and
Table I.
both a t 25" C. and p = 2. Since [Ce(IV)totall = [Ce(OH)+31 2[CeOCe+6],in 0.025M[Ce(IV)t,t,~], Ce+4 = 0.0054, and
+
+
0.0054 -1.71 = Eo - 0.59 log 0.025 Eo = -1.75 volts
This agrees well with the value calculated from the sulfate data. Hardwick and Robertson showed that changes in ionic strength have little or no effect on the hydrolysis constants in perchloric acid. Under these conditions it is possible to calculate Eo as a function of ionic strength (Table 11). Duke and Bremer (6) have correlated these potentials empirically with the water activity in perchlorate solutions. Data on complexing of nitrate ions by cerium(TV) are not available. Noyes and Garner (16) showed that the potential in the range from 0.5 to 2M nitric acid is very nearly independent of acidity and ionic strength. Their value agreed with the results of Smith and Getz (18). To explain the acid independence and a t the same time reconcile these results with the Eo's calculated above, one can write: Ce+4
+
+
SO3H 2 0 7 2 [Ce(N03) H+ (OH)] ++
+
[Ce(KOs)(OH)++] [H+] K = [CeA4][NO3-] This constant must have a value of about IO2, to agree with the results in perchlorate and sulfate media. The results of Blaustein and Gq-der (2) indicate strongly that the situation in nitrate solutions is much more complicated than this, n-ith dimerization of this species and other reactions occur-
Acid Normal-
Cerium(ll1)-Cerium(lV) HalfCell Potentials
Measured E HC1Od
ity 1
-1.70 -1.71 -1.75 -1.82 -1.87
2 4 6 8
HC1
"03
-1.61 -1.62 -1.61 -1.56
...
-1.44 -1.44 -1.43
-1.28
..,
-1.42
anions mould clarify the complexing and hydrolysis picture; and when used in conjunction with the work of Blaustein and Gryder ( 2 ) )such spectrophotometric data should allow a detailed description of the status of cerium(1V) in nitrate solution. It is probable that a t low temperature cerium(1V) in the presence of chloride is sufficiently stable to lend itself to a similar spectrophotometric study.
Table 11. Standard Potential as a Function of Ionic Strength P 1 2 4 6
8
LITERATURE CITED
[H +I
Eo
Bauer, E., Glaessner, A,, Z . Elektro-
1 2 4 6 8
1.75 1.76 1.7R 1.82 1.87
Blaustein, B. D., Gryder, J. W., J . Am. Chem. SOC.79, 540 (1957). Connick, R. E., Mayer, S. W., Zbid.,
chem. 9, 534 (1903).
73, 1176 (1951).
Duke, F. R., Borchers, C. E., Zbid., 75, 5186 (1953).
ring (9). There is little doubt that the lower potential a t higher nitric acid concentrations is a consequence of substitution of nitrate for hydroxyl in the complex, but no quantitative data apart from the potentials are available. If the thermodynamic (zero ionic strength) potential is to be obtained, potential as well as complex and hydrolysis constants must be measured a t much lower ionic strengths. There are indications that such work might be very difficult, as perchlorate solutions of cerium(1V) hydrolyze and polymerize to the extent of being insoluble in low concentrations of acid; and in sulfate solutions a t low ionic strengths, both hydrolysis and polymerization would probably occur. However, the utility of the true potential is very limited, as cerium(1V) is not used practically at very low ionic strengths. Further studies of cerium(1V) in the presence of nitrate and chloride ions need to be done; particularly, work similar to that of Hardwic$ and Robertson (10, 11) in the presence of these
Duke, F. R., Bremer, R. F., ANAL. CHEW23, 1516 (1951). Duke. F. R.. Parchen. F. R.. J . Am. C h e k Soc: 78,1940 11956): (7) Fronaeus, S., Svensk Kem. Tidskr. 64, 317 (1952).
(8) Fronaeus, S., Ostman, O., Acta Chem. Scand. 10, 769 (1956). (9) Gryder, J. W., Dodson, R. W., J. Am. Chem. SOC.71, 1894 (1949);
73. 289n ~ ---- ( I R . I (IO) Haidwick, T. J., Robertson, E., Can. J . Chem. 29,818 (1951). (11) Ibid., p. 828. (12) Jones, E. G., Soper, F. G., J. Am. Chem. SOC.57,802 (1935). (13) Kuna, A. H., Zbid., 53, 98 (1931). (14) Moore, R. L., Anderson, R. L., Zbid., 67, 167 (1945). (15) Newton, T. W., Arcand, G. M., Zbid., 75, 2449 (1953). (16) Noyes, A. A., Garner, C. S., Zbid., I
\ - - - - I .
