larography a t stationary electrodes. An extension of this technique, in which an electronic phase-sensitive detector allows the rejection of the charging current while retaining a major portion of the faradaic current, has been under study in our laboratories and preliminary results show it to be of extremely high sensitivity. Figure 1 shows a polarogram of 10-6LU Cd++ in 0.1M MC1. RepeG itive runs on the same solution show reproducibility of about 1% and it appears that the sensitivihy of the instrument will allow determinations in solutions at least an order of magnitude more dilute. The technique should be very useful in the study of kinetics of fast electrode processes, since high frequencies, a t which the capacitive current is usually the major a.c. component, are often necessary in such studies. A solution of 1013M Cd++ in 0.1M KC1 a t 620 c.p.s. has a well defined wave for Cd++ when the detector is used; without the
the instrument will be submitted in the near future. LITERATURE ClTED
(1) Adams, R. N., Walker, D. E., Juliard, A. L., ANAL.CHEM.32, 1526 (1960). (2) Barker, G. C., Anal. Chim. Acto 18, 118 (1958). (3) DeMars, R. D., Shain, I., ANAL. CHEM.29,1825 (1957). (4) Jessop, G., Brit. Patent 640,768 ( 1950). ( 5 ) Juliard, A. L., J . Electroanal. Chem. 1,101 (1959). (6) Juliard, A. L., Nature 183, 1040 (1959). (7) Kemula, W., Kublik, Z., Anal. Chhim. Acta 18, 104 (1958).
Figure 1. Alternating current polarographic waves at hanging mercury drop with lO-*M Cd f 2 in 0.1OM KCI Alternating potential. 38 c.p.s.1 18 mv. [peakto-peak). Scan rate. 0.6 volt per mlnute
detector the wave is barely discernible atop the large charging current. Detailed studies and a description of
(8) Milner, G. W. C., “Principles and Applications of Polarograph ” pp. 132-3, Longmans, Green & New
&.,
York, 1957. (9) Nikelly, J. G., Cooke, W. D., ANAL. CHEM.29,933 (1957). DOKALD E. SMITH W. H. REINMUTH Havemeyer Hall Columbia University New York 27, N. Y. RECEIVED for review October 7, 1960. Accepted October 20, 1960.
athematical Expression of the Sup Action o Some Cap ry-Inactive M et a l k he Polar aphic Maximum of SIR: Under special conditions it is possible to express by a simple equation the maximum current of nickel ion, produced by the electroreduction of that ion a t the dropping mercury electrode, as a function of the bulk concentration of the ions of barium, calcium, and magnesium used as maximum suppressors (1) : IP = -kc”*
+I,
(1)
where I, = maximum current-that is, current a t the peak of maximum in the currentvoltage curve-at C concentration of suppressor ion, barium, calcium, or magnesium I , = maximum current in the absence of suppressor ion L = a constant C = concentration of suppressor ion in the bulk of the solution There are two special conditions under which the equation is valid.
where A Cr = change in the total ionic concentration, and AC, = change in
the concentration of the particular suppressor ion. B. Constant capillary characteristics
To satisfy condition A, potassium chloride is added to the solution in relatively large excess of the suppressor ion, so that small changes in the suppressor concentration will have a negligible effect on the total concentration of the indifferent ions which serve as supporting electrolytes. Values of C larger than the minimal required to suppress a certain maximum completely render the equation meaningless. EXPERIMENTAL
Solutions of ca. 2 to 3 X 10-9M in nickel ion and 0.lM in potassium chloride were prepared in distilIed water. Exactly 20 ml. of solution were introduced into the electrolysis cell, consisting of the saturated calomel as the reference electrode, and the dropping mercury (m = 0.0110 gram, t = 3 seconds per drop) as the cathode. Polarograms of the solution, after expulsion of oxygen by nitrogen flow through the solution, were automatically recorded with a Sargent Polarograph Model XV.
First, polarograms in the absence of a suppressor were obtained. Polarorams were run a t least in triplicate. mall increments (0.1 ml. of 0.05M solution) of suppressor ion were added to the solution in the cell. After removal of oxygen by nitrogen and thorough mixing of the solution, polarograms were recorded for each increment of suppressor added. In measuring the current, the top of the pen oscillBtions was read (this represented maximal current during a drop’s life). Correction was made for the dilution effect.
