divided by concentration show the proportionality of the square-wave current n-ith concentration as predicted by theory. The half-wave reduction potential for plutonium(1V) to (111) was found to be +O.T1 volt us. S.C.E. in 1V hydrochloric acid and $0.66 volt in 2 V nitric acid. These values agree closely n i t h those obtained by Scott and Peekema (12) by controlled potential coulometry. DISCUSSION
I n nitric acid systems, the presence of nitrite introduces a very high background or residual current which makes it impossible to obtain reduction waves for low concentrations of plutonium. The addition of a small amount of sulfamic acid was found to remove the interfering effects of nitrite. I n general, the residual current for a nitric acid solution is higher than for hydrochloric acid solution. Interference from iron(III), which has a half-wave potential of about $0.45 volt us. S.C.E., is much more pronounced in nitric acid than in hydrochloric acid solutions. I n nitric acid very little separation b e h e e n the plutonium and iron waves exists when the iron content reaches about five times the plutonium concentration.
The continual scanning of plutonium, particularly in nitric acid solutions, apparently produces an oxide layer on the surface of the platinum electrode resulting in a high residual current which virtually masks the reduction nave of interest. Investigators have used various methods, such as an aqua regia or a hot cleaning solution treatment, in rejuvenating solid electrodes. All of these practices were unsatisfactory in cleaning the platinum used in this study; hom-ever, a periodic evolution of hydrogen, accomplished by applying a small negative potential to the electrode returned the electrode to a usable condition. Square-wave polarography has higher sensitivity than conventional polarography, derivative type waves which are easily interpreted, no effects from sample agitation, and negligible effects from irreversibly reduced materials, such as oxygen, on the measurement of reversibly reduced ions. The instrument is potentially capable of operating below the 10-6 mole per liter region.
ACKNOWLEDGMENT
The author thanks R. E. Connally for his assistance in the electronics of the instrument.
LITERATURE CITED
(1) Barker,
G. C., Faircloth, R. L., Gardner, 4. W., Brit,. Atomic Energy Research Establishment,, Rept. AERE C/R 1786 (Feb. 6, 1956). (2) Barker, G. C., Jenkins, I. L., Analyst 77, 685 (1952). (3) Cook, G. P., Foreman, J. K., Kemp, E. F., Anal. Chim.Acta 19, 174 (1958). ( 4 ) Ferrett, D. J., hlilner, G. W. C., Analyst 80, 132 (1955). (5) Ibid., 81, 193 (1956). (6) Ferrett, D. J., Milner) G. TV. C., J . Chem. SOC.1956, 1186. ( 7 ) Ferrett, D. J., Miher, G. W. C., Shalgosky, H. I., Slee, L. J., Analyst 81, 506 (1956). (8) Hamm, R. E., ANAL. CHEM. 30, 350 (1958). (9) Hamm,. R. E., U. S. Atomic Energy Commission, Rept. HW-52915 (Oct. 7, 1957) declassified. (10) Harvey, B. G., Heal, H. G., Maddock, A. G., Rowley, E. C., J. Chem. SOC.1947, 1010. (11) Kambara, R., Bull. Chem. SOC. Japan 27, 523, 527, 529 (1954). (12) Scot,t, F. A,, Peekema, R. ll., “Analysis for Plutonium by Controlled Potential Coulometry,” Proc. 2nd Intern. Coni. on Peaceful Uses of Atomic Energy 28, 573 (195S)> Paper P-914. (13) Warren, C. G., U. S.Atomic Energy Commission, Rept. LA-1843 (July 1953) unclassified. RECEIVED for review October 12, 1959. Accepted December 28, 1959. Work performed under Contract No. W-31109-Eng-52 bet-xeen the U.S. Atomic Energy Commission and General Electric Co.
