Table I V . Analysis of Mixtures of Polythionates. Thiosulfate. and Sulfite Taken, pmoles
Found. pmoles
Total
Total amount Of
0.07 0.50
0.07
0.50
0.07 0.50
0.21 1.50
0.20 0.30
0.20
0.20
0.50
0.50
0.20
0.10 0.30
0.60 0.90 1 .oo
obtained by adding a difference in absorbance between the reagent blank and the polythionate in procedure A-I1 to the absorbance measured according to the treatment of procedure A-I. A number of known mixtures were analyzed using procedure A. Typical results, shown in Table 111, demonstrate good recoveries of total amounts of added polythionates. The method was extremely accurate, and the deviation for the amount of these three polythionates separately or in mixtures never exceeded hO.01 @mole. Analysis of Mixtures of Polythionates, Thiosulfate, and Sulfite. The absorbance obtained by procedure B-I corresponds to the sum of tetra-, penta-, and hexathionate and thiosulfate in the mixtures, sulfite being masked by the formaldehyde added for removing the excess of cyanide. The absorbance obtained by procedure B-11, where cyanolysis of polythionate was not carried out, corresponds to only the amount of thiosulfate. The absorbance
0.75
0.30 0.40 1 .oo
0.10 0.15 0.25 0.25
0.50 0.50
s~o6~-
s2032-
SO&
0.20 1.51
0.30
0.75
0.40
0.61
0.99
0.90 0.99
0.51 0.51
0.1 1 0.14 0.24 0.24
of procedure B-I11 corresponds to the sum of the thiosulfate and twice the sulfite in the mixture solution. Moreover, the calibration graphs for the three polythionates, thiosulfate, and sulfite were in full agreement with one another when plotted as equivalent concentrations. Therefore, the following equations can be obtained: (S,0e2-) = I - 11, ( S 2 0 3 2 - ) = 11, and (SO32-) = (I11 - II)/2 where I, 11, and I11 indicate the absorbances obtained by procedures B-I, B-II, and B-111, respectively. These sulfur compounds in mixtures could be readily determined from the calibration graph for thiosulfate in Figure 1. The results, Table IV, show that the above technique can be accurately applied to the determination of polythionates, thiosulfate. and sulfite mixed in various ratios. Received for review March 12. 1973. Accepted May 10, 1973.
Automated Rapid Scan Instrument for Spectroelectrochemistry in the Visible Region Eugene E. Wells, Jr. Electrochemistry Branch, Naval Research Laboratory, Washington, D.C.20375
APPARATUS An instrument which uses a computer to control and collect data from a rapid scanning visible spectrophotometer, and which simultaneously operates a potentiostat to control generation of electrochemical intermediates is described. The 370-700 nm spectral range may be swept in as little as 5 msec, and by using real time control to zero the spectral background repetitive spectra may be signal averaged to give an ultimate sensitivity of absorbance unit. For peak monitoring at fixed wavelength, data may be taken as soon as 20 psec after the application of the reaction initiating potential step.
The power of in situ spectroelectrochemistry lies in the hope of identifying both the type and amount of redox species produced in an electrochemical step. Our interest in the solution kinetics of shortlived electrochemically generated intermediates has led us to develop instrumentation designed for both rapid scanning, to obtain spectra, and extreme sensitivity, to monitor intermediate concentrations a t very short times a t fixed wavelengths. 2022
T h e basic design of the monochromator is due to Strojek, Gruver, and Kuwana ( I ) . This design was chosen over a number of others offering rapid scan (2) because it has one shot as opposed to free running, capability, because the wavelength can be easily controlled by either a digital source or an analog waveform generator, and because it has dual beam operation, which reduces substantially the frequency demands of the final amplification stages and makes possible dynamic base-line correction. The monochromator consists of a galvanometer mirror movement which reflects the beam from the entrance slit SI onto the grating, G, via a lens, L (Figure 1).If a current is applied to the galvanometer coil. the mirror assumes a new angle, changing the angle of incidence of the beam on L and, hence, also on G because of the refraction of L. Thus the spectrum sweeps across the exit slit, Sa, and the wavelength passed changes in a manner related to the current flowing through the galvanometer coil. Although the mirror is not in phase with the driving waveform. which is normally a ramp, no evidence of nonlinearity in the wavelength axis has appeared, and the phase problem is obviated by calibrating the instrument as described below a t the desired rate of scan. (1) J . W . Strojek. G . A . Gruver, and T . Kuwana, A n a / . Chem.. 41, 481 (1969). (2) G . C. Pimental, Appi. Opt.. 7,2155 (1968)