8
Figures 1 and 2 are typical polarograms and graphical representations of the experimental results according to the equation described. All cations were obtained from their respective chlorides. THEORETICAL DlSCUSSlON
A reasonable hypothesis for a qualitative explanation of the empirical equation may be developed on theoretical grounds. The thickness of the electrical double layer a t the interface of the mercury electrode and the solution can be expressed by the equation (4) VOL. 32, NO. 13, DECEM
p,
i
Equation 1 may now be written as IC
1,
= -kK ~
f 1%
(3)
The current, I, is imagined t o be the algebraic sum of two opposing currents
I, = -I +I,
(4)
where
The inner part of the double layer is amumed to consist predominantly of suppressor ions; this part constitutes is, the effective double layer-that the part connected with the suppression of the maximum. The thickness of the effective double layer may be approximately expressed by Equation 2 (C = ionic concentration of suppressor ion in the bulk of the solution).
The hypothetical negative current, -1. has meaning only in so far as it expresses the fact that reducible nickel ions are repelled by the effective double layer towards the interior of the solution. This negative current may be expected t o approach inverse proportionality with A. Combination of Relationships 2 and 5 leads directly to the empirical equation. This explanation emanates from the modern theories on polarographic maxima (2, 3). I t is assumed that the physical causes responsible for the appearance of the maximum keep the solution around the electrode in fairly good constant motion, and as a consequence the nickel concentration near the fixed effective double layer is constant. The current now depends on the rate at which nickel ions penetrate the effective double layer. This current is not diffusion-controlled. When the applied voltage increases to the point where the electrokinetic phenomena causative of the maximurn cease to exist, the solution near the electrode cannot be stirred, and eventually becomes depleted in nickel ions. The current from now on will have to depend on the rate a t which nickel ions diffuse to the vicinity adjacent to the effective double layer (migration current has been eliminated by the presence of the supporting electrolyte, potassium chloride). The nickel ions still must penetrate the double layer, but the rate of diffusion is slower than that of penetration of the layer, and as a
SIR: Samples containing 0.1 to 1.0mg. of isopropyl. alcohol in 5 ml. of aqueous solution are assayed by oxidation and direct colorimetric determination of the acetone. Several methods reported in the literature use a similar oxidation to acetone, but the intense
color of the oxidizing agent, usually potassiuni dichromate, either requires that the acetone be distilled before a colorimetric method can be applied (1, Q, b ) , or the subsequent method of determining acetone ii3 limited to accommodate this color (8). If such color-
-110 -120 -130 APPLIED EMF VS 8C.E
-100
Figure 1.
Typical polarograms of 2.3
X 1Q-3MNi ion in Q.1M KCI with varying amaunts of Ca ion as maximum suppressor Concn. of suppressor ion, M
A. 2.5 X B. 7.5 x 10-4 C. D.
E.
1.25 X 10-3 2.5 x 10-3 3.25 x 10-8
where h = thickness of layer C = ionic concentration in the bulk
K
1
of the solution
= a constant
e
ANALYTICAL CHEMISTRY
, 00
IO
20
30
40
50
60
c % x 158XIO.* Figure 2. Plot of current at peak of maximum of nickel ion vs. square root of molar concentration of ions employed as maximum suppressors in 0.1 M KCI solution
4.6 X lQ-aM Ni solution 5. 2.3 X 10-‘M 0 Ba A Ca Mg A.
result, the rate of diffusion is the determining step in regard t o production of current. The HlkoviE equation can now be applied. LITERATURE CITED
(1) Emelianova, N. V., Heyrovskp, S., Trans. Faraday SOC.24 257 (1928). (2) Frumkin, A. N., Zkur. Fia. Khim. 29, 1318 (1955). (3) Stackelberg, M. V., Fortschr. Chem. Forsch. 2, 229-72 (1951).
(4) Taylor, H. S Glasstone, S., “Treatise on Physical 2henlistry,” Vol. 2, p . 635-6, Van Nostrand, Yew Yo& 1952.
DEMETRIOS KYRIACOU Aerojet-General Corp. Sacramento, Calif. RECEIVEDfor review August 29, 1960 Accepted October 7, 1960.
producing reagents are eliminated, the determination of isopropyl alcohol is more rapid and more accurate. Feigl (3) suggesk that “suitable oxidants such as alkaline persulfate readily convert isopropyl alcohol to acetone.” This reaction was utilized