58. 1264 (19361. - - - ~ \----,(17) ShlFrill, M. S., King, C. G., Spooner, R. C., Ibid., 65,170 (1943). I
(18) Smith, G. F., Getz, C. A,, IND. ENG.CHEM..AKAL. ED. 10. 191 119381. (19) Spedding, F. H., Jaffe, S., J . Am. Chem. SOC.76,882 (1954). (20) Vetter, K. J., 2. physilz. Chem. 196, 360 (1951).
RECEIVED for review December 31, 1956. Accepted July 24, 1957.
Anodic Stripping Voltammetry Using the Hanging Mercury Drop Electrode RICHARD D. DeMARS and IRVING SHAIN Chemisfry Department, University o f Wisconsin, Madison 6, Wis.
b Anodic stripping voltammetry using the hanging mercury drop electrode offers a rapid and convenient method for analyzing extremely dilute solutions of metals which form amalgams. The anodic stripping is performed using the techniques of voltammetry with continuously varying potential, and the anodic peak current is a function of the concentration of the ion in the
solution and the cathodic plating time. As examples the method was applied to cadmium and thallous ions in the 10-6 to 10-9M concentration range and to mixtures of cadmium and zinc in the to 10-8M concentration range.
T
of certain metal ions into a mercury cathode a t conHE PLATING
trolled cathode potential has been used many times to concentrate and separate these metals from rather dilute solutions ( 5 ) . Subsequent anodic stripping of these amalgams may be used to concentrate the sample for some conventional method of analysis (10). The anodic stripping process also has been the basis of direct coulometric determinations ( I , 3, 8). Nkelly and VOL. 29, NO. 12, DECEMBER 1957
1825
Cooke ( 7 ) reported a direct method using voltammetry with continuously varying potential and a mercury pool electrode. Hickling. hIaxwel1, and Shennan (8) reported a similar but less sensitive method using a mercury pool electrode and conventional polarographic equipment. Delahay and coworkers (4) studied some of the theoretical aspects of the anodic stripping process for the conditions of voltamnietry a t constant anode potential and also a t constant current. METHOD
A hanging mercury drop ( 9 ) mas used as a stationary mercury electrode. The niethod involves plating a metal into this electrode from a stirred solution for a predetermined length of time. The stirring must be reproducible; thus, placenient of the electrode and stirrer, volume of solution, and rate of stirring must be fairly reproducible. The stirring may be vigorous without dislodging the hanging drop electrode. The potential of the electrode during this initial plating time should be about 0.2 volt more cathodic than the polarographic half-wave potential for the same reaction a t a dropping mercury electrode. Care should be taken not to exceed the decomposition potential of any possible interfering substances which are reduced at more cathodic potentials. The electrolysis time depends on the concentration of the ion in solution. I n general. 5 minutes is sufficient for concentrations above lO-7-lf, 15 minutes for 10-*V, and 60 minutes for 10-9ilf. After the appropriate electrolysis time has elapsed, the stirring is stopped and 30 seconds is allowed for the solution to come to rest. Then the potential is scanned in an anodic direction using the equipment and technique of voltammetry ~ i t hcontinuously varying potential (9). Typical current-voltage curves are shown in Figure 1. All curves were run a t the same sensitivity. Curve A s h o m the cathodic residual current. Under these conditions the peak current for a 10-8.1f cadmium solution would be 1.49 x 10-4 pa. and thus rvould be entirely masked by the residual current. Curves B and C are the anodic curves obtained after a 15-minute electrolysis on the indifferent electrolyte and a 10-8Jf solution of cadmium ion. To investigate the precision, accuracy, and applicability of the method, cadmium and thallous ions were studied in the concentration range from to 10-9Jf. Mixtures of cadmium and zinc \yere studied in the concentration range from 10-4 to 10-6.11, using the combined techniques of cathodic voltammetry and anodic stripping with continuously varying potential. 1826
ANALYTICAL CHEMISTRY
Materials. All chemicals were reagent grade, and, except for the indifferent electrolyte, were used without further purification. Reagent grade potassium chloride had t o be purified by electrolysis at a mercury pool cathode (6) before use. All solutions were prepared with triple-distilled water. Linde high purity nitrogen was used to remol-e oxygen from the electrolysis cell. A vanadous sulfate scrubber \vas used to remove the last traces of oxvgen from . the nitrogen. Solution Preoaration. At t h e extremely lorn concentrations encountered in this work, two difficulties arise in solution preparation: contamination from container walls, and adsorption of t h e sample by t h e container. I n order t o prepare solutions fairly accurately, it was necessary t o use a rather long equilibration procedure. A set of new volumetric flasks and a set of new polyethylene bottles were leached with several changes of distilled water for several days before use. A series of solutions from 10-6 to 10-9M was then prepared in the volumetric flasks. These solutions were equilibrated (with vigorous periodic shaking) for 12 to 24 hours. At that time the solutions were transferred to the polyethylene bottles, and a new set of solutions was prepared in the volumetric flasks. The procedure was repeated four times. A fifth set of solutions then was prepared and transferred immediately to the polyethylene bottles. These last solutions could be stored safely in the polyethylene bottles for several weeks. It was also necessary to equilibrate the cell and electrode assembly before running a particular series of solutions. No systematic study of the minimum equilibration time was made. It is possible that these times can be reduced considerably.