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO. 12, OCTOBER 1973
Dual beam operation, which uses spectrally matched photomultipliers, and matched preamplifiers and logarithmic amplifiers, provides direct absorbance readout for the spectrophotometer (Figure 1). It should be mentioned that the bandpass of logarithmic amplifiers is inversely dependent upon signal strength, and therefore varies with wavelength due to the non-uniform spectral response of the phototubes. In order to be sure of adequate frequency response, it is necessary to adjust the preamplifier gain and phototube voltage such that the phototube spectral response curve spans approximately one fourth of the input range of the log amplifier, and to bias the entering signal toward the high end of the input range. Under t,hese conditions, the 100-KHz response which is typical of these amplifiers is adequate to handle the phototube spectral response. Since in normal spectrophotometer usage, sample peaks are very small and rarely sharp deviations superposed on the response curve, it is assumed that the spectrum of the sample is accurately transmitted. The computer used for the work is a Digital Equipment Corporation PDP-8/1 equipped with an AX-08 8-bit analog-to-digital (A/D) converter, digital and pulse input and output, clock, oscilloscope, and AA-01 12-bit D/A converter. The potentiostat system is a Tacussel PIT 20-2A with GSTP-2 waveform generator. The apparatus is configured as shown in Figure 2. The ramp generator for the spectrophotometer wavelength drive and the potentiostat pulse generator are each controlled by a trigger pulse from the computer. The species generation time, which is the interval between the two trigger pulses, is controlled by the computer through the use of its internal real time clock. Allowable values range from 100 milliseconds to several seconds, limited by a desire to keep the scan fast relative to the change in concentration of intermediate in the first case, and by convection of the solution in the latter. After the wavelength scan is initiated, the absorbance signal is collected by the A/D converter and stored in memory for possible averaging with later runs. The D/A converter output, which is shown mixed with the absorbance signal prior to collection provides dynamic base-line control, a feature which will be explained a t some length below. Data obtained from the experiment are logged on the teletype and plotter. The electrochemical cells used in the work are of the transmission type, in which the beam from the monochromator passes through a n optically transparent electrode of platinum (3). Nothing in the design of the system limits sampling by reflection ( 4 ) or attenuated total reflection ( 5 ) .In fact, the latter technique, which promises considerable selectivity against absorbing species outside the diffusion layer, should be substantially enhanced for spectral work by application of the concepts presented here.
DISCUSSION Detailed functioning of the apparatus is perhaps best illustrated through the example of a typical run, which begins with calibration of the spectrophotometer wavelength and absorbance scales. Calibration is conveniently accomplished by collecting the spectrum of a standard didymium glass filter, which has unusually sharp absorption peaks in the visible region. This spectrum provides the computer with reference voltages which contain implicitly all of the electronic gain factors, voltage offsets, etc., between the glass filter itself and the digitizer within the AID converter. Since the absorbance and wavelength data for the peaks are known ( 2 ) , and since both axes are known experimentally to be linear, it is a simple matter to calculate from any pair of peaks by difference the factors which convert the unscaled, internal representation of the spectrum into meaningful units. The computer then tabulates, on the teletype, both the unscaled and the scaled values it found for each peak. This calibration procedure has several distinct benefits. The entire spectrophotometer-computer apparatus, including intermediate amplifiers is calibrated simultaneously. The procedure is quick, taking only a few moments. The accuracy is sufficient for all practical purposes (*l nm in wavelength and 1% in absorbance for the stan(3) N. Winograd and T. Kuwana. A n a / . Chem., 4 3 , 2 5 2 (1971). (4) P. T. Kissinger and C. N . Reilley, AnaiChem.. 42, 12 (1970). (5) V . S. Srinivasan and T . Kuwana, J. Phys. Chem., 72, 1144 (1968).
-
I
SAMP
Figure 1. Block diagram of the spectrophotometer, showing the galvanometer mirror, M, lens, L, and grating, G , which are the heart of the monochromator, and the matched photomultiplier dual beam arrangement
I
PROCESSOR
I
I
L Figure 2.
