9
4
2 L W K
Z
0
c 0
1
2
TIME, MIN.
Figure 1 . Representative chromatogram Quantitative
analysis
of a 20.15% formaldehyde-water solu-
tion
cia1 detergents as Tide, Sail, and Fab on either support are similarly effective both for the qualitative and quantitative analysis of formaldehyde-containing solutions. The instrument used in these studies was a standard Model I< 1 Kromotog (Burrell Corp.). RESULTS
Quantitative Study. Analyses were run on each of five solutions of formaldehyde in water ranging in concentration from about 1 to 20% by weight, which were made by dilution of a 20.15% stock solution. The stock solution was prepared by boiling paraformaldehyde in distilled water and filtering, its formaldehyde content being determined by the standard hydroxylamine niethod. A typical chromatogram is given in Figure 1. This was obtained with helium flowing a t 20 ml. per minute
(exit conditions) (He backpressure 3 p.s.i.) and the column a t 145' C. The sample volume was 2 pl. These conditions were used to allow the water, which tails considerably, to pass through the column in the shortest time consistent with good separation. The elution time for formaldehyde in these conditions is 25 seconds. The corresponding elution time for air is about 4 seconds. The very small air peak is not apparent in Figure 1, because of the decreased recorder sensitivity required for the analysis shown. The formaldehyde peak was identified by applying the specific reaction with chromotropic acid to a sample trapped out of the column effluent. The response to formaldehyde as determined by this method was linear in the range 0.01 to 0.5 mg. of formaldehyde. At least 10 samples of each solution were analyzed with a coefficient of variation in the results of not more than =t3% and usually less than
TIME, MIN.
Figure 2. Chromatogram of a synthetic blend containing formaldehyde tane, formaldehyde, acetone, methanol, ethanol, and water. At this temperature water is retained for an additional period of about 25 minutes. Hence, although it tails badly, its presence in the mixture does not interfere with the analysis for the other components. Programmed temperature operation is indicated for the analysis of more complex mixtures containing water.
+1.50100.
Qualitative Analyses. The Sail surfactant supported on C 22 firebrick produced a general-purpose column for the separation of many polar and a few nonpolar compounds. Thus, it has resolved mixtures of the aliphatic aldehydes through isovaleraldehyde, several substituted pyridines, and a mixture of tertbutyl hydroperoxide, di-tert-butyl peroxide, and tert-butyl alcohol, and shows promise in the analysis of coolflame combustion products. In Figure 2 an example is given of the qualitative analysis on this column a t 95' C. of a synthetic blend of pen-
le Systems in SIR: Previous theoretical calculations (1, 8 ) of currents for voltammetry with linearly changing potential with electrochemica~ly irreversible reactions have obscured through their mathematical formulations certain features of the potential-time relations to be expected in such cases. Because these features are useful in making qualitative distinction between reversible and irreversible systems and further allow the simple determination of kinetic parameters in irreversible cases, we consider them here. Statements of the diffusion problem with boundary conditions have been given for planar electrod~sby Delahay (1) and for spherical electrodes by DeMars and Shain ( 2 ) . One of these
1.0 r
LITERATURE CITED
Decora, A. W., Dinneen, G. U., ANAL. CHEM.32,164 (1960). (2) Desty, D. H., Harbourn, C. L. A., Ibid., 31, 1965 (1959). (3) Kvryacoe, G., Menapace, K. R., Bodrd, C. E., Ibid., 31, 222 (1959). (4) Schepartz, A. I., RIcDowell, P. E., Ibzd., 32,723 (1960). (5) Yokley, C. R., Ferguson R. E., Combustion and Flame 2 , 117 (1958). QANDLER SAMUEL ROBERT STROM Departments of Chemical and Mechanical Engineering University of Toronto Toronto, Ontario, Canada RECEIVEDfor review August 29, 1960. Accepted September 29, 1960. (1)
tationary Electrode
conditions relates the flux of the reactant at the surface to the rate of the charge-transfer process. By assuming rate constants of the form predicted by absolute rate theory, this condition can be stated as follows: t>O,r = 0 D(bC/bz)
=
k,C exp(pt)
(1)
where the symbology is that of Delahay (1). D is the diffusion coefficient of the reactive species; C, its concentration; X, linear distance; t, time; ki, the rate constant a t the initial potential; p, the product of d E / d t and d In k/dE, where both differentials are assumed constant; and E, the applied potential. If the Jurface concentration were
maintained a t its initial value throughout the electrolysis, Equation 1 predicts that the current would be an exponentially increasing function of potential, but would be independent of scan rate and diffusion coefficient. In practice the passage of current causes the surface concentration to decrease with time and the experimental current passes through a maximum. The amount by which the concentration is decreased from its initia! value a t any specific potential is related roughly to the total amount of reaction prior to the time a t which that potential is reached. The deviation is therefore inversely related to the scan rate because the maximum instantaneous current a t any potential VOL. 32,
NO. 13,
DECEMBER I960
1893