CouIometric Titrations with EIectroIyticaIIy Generated Sulfhydryl Compounds Applications of Thiog lycollic Acid BARRY MILLER and DAVID
N. HUME
Department o f Chemistry and laboratory for Nuclear Science, Massachusetts institute of Technology, Cambridge
The feasibility of constant current coulometric generation of the sulfhydryl group is illustrated for thioglycollic acid, HSCH,COOH. Source of the reagent is the very stable mercuric complex, which is soluble at pH values above the pK, of the acid, 3.60. The response of a mercury p M electrode is generally used for end point indication. Amperometry at two mercury electrodes is also suitable. Determinations of mercury, gold, copper, and ferricyanide illustrate the utility of the generated sulfhydryl as a complexing agent for metals and as strong reducing agent in the neutral and alkaline regions.
524 *
ANALYTICAL CHEMISTRY
T
sulfhydryl group, through its affinity for metals and as a reducing agent, offers a wide range of applications to analysis. For metal determinations, sulfhydryl sources offer particular promise, because many of the metals whose affinity for sulfur is pronounced are those for which (ethylenedinitrilo) tetraacetic acid (EDTA) is least useful ( 1 2 ) . This group includes the platinum metals, silver, gold, and the thio-anion-forming elements of the acid hydrogen sulfide group. As a reductant, the sulfhydryl group has the advantage of being a strong reducing agent in the high p H range where there are fen- good reHE
39,
Mass.
agents available. For ordinary titrimetry, however, organically bound sulfhydryl suffers from the drawbacks of instability toward air oxidation and objectionable odor as well as possible difficulties due to limited solubility and excessive volatility. Internal generation by constant current titrimetry has made available many unstable but potentially useful reagents for chemical analysis ( 5 ) . Such a n approach has been taken for the generation of sulfhydryl and its applications have been explored. METHOD OF GENERATION
Free sulfhydryl may be readily pro-
duced through the reduction of the corresponding disulfide : RSSR
+ 2"
$- 2 e -
+
PRSH
Although coulometrically suitable in terms of current efficiency, the potentiometric irreversibility of this couple (3) makes it difficult to follow the reaction. The polarographic behavior of the disulfide-sulfhydryl system ( 2 ) indicates that the o\idation product of sulfhydryl a t a mercury electrode is a mercury mercaptide rather than a disulfide. Furthermore. the sulfhydrylmercury mpi captide couples examined have had s po1arogr:rphically reversible appearance (coincidence of anodic and cathodic potentials) as opposed to the definitely irreversible behavior of typical mercaptan-disulfide systems. Therefore, from a practical viewpoint, the use of a soluble mercuric complex of a sulfhydryl compound instead of a disulfide as a source for the coulometric generation of the group is far more attractive. One sulfhydryl per electron is produced b:, the deposition of mercury : Hg(SR)?
+ 2H+ + 5 -
+
Hg
+ SRSH
Titration is readily possible in both forward and backn-ard directions. Coulometric generation of mercury(1) and mercury(I1) for sulfhydryl determination has been elploited by Przybylonicz and Rogers (8).If sulfhydryl is to be generated from Hg(SR)?, it is necessary to select R such that the complex has sufficient aqueous solubility to maintain a titration efficiency of 100% for a mercury-generating electrode a t the current density chosen. The mercuric thioglycollate complex is one of the simplest sulfhydryl sources satisfying this requirement. Effects due to the specific nature of R are ignored in the follon ing arguments, but may be of importance in the equilibrium and kinetic factors determining the range of applicability of a particular sulfhydryl compound ( 6 ) . Stability constants for the types of hI(SR), complexes involved here are generally lacking for the more noble metals; hence the survey of the elements amenable to determination by this method was nwessarily empirical. END POINT DETECTION
Khere the reaction involved is purely one of metal complexation and for all titrations beyond the equivalence point (excess sulfhydryl), the potentiometric response of a mercury indicoting electrode serves to define the titration curve in the p l I sense of Reilley and conorkers (10, 11). The equilibrium espressions for the formation of the mercury-sulfhydryl complex and the complex of the metal ion, lI+., t o be determined may be combined with the Xernst expression for a mercury
electrode a t 25" C. to give the relation between indicator electrode potential and [hl+n].