EXPERIMENTAL
Apparatus. The equipment used was t h e same as described previously ( 9 ) with the following exceptions: The salt bridge and external reference electrode were replaced by a Beckman sleeve-type calomel electrode. The cell resistance under these conditions was 900 ohms. A Leeds & Northrup direct current microvolt amplifier was used as a preamplifier. During the plating period the solution was stirred with a magnetic stirrer driven by a synchronous motor. The electrolysis cell was polystyrene. The radius of the working electrode was 0.0652 em. : the area was 0.0557 sa. em. The rate of voltage scan was 0.0208 volt per second, Lvhich corresponds to 24 seconds for a 0.500-volt sweep. The electrolysis cell was not thermostated for this work on analytical applications.
In w K 0
a a 0
2 w
a 3 E
I
I
I40
0 65 VOLT
Cvs
I
/
RESULTS A N D DISCUSSION
0 90
SCE)
I
Single-Component Systems. This method was applied to t h e analysis of very dilute solutions of cadmium and thallous ions. A set of curves similar t o Figure 1 v-as obtained for each ion. The results (Table I) indicate t h a t t h e peak current is a linear function of t h e concentration of the ion in solution and t h e electrolysis time.
Figure 1. Current-voltage curves for anodic stripping of 10-*M cadmium solution in 0.1 M potassium chloride
A . Cathodic residual current B . Anodic residual current after 15minute electrolysis C. Anodic stripping curve for 10-8111 cadmium solution after 15-minute electrolysis
Table 1.
Peak Current as Function of Concentration and Electrolysis Time AV.
Ion Cd++
(0 I M KC1)
(0.131 KC1) a
Concn., Mole/Liter 1 00 I 00 1 00 1 00
x 10-6 x 10-7 x 10-8 x 10-9
x 1.00 x
1.00
2
2
2 2
ip/ta,, pa./Min. 10 x 10-1 09 x 10-2 io x 10-3 10 x 10-4 1
7 21
I ,
x x
-10-2 10-3
Average and average deviation of six determinations.
Dev. C Y /C
1 9
Electroll sie
Time, llinutes 5
24 2 4
5 15
3 0
60 5
3 0 4 1
0
15
Two-Component Systems. As examples of t h e application of this method t o mixtures, solutions containing both cadmium a n d zinc were studied. I n each case t h e ion present a t l O - * X was determined by the cathodic potential scan (9), and the ion present a t 10-6,11 was determined by anodic stripping. The results (Table 11) indicate that the method is feasible even in the case of Solution 2 , where both the cadmium and zinc are plated into the electrode, but only the zinc is anodically removed. ACKNOWLEDGMENT
This work was supported in part by the Kisconsin Alumni Research Foundation. LITERATURE CITED
(1) Gardiner, K. ANAL. CHEX.
W.,Rogers, L. B., 25, 1393 (1953).
(2) Hickling, .4.,Maxwell, J., Shennan, J. V., Anal. Chim. Acta 14, 287 (1956).
’ Table II.
Analysis of Two-Component Systems in 0.1M Potassium Chloride
Solution 1 Zn++. 1 00 X Cd++; 1 00 x Solution 2 c d + + , i 00 x Zn+-, 1 00 X (I
Peak Current,as* w.
AV. Dev.,* pa.