Block diagram of the spectroelectrochemical system
as a whole dard). Since the operator observes the raw internal values as part of the calibration procedure, it is easy to detect run-to-run changes or unreasonable results. The calibration program is resident in memory, and may be rerun a t any time that changes in the apparatus are suspected. Once the apparatus is calibrated there are two program options, depending on whether it is desired to obtain spectra of intermediates, or absorbance us. time curves for the study of kinetics. Both programs enhance the signal through the use of simple arithmetic averaging of the spectrum, point by point, with a capacity of 4096 spectra of 1024 points each, and both are designed to provide the utmost in sensitivity, so that very small quantities of absorber can be detected. The ensuing discussion will explain the system primarily as used for the former, after which the differences peculiar to the latter application will be pointed out. To achieve the optimum in sensitivity, it is necessary that the system operate under the greatest electronic gain which does not result in clipping of the signal-plus-noise by the limiting amplifier input range. At optimum gains, the significant change which can be detected, given enough averaging, is one half the value represented by a change in the least significant bit of the A/D converter. Notice that the greatest gain without clipping, and therefore the optimum sensitivity toward electrochemically generated intermediates, can be achieved only if the background spectrum in the absence of reaction, i e . , the base
ANALYTICAL C H E M I S T R Y , VOL. 4 5 , NO. 1 2 , OCTOBER 1973
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I
I
I ,IO
sec
I
A (nm)
Visible spectrum of the nitrobenzene radical anion in dimethyl sulfoxide-0.1M tetrapropylammonium perchlorate. The spectra of the millimolar nitrobenzene solutions were obtained by scanning at the indicated times after initiation of the electrochemical reduction Figure 3.
line, is truly flat. In fact, with imperfectly matched photomultiplier tubes and the possible buildup of colored products with successive runs, base-line imperfections quickly limit spectrophotometer sensitivity. Probably the most significant aspect of the spectrophotometer design was the use of the computer to dynamically control baseline flatness. The concept is an application of computer feedback control, in which a background spectrum (collected with the potential on the electrode maintained in a region of no reaction) is scaled for output a t the D/A converter, such that when mixed subtractively with the next spectral collection, point by point a t the mixing point, MX, it causes the signal appearing a t the A/D converter input to be approximately zero (Figure 2 ) . In brief, the D/A converter is used to feed back a signal of proper magnitude to force the base line to zero. The difficulty is that the background signal is itself buried in noise under conditions of normal operation of the spectrophotometer. Thus, it is necessary to establish how much of the raw background is background signal before the D/A image can be generated. This could be accomplished by extensive averaging of background signal, but a t high cost of time and computer storage, so a simpler method was sought. The compromise chosen was to extensively smooth the raw data of the feedback spectrum. Once smoothed, the correction spectrum is scaled and output a t the D/A converter synchronously with the collection of the next background spectrum. If all points in the new background, after smoothing, are not within predetermined limits about zero, the old background image is corrected and the procedure repeated. The smoothing procedure consists of replacing the center point of a “movable strip” of points by the simple average of all points of the strip. This is the “zero order” approximation of the general technique (6) of fitting a curve of a polynomial. I t works because the density of data is high, and because there are no peaks in the signal which are sharp relative to those of the noise. Both conditions hold under normal operation of the spectrophotometer, for several data points are collected for each nanometer of wavelength, and the background spectrum, if not initially so, becomes flat with iteration. In fact. the property of (6) F B Hildebrand Introduction to Numerical Analysis, Hill New York N Y 1956, p 295
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McGraw-
convergence to flatness makes possible the use of a very broad (several nanometers) “moving strip” for the smoothing without loss. of accuracy in the final base line. The smoothing program can therefore be relatively simple and efficient, a fact which is important for operations which are part of an iterative loop. An additional benefit of iteration is that backgrounds which are initially entirely offscale will be automatically and correctly zeroed. This aspect is essential a t the high gains used with the spectrophotometer in normal operation. Although the base line appearing at the A/D input converges to flatness, the spectrum is far from flat a t either input of the mixing amplifier, MX (Figure 2 ) . Thus, good frequency response is an essential attribute of MX and of the D/A converter, if these components are not to limit overall system performance a t high scan rates. Furthermore, frequency demands on