+ +
EE= ~ Eoa8++ 0.0296 log [Hg"+] (3) Eag = Eoag*+ 0.0296 log [Hg(SR)zI [RSHP-' K M[&1+"1 (4) [hI(SR),] [H+]"-' K H ~ Equation 4 shows that the response of the mercury electrode is linear rvith log [ M + n ] . Khere metals mill also be oxidizing agents v-ith respect to sulfhydryl, and for oxidants in general, the treatment of mercury electrode potentials must be different from that previously considered for the region before the end point. After the end point (specific effects of reduced products neglected) the electrode will respond according to Equations 1 and 3 combined. The mixed potential before the end point will depend on the reversibility of the oxidant couple and the limits imposed on the anodic range of a mercury electrode in the particular medium. A potential break ought to be expected if the equilibrium conSRSH + Red RSSR stant of Ox is of the ordinary magnitude required for complete reaction, because the disulfide formed is not involved in the potential-determining reaction-Le., not competed for by mercuric ion ( 7 ) . Attack of the mercury pool by any reagent n ill lead to the titration of a n equivalent amount of mercury ions or a compound such as mercuric oxide. The reaction may be slow in the latter case but it still will be stoichiometrically correct.
+
+
Table I.
Current, Na.
5.066 5.067 5.070 10.27 10.27 10.27 10.27 10.27
5,094 5.097 5.097 5.097 5.098
5.078 5.071
The superiority of a mercury system over other metal electrodes has been pointed out by Reilley (10, 1 1 ) . The high stability of mercury complexes permits the proper response of the p;ll electrode. For sulfhydryl the extreme affinity of mercury for sulfur gives K,, a magnitude of about (1). The potential relations of a mercury electrode in this system have been summarized in Figure 1. Curve I represents potentials calculated from Equations 1 and 3 for the values [RSH]
=
and [Hg(SR)*] = lo-*
which are the magnitudes corresponding to a 50% beyond the end point condition for the titrations described in this work. Leussing and Kolthoff (4) found a linear shift of 59 mv. per p H unit for the anodic wave of thioglycollic acid over the p H 4 to 10 range. At p H values above the p K z of thioglycollic acid the oxidation becomes pH-independent, because the sulfhydryl group is completely ionized. Curves 11, 111, IV, and V represent the upper potential limits of a mercury electrode in electrolytes of relevance here and follow the treatment of Reilley (10, 1 1 ) . Curve I1 is the limit imposed by the formation of mercuric oxide; 111, by the weak complexing effect of acetate; IV, by mercurous rhloride; and V, by ammonia complexation. On the mercury(I1)-rich side of the end point, the effect of the reaction H g + + Hg(SR)2 + 2HgSR' will also be limiting. I n the thioglycollate case the anodic range is also limited by the formation of other complexes ( I S ) besides Hg(SR)*. The potential region available is not severely restricted by this factor and the much higher stability of the Hg(SR)Z complex preserves the assumed stoichiometry.
+
Titrations of Mercury and Gold
Time, Taken, Found, Sec. Mg. Mg. Mercury (Potentiometric End Point) 423.0 2.232 2.227 2,232 2.241 425.6 423.3 2.232 2,231 Av. 2.233 390.5 4.161 4.172 391.6 4.161 4.183 391.5 4.161 4.182 390.4 4.161 4.170 4.161 4.169 390.3 Av. 4.175 Gold (Potentiometric End Point) 2.011 2 002 577,5 577.8 2.011 2.004 577.0 2.011 2.002 578.4 2.011 2.006 579.5 2.011 2.010 Av. 2.005 Gold (Amperometric End Point) 579.0 2.011 2.001 580.5 2.011 2.002
Error,
hIg. -0.005 $0 010 -0,001
$0 05% +o 011
+o +o +o +o +o
022
021 009 008 35%
-0 009 -0 007 -0 009 -0 005 -0.001 -0 3yc -0 010 -0 009
VOL. 32, NO. 4, APRIL 1960
525
PCI
P
I
100
80
+ 200
i
m
60 In
-
L
C
3 > 0
W
40
- 200 I-
\
20
0
I
I
I
I
I
I
I
i
i
I
I
2
3
4
5
6
7
8
9
IO
II
20
40
60 Sec.
Figure 2. Potentiometric and amperometric titrations of mercury(l1) in pH 7.5 mercuric thioglycollate systems Generating current 5.1 ma.
