cyclopentanone, the faster reacting component, in a cyclopentanone-3pentanoiie mixture. However, by judicious selection of reaction medium, 3-pentanone could have been actually made the faster reacting component. This would, therefore, also allow 3pentanone-cyclopentanone mixtures with small amount of 3-pentanone to be successfully analyzed by the secondorder extrapolation method. LITERATURE CITED
(1) Garmon, R. G., Reilley, C. N., ANAL. CHEM.34, 600 (1962).
(2) Mark, H. B. Jr., Greinke, R. A., Papa, L. J., “Proceedings of Society of Analytical Chemists Conference,” Nottingham, England, 1965 (in press),. (3) Mark, H. B. Jr., Papa, L. J., Reilley, C. N., “Advances in Analytical Chemistry and Instrumentation,” C. N. Reillev. Vol. .2, p. 255, Inter~. . ~ ed.. ~ ~ science, New York, 1963. (4) Papa, L. J., Patterson J. H., Mark, H. B., Jr., Reilley b. N., ANAL. CHEW 35.1889 ( 1 ~ f i ~ I (5) Reilley,. C. N;, J. Chem. Educ. 39, A853 (1962). (6) Roberts, ‘J. D., Regan, C., ANAL. CHEM.24, 360 (1952). (7) Siggia, S., Hanna, J. G., Ibid., 33, 896 (1961). I,
(8) Siggia, S., Hanna, J. G., Ibid., 36, 228 (1964). RONALD A. GREINKF, B. MARK,JR. HARRY Department of Chemistry The University of Michigan Anp Arbor, Mich. RESEARCH supported in art by a grant from the U.S. Army gesearch Office, Durham, Contract No. DA-31-124-AROD-284. One of us (RAG) is indebted to the National Aeronautics and Space Administration for a Graduate Traineeship in 1965. which made ossible. this work. Division ofAnalytica? Chemistry, 150th ACS Meeting, Phoenix, Arizona, 1966.
Application of Adsorption Electroanalysis to Trace Determination of Tetrabutylammonium Ion SIR: Investigations of the effects of adsorbable substances on the kinetics of electrochemical reactions have shown that the faradaic current falls rapidly toward zero for many depolarizer-surfactant combinations following adsorption of the surfactant ( 6 , 7 , 10, 11). The polarographic method has been most commonly used in these studies, and theoretical interpretations have been based on solution of Fick’s second law equation for an expanding plane electrode with the restriction that the electrode reaction is quasi-reversible or totally irreversible (6, 8, 11). In addition to these kinetic studies, the inhibiting effect of adsorbable substances on electrode reactions should be applicable to the electroanalytical determination of the particular surfactant under consideration. Because the adsorbing species need not be electrochemically reactive, a method based on adsorption electroanalysis would be especially useful in determining such substances as tetrabutylammonium ion and Triton X-100, surfactants which are normally irreducible or difficult to reduce. Such an analytical application is implied in the polarographic investigations of Schmid and Reilley (10) where, for several substances, a linear relation was obtained between the time a t which the instantaneous current fell to zero and the reciprocal of the square of the surfactant concentration. However, under conditions of diffusioncontrolled adsorption, considerable time is required before attainment of adsorption equilibrium, SO that analytical applications using a dropping mercury electrode are limited to about l O - 5 M because of the short drop-times normally used ( 3 ) . On the other hand, a stationary electrode should be more sensitive than a dropping electrode because the adsorbing substance is permitted to ac-
cumulate on the electrode surface. That is, for a stationary electrode, the fractional coverage a t a particular applied potential is limited by the bulk concentration of surfactant and the adsorption-desorption rates. In addition to these factors, the fractional coverage is also limited by the finite lifetime of the drop a t a dropping mercury electrode @). For this reason, a stationary electrode was used in the experimental procedure for the analytical applications investigated here. Because adsorption equilibrium is more rapidly attained under conditions of forced convection (S), a stirred solution was used. CONCENTRATION-TIME RELATION
Because a stationary mercury drop is used as the working electrode, Fick’s second law equation for spherically symmetrical mass transfer must be solved, Under steady-state conditions (stirred solut,ions), this equation may be written in the form