10-4M 10-631
1.92
0 30
10-4~ 10-6Jf
1.91
0 40
Peak Current,*,c pa./Min.
Dev.,*
0 188
1.40
0 189
1 75
AV.
nc
Cathodic potential scan.
* Average and average deviation of six determinations. Anodic stripping current after 5-minute electrolysis.
(3) Lord, S. S., J r . , O’Seill, It. C., Rogers, L. B., .$X’AL. CHEW 24, 209 (1952). (4) Mamantov, G., Papoff, P., Delahay, P., J . Am. Chem. SOC. 79, 4034 (1957).
(5) hlixireli, J. A., Graham, R. P., Chem. Revs. 46,471 (1950). (6) MeiteS, L., -4NAL. CHEM. 27, 416 (1955). (7) Nikelly, J. G., Cooke, W.D., Zbid., 29, 933 (1957).
(8) Porter, J. T., Cooke, K . D., J . A m . Cheni. SOC.77, 1481 (1955). (9) DeMars. R. D.. Shain. . . Ross. J. \I7.*
I., Ax.~L.’CHEM. 28, 1768 (1956): (10) Taylor, J. IC, Smith, S. IT.,J . Research S a t l . Bur. Standards 56, 301 (1956). RECEIVED for review March 30, 1957. Accepted June 28, 1957. Presented in part, 17th Midwest Regional Meeting, -4CS, Amee, Iowa, Sovemher 1956.
Generalized X-Ray Emission Spectrographic Calibration Applicable to Varying Compositions and Sample Forms H. D. BURNHAM, JOHN HOWER,’ and L. C. JONES
Wood River Research laboratory, Shell Oil Co., Wood River, 111.
b A general scheme of analysis based on the equations of Sherman has been attempted. Novel alterations and extensions of the original equations were required. For a three-component system the working equations take the form of three simultaneous equations, linear with respect to concentrations and reciprocal intensities and third order with respect to a geometrical factor. The value of the method is greatly enhanced b y use of time-saving graphical solutions for these equations. The x-ray emission spectrographic method developed can handle quantitatively samples of nonidentical geometryplate, wire, chips, turnings, and filings can b e treated with equal ease. Calculation of the interaction coefficients required in setting up the method from a series of standards has been facilitated b y IBM equipment, The method has been applied to the determination of chromium, iron, and nickel in steels.
THE
elemental composition of samples containing substantial amounts of three or more elements of high atomic nurnbrr by x-ray emission
spectroscopy has generally been determined by reference to standards whose compositions closely resemble the unknowns. The principal difficulty in deducing chemical composition directly from the fluorescent x-ray intensities lies in the mathematical complexity of representing the energy spectrum of the primary x-ray source, the attenuation suffered by each vave length of the primary beam in passing through the sample, the fluorescence yield of each element in the sample, and the attenuation of each fluorescence wave length in leaving the sample and entering the detector. A practical correlation between fluorescent x-ray intensity and chemical composition has recently been derived by Sherman (6). For limited ranges in composition a close linear approximation may be made; thus for a mixture of three elements of concentrations C1, C2, and C3, the folloiving equations may be used : - h)CI + a21 cz + a31 c3 = 0 c1 f (a22 - t 2 ) cZ + a32 c3 = 0 all c1 f a23 CZ (a33 - t 3 ) C3 = 0 c1 + Cz + C3 = 100 (UII
a12
+
(1)
(2) (3) (4)
The reciprocal intensities of the coinponents of the fluorescent spectrum is, are measured by t l , tz, and +that the time for each component to register the same fixed count-while ail, u22, and u33are counting times for the pure elements. The six a,,’s are parameters to be computed from observations on samples of known composition. Sherman tested the equations on a series of paint pigments containing chromium, iron, and nickel oxides, with fair success. I n this case with finely divided and well mixed powders it m s easy to arrange constant sample geometry. Similar sets of equations were used by Noakes (4) and Beattie and Brissey ( 1 ) ; with flat plate samples of equal area, constant sample geometry was readily achieved. A method to be of greatest value in the analytical laboratory, hon-ever, niust handle chips, turnings, filings, wire, and plates with equal ease. Therefore the validity of Sherman’s proposed equations was tested for a ternary mixture over a substantial range of compositions and means of handling samples of various 1 Present address, Stanolind Oil and Gas Co., Tulsa, Okla.
VOL. 29, NO. 12, DECEMBER 1957
1827