PH Figure 1. Potential collate electrode I. 11. 111. IV. V.
-
p H diagram for mercury-thiogly-
[RSH] = Mercuric oxide 0.1 M acetate Chloride 0.01M ammonia
[Hg(SR)?]
Of particular interest here are the very large potential breaks available in the neutral and alkaline regions and the ability of the system to tolerate appreciable amounts of interfering ions like chloride. The presence of oxygen imposes a lower limit varying from - 30 to -100 mv. us. S.C.E. over pH 3 to 10 ( I I ) , so all work has been done under nitrogen deaeration. The reversibility of the possible anodic and cathodic reactions for a mercury electrode in this system leads to the conclusion that two-indicatorelectrode amperometry should also serve as a means of end point detection. I n mercury titration a sharp minimum of current would characterize the end point. EXPERIMENTAL
T h e constant current source was t h a t of Reilleg, Cooke, and Furman (9), and the timer was a Standard Electric Time Co. Model S-10. Potentials were measured with a Leeds &- Northrup Model 7664 pH meter against a mercury-mercurous sulfate reference (+405 mv. us. S.C.E.). An Apparatus.
526
0
ANALYTICAL CHEMISTRY
=
lo-?
amalgamated gold wire electrode was employed as indicator. For amperometry, a Fisher Elecdropode n i t h external Rubicon galvanometer was used and the polarizing potential of 150 mv. impressed across an amalgamated wire electrode and the generating pool or a second wire. The titration cell was a cylindrical vessel of 3.3-em. diameter made of borosilicate glass with a platinum wire sealed into the base. Approximately 25 ml. of solution n as contained above the magnetically stirred mercury-pool generating electrode. The platinum foil electrode which completed the generating circuit was separated by medium-porosity fritted-glass disks in a bridge. Reagents and Solutions. All chemicals were reagent grade, with the exception of t h e thioglycollic acid, which was Eastman 807, analytical grade. Potassiuni ferricyanide n a s recrystallized from t h e reagent grade for preparation of standard solutions. hlercury(II), as perchlorate, and copper(II), as sulfate, stock solutions were standardized against t h e pure disodium salt of E D T A (J. T. Baker Chemical Co.). Gold(II1) standard solution was prepared by dissolving in aqua regia the pure metal supplied by
Baker Platinum Division, Englehard Industries, and nitrate was removed by evaporations with hydrochloric acid. Nercuric thioglycollate complex was prepared by mixing stoichiometric amounts of thioglvcollic acid and niercuric chloride. The resulting white precipitate, after filtration and washing, was treated with a slight excess of sodium hydroxide until completely dissolved. This stock solution n-as made about 0.1X as mercuric complex. Some slow decomposition is noted on several days’ standing when light brown sedimentation appears, but on filtration the titration properties of the stock seem unaffected. Molar acetic acid-sodium acetate mixtures were employed for work at pH 5 and 1111 ammonium acetate containing a small amount of ammonia served as the buffer a t pH 7 . 5 . The pH range from 5 to 10 may be used according to its desirability in terms of end point sensitivity and the pH stability of the component to be determined. PROCEDURE
Approximately equal volumes of buffer and stock mercuric thioglycollate are mixed for titration purposes. This solution may contain a slight excess of mercuric or sulfhydryl, depending on the method of preparation. Oxygen is removed by passing prepurified nitrogen through the cell and a slow stream of gas is maintained during the entire titration procedure. Before titration of samples, the solution is pretitrated to the potentiometric inflection point by appropriate current increments. Sam-
IO0
Lj
- 100 -
0 v,
80
v)
3
E
-200 -
0
60 v) L
.-
C
20
40
60
80
100
120 Sec
Figure 4. Titration of copper(l1) in p H 5 mercuric thioglycollate system
3 S -
Generating current 10 ma.
