at least eight measurements obtained between 400 and 800 Ha. (9) J. K. Frischmann, Ph.D. Thesis, Michigan State University, 1966. (10) J. K. Frischmann and A. Timnick, Anal. Chem., 39, 507 (1967). Volume 7.9, Number 10 October 1068
3686
NOTES
Similarly obtained slopes at E,,,, E',,,, and Ea,, were analyzed by a third program to calculate the transfer coefficient, a, using the approach of Frischmann and Timnick.lo Rate constants reported here for gallium were not subjected t o the usual Frumkin double-layer correction, as any attempt t o apply classical doublelayer theory quantitatively t o rate data obtained in 6.0 M NaC104 could only be viewed as specious.
Acknowledgment. G. 14. F. is indebted to the National Aeronautics and Space Administration for the award of a predoctoral traineeship.
Results and Discussion Rate o j Cd(II) Reduction. To establish a frame of
The Effect of Micelles on the Kinetics of the
reference for the measurement and calculational procedures adopted for determination of the Ga rate (vide infra), a preliminary, independent measurement of the heterogeneous rate constant for reduction of Cd(I1) was first undertaken using several supporting electrolytes. Cadmium was selected as a reference because it is a comparatively simple, well-studied system and because there recently appeared'O a set of rate parameters for Cd(I1) reduction obtained by virtually the same technique used in this investigation. The cadmium rate data obtained in our study for NaC104 and HzSO4 electrolytes are summarized in Table I, where they may be compared with the data obtained by Frischmann and Timnick.lo The good agreement between these two independent sets of figures is apparent, and this provided some assurance of the absence of systematic errors in our measurement procedures. Rate of Gu(III) Reduclion. Previous investigation3 established that the polarographic reduction of Ga(II1) from acidified (measured pH 1.0 HC104) G.0 M NaC104 attained dc reversibility over a range of NaSCN concentration from 0.05 to 0.10 M . Therefore, in the present study it was decided t o evaluate the Ga rate constant at these two concentrations. From 0.1 M SCN--containing solution a was determined (vide supra) t o be 0.25 f 9.03. Using this value and the values Do = 3.06 X cm2sec-12 and DIE= 15.7 X 10-6 cm2 sec-',l' D for Ga(II1) reduction at the dme was calculated to be 4.63 X cm2 sec-'. The cot d, vs. wl/' plots for Ga best-fitted straight lines passing through an intercept of 1.0. If one invokes the criteria of Smith,s such behavior would seem consistent with a reduction mechanism controlled by simple chargetransfer kinetics, i.e., no indication of positive or negative deviations, or curvature of the plot reportedly characteristic of the presence of rate-controlling pre- or postchemical reactions, or reactant adsorption. The charge-transfer rate constants calculated for gallium are listed in Table I. It can be seen that the twofold increase in SCN- causes the rate to increase by about 62y0, and this was reflected in an increase of similar magnitude in the peak height of the ac polarogram. We wish to report here a value of k ' s , ~ aof 0.026 A 0.003 cm sec-' (30 0.05') for the reduction of Ga(II1) to the amalgam from 0.1 M NaSCN and 6.0 M NaC104 (pH 1, HC104). The Journal of Physical Chemistrg
(11) A. G Stromberg and E. A. Zakharova, Elektrokhimayu, 1, 1036 (1965).
Cannizzaro Reaction
by L. R. Cramer and J. C. Berg Department of Chemical Engineering, University of Washington, Seattle, Washington 98106 (Received May 81, 1068)
I t has long been well known that the solubility of nonpolar solutes in an aqueous medium may be greatly enhanced by the addition of micelle-forming surfaceactive agents to the solution, and it has also been shown in numerous studies that advantage may be taken of such solubilization in the enhancement or control of chemical reaction rates. A fairly large number of chemical processes involve the reaction of components in aqueous solution with components which are insoluble In water; e.g., acid- or base-catalyzed hydrolysis reactions are often of this type. The rates of such reactions are severely controlled by the necessity of the reactants meeting at whatever aqueous-organic interfacial area is available to them. The solubilization of the organic reactants into surfactant micelles dissolved in an aqueous medium greatly increases the effective interfacial area and in fact renders the reaction homogeneous. As has been shown in the work of Duynstee and Grunwald,' Cordes and coworker^,^-^ and other~,5--2~ one can, with the appropriate choice of the (1) E. F. J. Duynstee and E. Grunwald, J . Amer. Chem. Soc., 81, 4540, 4542 (1959). (2) J. G. Fullington and E. H. Cordes, Proc. Chem. Soc., 224 (1964). (3) M. T. A. Behme and E. H. Cordes, J . Amer. Chem. SOC., 87, 260 (1965). (4) M. T. A. Behme, J. G. Fullington, R. Noel, and E. H. Cordea, ibid., 87,266 (1965). (5) T. C. Bruice, J. Katzhendler, and L. R. Fedor, J . Phys. Chem., 71, 1961 (1967); T. C. Bruice, J. Katrhendler, and L. d F e d o r , J . Amer. Chem. Soc., 90, 1333 (1968). (6) E. F. J. Duynstee and E. Grunwald, Tetrahedron, 21, 2401 (1965). (7) D. G. Herries, W. Bishop, and F. M. Richards, J . Phys. Chem., 68, 1842 (1964). (8) J. L. Kurz, ibid., 66,2239 (1962). (9) R. L. Letsinger and T. E. Wagner, J . Amer. Chem. Soc., 88, 2062 (1966). (10) M. B. Lowe and J. N. Phillips, Nature, 190, 262 (1962). (11) F. M. Menger and C. E. Portnoy, J . Amer. Chem. Soc., 89,4698 (1967). (12) A. G. Mitchell, J . Phurm, Pharrnacol., 14, 172 (1962). (13) C. W. Moore and R. B. Hardwicke, Ind. Chem., 40, 146 (1964).