the D/A converter would be much greater were it not for the dual beam operation of the spectrophotometer, which eliminates the problem of varying spectral sensitivity of the photomultipliers a t an earlier stage in the amplification chain. The system as presented appears to be near optimum in the matching of components to achieve good frequency throughout. Once the background has been zeroed, the computer emits a trigger pulse which causes the potentiostat to step the potential of the optically transparent working electrode into a region of reaction (the limiting current plateau), and the reduction (or oxidation) proceeds a t the diffusion controlled rate. This is the typical chronoamperometric experiment, and the cell current us. time behavior may be analyzed using well developed approaches ( 7 ) . After the potential step is applied, the computer clocks the generation time of the intermediates. When the preselected period has elapsed, a trigger pulse is sent to the spectrophotometer and the spectrum of the solution is collected using the D/A base-line correction obtained above. The spectrum is added point-by-point to a running sum of spectra (the signal averaging sum), the working electrode potential returns to a region of no reaction, and the system enters a waiting state to give the electrochemical system time to relax to the original conditions. After the wait period is ended, a new background, which may now contain the undesired spectra of stable reaction products, is collected and zeroed and another cycle begins. After the desired number of runs have been collected and averaged, the computer determines the absorbance a t t e peak maxima and types these on the teletype in order o wavelength. If desired, the averaged spectrum will be plotted, properly and automatically scaled to the dimensions of the chart paper, and if there is need for saving the digital data, the entire spectrum can be dumped to the high speed paper tape punch. As an example of spectrophotometer performance using the spectral program, Figure 3 shows results from millimolar solutions of nitrobenzene in dry dimethyl sulfoxide a t several different times after the potential was stepped into the limiting current region (1.35 V cathodic of aqueous SCE). In the 370-700 nm region, only a single peak a t 461 nm occurs. This agrees well with the 460-nm peak a t tributed to the radical ion in dimethyl formamide by Kalyanaraman, Rao, and George ( 8 ) . If the monochromator is now adjusted manually to the 461-nm peak maximum, it is possible to perform the other major experiment for which the spectrophotometer is ideally suited: the observation of absorbance us. time behav-
P
(7) D. K. Roe, Anal. Chem.. 44, 85R (1972). (8) V . Kalyanaraman, C. N. R . Rao. and M . V. George, Tetrahedron Lett.. 1969, 4889.
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, N O . 12, OCTOBER 1973
ior. The absorbance in the absence of reaction is expected to be constant with time, but may be nonzero due to absorbance from starting material or products of earlier runs. Thus, for this experiment the feedback from the D/A converter is used to offset the base line by an amount which is constant over the data collection period. The background correction is obtained by taking the mean of all points in the raw background and scaling. The procedure is equivalent to the smoothing step described earlier, but here the “moving strip” of points is the entire data array, and only one pass is necessary. Once the base line is brought to within suitable limits iteratively, the potentiostat is triggered to begin generation of the intermediate, and the collection of the absorbance data begins immediately. After the requisite data have been collected. they are added to the running sum, point by point, the system enters a wait period for the electrochemical system to relax, and the procedure begins anew. Output options, with the exception of peak printout, are as in the spectral collection program. The fundamental similarity of the spectral collection and the absorbance us time operations has made it possible to modularize the software, and to utilize many of the same building blocks for both types of experiment. The computer program actually consists of a series of assembly language subroutines ( 9 ) , each of which is capable of performing a specific real time task, for example collecting a given number of data points on a given A/D channel. The overall task is accomplished by chaining these subroutines under the control of a simple driver program. The spectrophotometer drivers, one for spectral collection, the other for kinetics a t fixed wavelength, require about 250 assembly language statements each, and can be rewritten or modified to perform an entirely new task in a few hours. This ability to utilize basic operations in different ways depending on the task has made it possible to fit all of the programming into about 2.5K of memory (not counting data array storage of floating point data handling routines which require the remainder of 8K for 1024 point spectra). The absorbance cs time program yields results of the type shown in Figure 4, here plotted as A cs tl 2 . If nitrobenzene is reversibly reduced in a one-electron reaction and yields a stable intermediate as expected from results of ESR studies ( I O ) , the absorbance due to the intermediate should follow the law ( 2 1 )
&RC’(Dot)”’ AR
=
Ai/?