0
W
40
reaction permits only two or three samples to be titrated with good accuracy in the same generating solution. RESULTS A N D DISCUSSION
20
0
20
40
Titrations with electrogenerated thioglycollate were quantitative and rapid for mercury, gold, copper, and ferricyanide. The influence of the organic structure has been largely neglected in discussion to this point, but was found limiting in the extension of the thioglycollate generation to other metals
60 Sec.
Figure 3. Titrations of gold(lll) under conditions of Figure 2
ples are then injected into the cell by calibrated syringe pipets (Macalaster Bicknell Co.. Cambridge, Mass.) of 1-ml. or less capacity with precision of delivery to +O,l’%. Cathodic generating current is initiated a t the mercury pool and indicator potentials are read at intervals with generating current off. Equilibrium is reached rapidly (within 1 minute) for all titrations cited. The end point is taken a s the point of maximum potential inflection. Successive samples may be run by determining the current-time product between maximum inflections Tvithout reversing current a t any time. HOWever, if more than a fern minutes elapse b e t w e n sample additions. i t is best to pretitrate to the potential of maximum inflection to avoid the slight positive error that will result if any of the excess sulfhydryl is air-oxidized. If the end point is overshot, the current may be reversed and the excess sulfhydryl back-titrated. All titration data were plotted manually and recording of curves was not investigated. I n the amperometric end point procedure, generating current is applied and the indicator current measured until the initial current miilimum is well defined. Sample is then added and generation continued, the time between extrapolated current, minima being taken for coulomb calculation. Potentiometry is preferable for general use because of convenience but the amperometric end point offers higher sensitivity for low levels. I n the titration of mercury(II), gold (III),and ferricyanide, many successive samples may be run in the same solution. For copper(I1) the nature of the
Table
II.
Current, Ma. 10.66
Determination of Copper in Mercuric Thioglycollate System
Time, See.
118.5 10.66 117.2 5.058 236.5 5.059 236.0 10.66 237.3 ilv. for 0.780 mg. taken
Taken, hfg. Titrations 0.780 0.780 0,780 0 . 780 1.561
Found, Mg. 0.787 0.777 0.787 0 . 785 1.577 0,7835 mg.
Error, Mg. +0.007 -0.003 + O . 007 + O . 005 0,016
+
Determination of Copper in Alloys NBS KO.52 Brass Sample, Hach Ver Yo. 71, % Cast Bronze, 70 Cu 88.33 Cu 73.33 Sn 5.74 Sn 7.90 Zn 1.89 Pb 6.78 Pb 1.52 Zn 13.60 Xi 0.46 Sb 0.16 Ni 0.13 Fe 0.22 Fe 0.12 Total 1o0.05 100.13 Copper
Copper, Mg. Copper, Mg. Taken Found Taken Found 1 2.799 2.764 2.259 2,264 2 2.770 2.280 3 2.779 2.264 4 2.789 2.278 5 2.786 6 2.784 7 2.796 8 2.796 Av . 2.783 (87.83%) 2.271 (73.7270) Std. dev. 0.4% 0.4% Error -0,5770 0.55% With KBS 52 Nos. 1-6 represent nitric acid-dissolved samples titrated a t pH 7.5 (1to 4) and pH 5 (5 and 6). Samples 7 and 8 were dissolved in aqua regia and titrated a t pH 6. Brass samples were aliquots of an aqua regia solution and were titrated at pH 5.5. All end points vere determined potentiometrically. 1-0.
VOL. 32, NO. 4, APRIL 1960
527
Table 111.