is fixed while the time required to traverse a given potential interval is set by the scan rate. The more rapid the scan rate, the larger the potential region in which the current obeys the simple exponential relation. However, in any case this relation gives the limiting behavior a t the foot ofthe wave. Thus the behavior of the system on variation of scan rate is qualitatively that shown in Figure 1. The region in which the current obeys the simple exponential relation can be defined quantitatively by the following procedure. The maximum flux which can be obtained is given by Equation 1, with the bulk concentration replacing the instantaneous concentration. If this maximum flux is used as a boundary condition in the solution of the Fick's law equation, the resulting surface Concentration is the minimum which could be observed. If it is assumed that currents can be measured to an accuracy of I%, then the simple exponential relation is obeyed when the minimum surface concentration calculated by this procedure differs from the initial concentration by less than 1%or when
---7/
POTENTIAL
Figure I . Current-potential behavior at the foot of a stationary electrode polarogram as function of potential scan rate 1 to 4. Increasing scan rate
0.341 aec.-l/a (4) assuming a drop time of 5 seconds for the dropping electrode. I n order for the simple exponential relation to be obeyed in stationary electrode polarography a t the potential corresponding
to the conventional polarographic Ex/,, the scan rate would have to be 60 volts per second, assuming an = 0.5 (where a is the charge transfer coefficient) and a temperature of 25" C. This corresponds to a 30-C.P.S. triangular wave of 1volt amplitude, a simply attainable experimental value. The fact that the current is independent of scan rate a t fixed potential a t the foot of irreversible waves allow rapid and simple distinction between these and reversible systeme In cases of the latter type the current i s proportional to the square root of scan rate over the entire polarogram t6), while in irreversible cases square root dependence is achieved only near and beyond the peak potential ( I ) . The analogous criterion of reversibility in conventional polarography, dependence of current on mercury height, has been employed ( 3 ) . The basic principles underlying the two cases are identical. Clearly the increase of current in Nernstian systems with the square root of scan rate can continue only until the current approaches the limit set by the rate of the charge-transfer process.
SIR: Much interest has attended the determination of trace amounts of metals by voltammetric methods. With conventional techniques the limiting factor appears to be the capacitive current associated with the charging of the electrical double layer. Attempts to circumvent this problem have been made in a number of ways, but electrolytic concentration in the
electrode phase prior to determination (3, 7, 9) and electronic separation of the faradaic and capacitive currents (3, 4) have been the most promising. Techniques of the former type suffer the disadvantages that the extra (preelectrolysis) step is time-consuming and increases error, and that they are limited to substances that can be so concentrated. Techniques of the latter type have been
The factor bi exp(Bt) is the rate constant a t the potential considered. Generally the argument of the error function in regions of interest i s sufficiently large that that function reduces to unity. Equation 2 then becomes k/dpT
To put this shown from (4) that a t graphic Eliz
e
(3)
in perspective, it can be the theory of Kouteckjy the conventional polarofor an irreversible system
k / G
1
5 Q.01
5
ANALYTICAL CHEMISTRY
Thus, it IS to be expected that at SUEciently high scan rates any system can be made to conform to the behavior herein discussed. When it has been ascertained that current a t a particular potentid is independent of scan rate, the rate constant for the charge-transfer reaction can be computed directly from the concentration of the species in solution and the measured current. The transfer coefficient is then obtainable from the slope of a log k us. E plot. I n experiments a t very high scan rates, correction for capacitive charging becomes imperative. This can be accomplished readily by measuring current a t several scan rates and performing a straightline extrapolation to the value a t zero scan rate. Linearity of the plot verifies that Equation 3 is satisfied. In studies of this type there are advantages t o employing B bnormally high concentrations of the electroactive species. The analog of this procedure in conventional polarography has been employed by Laitinen and Bubcasky (5). Applications of this technique to the study of the mechanism of electroreduc. tion of cyclo-octatetraene will be reported in the near future (7). LITERATURE CITED
W. H. REIMMUTH Department of chemistry Columbia University New York 27, K.Y .
RECEIVED for review October 3, Accepted October 20, 1960.
1960.
applied almost exclusively a t the dropping mercury electrode, where capillary noise (8) limits sensitivity. I n addition, in most variations they require very sophisticated electronic circuitry (8) or electromechanical switching arrangemeat of iimited frequency response and .high inherent noise (4, 8). Recently Juliard and coworkers (1, 6, 6) have utilized small-amplitude a.c. po-