In this equatiop, r is the radial distance measured from the center of the electrode toward the interior of the solution, and CA is the time-independent concentration of the adsorbable substance. Equation 1 applies to diffusion of this substance through a thin layer oi solution immediately adjacent to the electrode surface : the Nernst diffusion layer (3). If the boundaries of this layer are defined as a and b [the inner and outer radii, respectively, of a spherioally symmetrical shell (1)1, then the appropriate boundary conditions required to solve Equation 1 are: r = a : CA=O r
=
b: CA = CA”
(2) (3)
Equation 2 specifies that the surfactant concentration at the electrodesolution interface, r = a , is zero throughout the experiment. I n Equation 3, it is assumed that the concentration of the surfactant over the entire solution volume immediately adjacent to the electrode surface a t T = b is constant and equal to its value in the bulk of the solution, CA”. The flux of the adsorbable substance at the electrode surface is obtained from solution of Equations 1 to 3 :
Here, DA is the diffusion coefficient of the surfactant. Equating the material flux in Equation 4 to the rate of surface coverage, d r / d t , and integrating gives the desired relation between the bulk surfactant concentration, CA”, and the time required, to, for coating the electrode with the equilibrium concentration of surfactant, re: to =
a(b - a) I’. bDA
_1_ ’
CA”
(5)
I n deriving Equation 5, it has been tacitly assumed that there is no adsorption before the start of the experiment. Because adsorption processes are charge dependent (2, 9 ) , this assumption may often be realized experimentally by applying a sufficiently large anodic or cathodic initial potential. According to Equation 5, to varies as l/cAo, while for diffusion-controlled adsorption, t o l l 2 varies as l/Ca” (3). A comparison of these two relations shows that smaller values of CA’ are required to attain a particular value of to for a stirred solution, so that complete coverage under this condition is more rapidly attained than for diffusioncontrolled adsorption. Delahay and Trachtenberg predict a similarly more rapid coverage a t a planar electrode VOL. 38, NO. 2, FEBRUARY 1966
343
using a stirred solution for a Henry’s law isotherm (3). EXPERIMENTAL
Several metal ions in various electrolytes were investigated to determine the degree of inhibition of the electrode reaction by various surfactants. Of these, cadmium(I1) in a 0.1M perchloric acid solution was chosen for further investigation because the reduction step was markedly inhibited by traces of surfactants. Tetrabutylammonium ion was selected as the adsorbable substance because it inhibits the electroreduction of cadmium(I1) (Q), and does not adsorb a t potentials appreciably positive of the electrocapillary maximum. Equipment. The cell and stirring arrangement used was essentially identical with that normally employed in anodic stripping analysis. The cell was an 85-ml. capacity weighing bottle terminating in a T50/12 joint. A Teflon (polytetrafluoroethylene, E. I d u Pont de Nemours & Co.) lid was machined to fit snugly over the top of this cell, and the electrodes, nitrogen inlet, dropping mercury capillary, and Teflon scoop projected through this lid into the cell. Stirring was provided by a Sargent synchronous stirrer which rotated a horseshoe magnet a t 600 r.p.m. A Teflon-sealed, micro stirring bar, l/* inch in diameter and l/z inch long, was used to stir the electrolytic solution. The cell geometry and placement of this stirring bar must be consistent to obtain reproducible results. A Wenking potentiostat, Model 61-R, was used to provide the constant applied potential. External readout was accomplished by passing the faradaic current through a decade load resistor,
Table 1. Analysis of Tetrabutylammonium Ion (TBA)
Supporting electrolyte, 0.1M HClOa, 1.64 X 10-SM Cd(I1) TBA CAY,, Dev., to, concn., CA’ moles/liter see.’ X.106 S7,a 6.80 4.3 4.00 X lo-’ 170 3.0 67.7 6.77 1.00 x 10-6 2.9 32.6 6.52 2.00 6.57 2.0 21.9 3.00 6.68 1.8 16.7 4.00 1.6 11.1 6.66 6.00 1.5 8.00 6.40 8.00 a Avg. and avg. dev. of 3-5 determinations. Table II. Effect of Adsorbable Substances on Electroreduction of Cadmium(l1) in 0.1 M Perchloric Acid
Inhibition Tributylamine Triton X-100 Fluorescein Eosin
344
No inhibition Tetramethylammonium ion Acetylcholine Methylene blue Catechol
ANALYTICAL CHEMISTRY
t
2
24t O L TIME, SEC.