where t R is the molar absorptivity, Co is the bulk concentration of nitrobenzene, and DO is the nitrobenzene diffusion coefficient. The data of Figure 4 which provide a good fit to the least squares line shown, with no trace of curvature over several orders of magnitude in time, with zero intercept, and with envelope parallel to the line, suggest that the equation is obeyed, and that all deviations are due to random noise. This is the strongest published evidence that the species being observed in the visible spectrum is the nitrobenzene radical anion and not some colored product of post reaction of that species, which might coexist with the radical ion seen in the ESR ( I O ) . Based on the reversible mechanism with stable radical ion, using runs with solutions having concentrations in the range E. E. Wells, Jr., “ A Library of Data Collection and Manipulation Subroutines for the PDP-8/1 Minicomputer,” ECOM Rep 3486, Sept. 1971, 46 pp. available CFSTI, Springfield. Va. D. H . Geske and A . H . Maki. J. Amer Chem. SOC.. 82, 2671 (1960) J. W. Strojek, J. Kuwana. and S. W. Feldberg, J . Amer Chem. SOC.. 90, 1353 (1968).
Figure 4. Time dependence of absorbance at the nitrobenzene radical anion peak, 461 nm. The functionality is that predicted by the equation for a reversible, diffusion controlled reaction. The curve was obtained on a millimolar solution of nitrobenzene in dimethyl sulfoxide-0.1M tetrapropylammonium perchlorate
0.5 to 2.0 millimolar, and assuming a nitrobenzene diffusion coefficient of 1.42 X cm2/sec [compare (12) 1.8 x 10-5 in methanol of benzene] calculated from in situ cyclic voltammetry, the absorptivity of the 461-nm peak is 1609 a.u.-cm2/mole (average deviation about 6%). Using these data as a first approximation, it can be estimated that if the radical ion actually disappears in a pseudo first order chemical reaction to give the species which we are observing, then the rate constant for the reaction would necessarily exceed 100/sec, or Figure 4 would show detectable curvature (13). Presumably, therefore, we are observing the nitrobenzene radical anion, although a very fast post-reaction of the radical ion to give the species being monitored spectrally still cannot be ruled out. While these results illustrate the technique, they do not plumb the sensitivity limit of the spectrophotometer, which determines the minimum quantity of species which may be examined. Ultimately, the noise places a lower limit on the distinguishable signal, since signal averaging cannot reduce signal-plus-noise to a value less than the minimum resolution of the A/D converter (one part in 128 in our case), but since instrument resolution strongly determines the signal-to-noise ratio, it is necessary to include these parameters in the consideration. The measurements presented here use the terms spectral band width, SBW, defined as the ratio of slit width to dispersion function, and natural band width, NBW, which is the width of the spectral peak a t half-height. Because the dispersion function is a measure of the width of dispersed spectrum per angstrom in the plane of the exit slit, it is easy to see that SBW is the inverse of the qualitative idea “resolution.” On the other hand, NBW is characteristic of the molecule only. These concepts are interdependent and, if the peak shapes are assumed gaussian, it is possible to calculate (14) that if the SBW of the instrument is held to one tenth of the NBW, the peak height will be 99.5% of its “true value.” At SBW/NBW = 0.5, the peak height is 90% of “true,” etc. Similar estimates of the ability to separate peaks are possible. Thus, increasing the SBW by opening the slits improves the signal-to-noise ratio, for more signal energy reaches the phototube, but accuracy of peak height and separation of peaks decreases. (12) J. Thorvert,Ann. Phys.. 2, 369 (1915). (13) G. C. Grant and T. Kuwana, J . E/ectroana/. Chem.. 24, 11 (1970). (14) “Optimum Spectrophotometer Parameters,’ Appi. Rep. AR 14-2, Cary Instruments, A Varian Subsidiary, Monrovia, Calif., 16 pp.
ANALYTICAL
C H E M I S T R Y . VOL. 45, NO. 1 2 , OCTOBER 1973
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Table I. Noise Limited Instrument Sensitivity Conditiona
SBW
Sensitivityb
N o OTE in path L o w resolution M o d e r a t e resolution High resolution
165 A 165 A 130 A 32.5A
7.2 x 10-5 1.9x 10-4 2.5 x 10-4 1 x 10-3
a Except as noted, results obtained with optically transparent electrode (OTE) in the sample beam, and at 700 nm. i n absorbance units. Based on SIN enhancement of 128 through signal averaging.