Figure 1. Current-time curves obtained from stirred solutions Supporting electrolyte 1.64 X 10-SM cadmium (111, 0.1M perchloric acid Tetrabutylammonium ion concentration:
A. 2.00 X 10-W B. 3.00 X C. 4.00 X D. 6.00 X E. 8.00 X
10-6M 10% 10 -OM
lO-‘jM
then recording the resulting IR drop on either a Sargent Model SR pen and ink recorder, or a Leeds and Northrup Type G Speedomax recorder with a chart speed of 20.2 inches per minute and a 1-second full-scale pen response time. Chemicals. All chemicals were reagent grade. The tetrabutylammonium ion stock solution was prepared by dilution of a standardized solution of tetrabutylammonium hydroxide solution in methanol (K & K Laboratories). A satisfactory blank was obtained using the experimental procedure described below in the presence and absence of methanol. Consequently, the chemicals were not further purified. The water used was distilled twice, the second distillation being made from an alkaline permanganate solution using a borosilicate glass apparatus. Procedure. The electroreducible substance was a 1.64 X 10-3M solution of cadmium(I1) in 0.1M perchloric acid solution. A suitable aliquot of a solution of tetrabutylammonium ion was added to the electrolysis cell and the solution stirred by a magnetic stirrer. A mercury drop (0.052-cm. radius) was then attached to the working electrode while applying the initial potential across the cell. The initial potential was +0.25 volt us. S.C.E., and the plating-adsorption potential wm -0.70 volt. The solution was stirred immediately after the mercury drop electrode was hung, and current-time curves recorded on application of the plating-adsorption potential until the faradaic current fell to a steady-state value significantly less than the initial value. Replicate results were obtained readily by hanging a fresh mercury drop and repeating the procedure. RESULTS A N D DISCUSSION
Typical current-time curves obtained, using stirred solut,ions, are shown in Figure 1. The values of to were deter-
mined from current time curves such as these by linear extrRpolation of the falling portion of the curves to the steady-state value. The electrolysis current fluctuated about 2 bamps above and below the average value shown in this figure prior to adsorption of the surfactants, but current fluctuations were entirely absent after adsorption took place a t all surfactant concentrations except the most dilute (10-7~). Consideration of Equation 5 shows that the product t a c A o should be constant, and this quantity is tabulated a t each given concentration in Table I. Effect of Other Adsorbable Substances. Application of this adsorption analytical method t o a particular substance requires only that the substance inhibit the electrode reaction. In this respect, a number of surfactants were investigated to determine their effect on the reduction of cadmium(I1) in 0.1M perchloric acid using a stirred solution, and the data are shown in Table 11. As might be expected, the current-time curves for the inhibiting substances were not always identical to those shown in Figure 1 for tetrabutylammonium ion. Thus, the curves for fluorescein and eosin indicated some adsorption a t the initial potential, while the current did not fall to zero when tributylamine was the added inhibitor. However, the current-time curves for Triton X-100 ‘were essentially identical to those shown in Figure 1. LITERATURE CITED
(1) Barrer, R. M., “Diffusion in and Through Solids,” p. 6, Cambridge University Press, New York, 1951. (2) Butler, J. A. V., Proc. Roy. Sac. A122, 399 (1929). (3) Delahay, P., Trachtenberg, I., J . Am. Chem. Sac. 79, 2355 (1957). (4) Frumkin, A. N., in “Electrical Phenomena and Solid/Liquid Interface,” J. H. Schulman, ed., Vol. 111, Academic Press, New York, 1957. (5) Holleck, L., Kastening, B., Williams, R. D., 2. Elektrochem. 66, 396 (1962). (6) Kastening, B., J . ElectroanaL Chem. 9, 41 (1965). (7) Koryta, J., Collection Czech. Chem. Commun. 18, 206 (1953). (8) Koutecky, J., Weber, J., Ibid., 25, 1423 (1960). (9) Parsons, R., in “Advances in Electrochemistry and Electrochemical Engineering,” Delahay and Tobias, eds., Vol. 1, Interscience, New York, 1961. (10) Schmid, R. W., Reilley, C. N., J . Am. Chem. Sac. 80, 2087 (1958). (11) Weber, J., Koutecky, J., Koryta, J., 2. Elektrochem. 6 3 , 583 (1959). SIDNEY L. PHILLIPS I.B.X. Corp. Box 390, Dept. C27 Poughkeepsie, N. Y. 12602 PRESENTED in part, Division of Analytical Chemistry, 150th Meeting, ACS, Atlantic City, N. J., September 1965.