Although there is an optimum adjustment, for mechanistic work the high signal-to-noise ratio, low resolution end of the scale is favored, for here it is the functionality of the absorbance us. time plot which is more important than the absolute value of absorbance. Too, peaks from solution spectra in the visible region are quite broad, having typical NBW of 300-500 angstroms (14), thus allowing large SBW with minimal inaccuracy in peak height. Two other factors which strongly affect sensitivity are the photomultiplier spectral sensitivity profile and the absolute absorbance of the sample. The photomultipliers used in this work are most sensitive a t about 550 nm, with a loss of nearly an order of magnitude in sensitivity a t the two extremes of our spectrophotometer scan. Clearly, one expects the optimum signal-to-noise ratio a t the sensitivity peak, for here is found the greatest signal per incident photon, while photomultiplier shot noise is independent of wavelength. The effect of a strong absorber such as the optically transparent electrode or colored products in the beam is similar. In this case, the signal is reduced (by an order of magnitude per absorbance unit, no less) while noise is unaffected. The results of measuring the spectrophotometer noise which appears at the input of the A/D converter under various conditions are presented in Table I. Although these data reflect conditions of actual usage of the spectrophotometer, they are overly optimistic in the sense that software limits the number of averageable runs to 4096. If
the square root law for the number of runs (15) holds, signal-to-noise enhancement by averaging will be 64, a factor of two less than the results in the table would indicate. This particular limitation would be easy to remove, but our usage to date has not required it. For the nitrobenzene radical anion, a sensitivity of 1.9 x a.u. implies, using the equation and assuming a bulk concentration one millimolar in nitrobenzene, that detection would occur in 1.13 msec. Compounds having greater molar absorptivities, or present in greater concentrations, would be detectable a t correspondingly shorter times. Thus, the apparatus described is capable of recording spectra of species with half-lives of the order of milliseconds. It does so by using the unique capabilities of the computer to remove the base-line irregularities which limited sensitivity of the spectrophotometer alone, and by signal averaging. Beyond this, the system is capable of managing the very complex in situ spectroelectrochemical experiment to obtain results which are virtually impossible to accomplish if attempted manually.
ACKNOWLEDGMENT The author is grateful to T . Kuwana and G. C. Grant for assistance in the construction of the spectrophotometer, and to A. Pilla for encouragement in the early phases of the work. Received for review January 23, 1973. Accepted May 9, 1973. Thanks are due to the Electrochemical Society, Inc., for permission to publish this work, part of which was presented at the symposium on Spectroscopic Methods of Electrochemistry, 141st Meeting of the Electrochemical Society, Houston, Texas, 1972. Part of this work was performed a t the U.S. Army Electronics Command, Fort Monmouth, N.J. (15) John C. Fisher. "Lock in the Devil, Educe Him. or Take Him for the Last Ride in a Boxcar'", Princeton Applied Research Corp., Tek Talk, 6, No. 1
Analytical Application of High Frequency, Phase-Sensitive Short Controlled Drop Time Alternating Current Polarography A. M . Bond
Department of lnorganic Chemistry. University of Melbourne. Parkville. 3052, Victoria. Austraiia
I n general, polarographic methods do not have the specificity for the interference free direct determipation of elements in complex mixtures nor are they often sufficiently rapid to be competitive with other techniques. This paper describes the analytical use of rapid, short controlled drop time, high frequency, 3-electrode, phase-sensitive ac polarography. The use of high frequencies (500 to 1000 Hz) instead of the usually recommended low frequencies, (10 to 100 Hz) can provide considerable discrimination against unwanted electrode processes. The medium for dissolution of many samples prior to their determination is often acidic, and in such media, and with the technique proposed, removal of oxygen is often 2026
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO.
unnecessary. This plus the use of short controlled drop times and fast scan rates of potential, provide a route to an attractive method of analysis having a time scale close to that for atomic absorption spectrometry, linear calibration curves over several orders of magnitude of concentration, ready checks on interference, and other useful features. The determination of tin and a comparison of results with those obtained independently by several other laboratories using Atomic Absorption Spectrophotometry, X-Ray Fluorescence, and Colorimetric methods is given, to demonstrate the usefulness of the method. Other examples are also given-the determinations of U, Pb, and Cu.
12, OCTOBER 1973