Current, Ma. 2 , ’721 2.720 2,720
Titrations of Ferricyanide (Potentiometric End Point)
5.516 5.516
Time, See. 175.7 176.5 176.9 86.5 86.9 86.7
5.101 5.101 5.101 5,101 5.101
184.1 183.9 183.8 184.0 184.2
0.5457 0.5457 0.5457 0.5457 0,5457
5.103 5.103 5.103 5.104 13 59 13 73 13 74 13 76
367.3 369.4 366.7 366.5 138 0 136 5 136 8 136 3
1,088 1,088 1.088
5.518
Taken, 0.2762 0.2762 0.2762 0.2762 0.2762 0.2762
1.OS8 1 OS8 1 088 1 088 1 088
of strong affinity for sulfhydryl. With platinum(II), platinum(IV), and silver, the apparent end points are premature, the curves poorly defined, and the reactions slow. For these metals secondary reactions with the carboxyl apparently alter the assumed stoichiometry because of the competing complexes which result. A similar difficulty arises for o-mercaptobenzoic acid, which works well for the elements for which thioglycollic acid is quantitative. Another reagent, monothioethylene glycol (2mercaptoethanol) was of nider applicability; its application will be reported in another communication (6). The titration curves of mercury(I1) and gold(lI1) with potentiometric and amperometric indication are shall n in Figures 2 and 3. The behavior of gold is very similar in all respects to that of mercury. Typical results for these metals are given in Table I. Accuracy to =t0.5% is obtained a t the milligram level. Although the potentiometric curve for gold shows a single break a t three sulfhydryl radicals per gold atom, other evidence (6) indicates that the reaction occurs in two steps,
+ +
Au(II1) 2RS--t .4u(I) and Au(1) RS- -t AuSR
+ RSSR
The anodic range of the electrode does not permit potentiometric separation of these reactions. The possibility of some direct reduction of gold(II1) t o the metal causes no error, because the same number of electrons are involved. Copper alone among the remaining common acid hydrogen sulfide group elements titrates by this method. The reaction under titration conditions is stoichiometrically 1 to 1, indicating 528
e
Found,
Rlg., as Fe
ANALYTICAL CHEMISTRY
Error, Mg. 0.2767 +o. 0015 +O. 0017 0.2779 0.2785 +0.0023 0.2762 0 0.2774 0.0012 0.2768 +0.0006 Av. 0.2772 +o. 4% Std. dev. 0.3% 0.5435 -0.0022 0.5429 - 0.0028 0.5427 - 0.0030 0,5433 -0,0024 0.5438 - 0,0019 A V . 0.5433 Std. dev. Mg., as Fe
+
1.085 1.091 1.083 1.083 1.085 1.085 1,088 1.OS6 Av. 1.086 Std. dev.
Cu(I1)
+ 2RSH
-t
-0.003 + O . 003 -0.005 -0.005 -0.003 -0.003 0 -0.002
-0.27~ 0.2570
2Cu(I)
+ RSSR + 2H+
titration of ferricyanide ion. The results summarized in Table I11 show the reaction to be both rapid and quantitative a t pH 7.5. The potentiometric curves in this system are essentially those for the mercury titration after the first fraction of ferricyanide is titrated, as the anodic limiting factors are the same. According to the 50% titration points, -50 mv. z’s. S.C.E., any couple having a formal potential valueno more positive than this could be titrated a t pH 7 . 5 if the reaction involved n’ere sufficiently rapid. Another 120 mv. of reducing power can be obtained byoperation a t p H 9.5. I n the determination of very pon erful oxidizing agents, errors can arise from the nonstoichiometric oxidation of thioglycollate beyond the disulfide stage. This difficulty can be circumvented by having an excess of ferrocyanide present in the titration medium prior to the addition of the sample. The ferrocyanide-mercuric thioglycollate mixture is pretitrated according to the standard procedure, the sample is added, and the resulting ferricyanide equivalent to the oxidant being determined is titrated in the usual way. ACKNOWLEDGMENT
The titration of the copper(1) produced gives only a faint inflection a t p H 7.5 and none at p H 5. The redox break (Figure 4) is relatively smaller than for the mercury and gold curves, and the accuracy obtainable is therefore somewhat less. The accumulation of cuprous ions tends to reduce the size of the break with successive titrations. Values for thioglycollic acid stability constants show K.+f to be about for zinc, cadmium, and lead ( I ) , in agreement with their failure to titrate by this method. An interesting consequence of this behavior is that copper may be determined directly in brass and bronze alloys without any prior separations. Direct solution of the sample in a minimal amount of aqua regia and dilution to volume with 131 ammonium acetate give a neutral solution from 11hich tin hydrolyzes only s l o ly, ~ making available a homogeneous aliquot for immediate titration. Samples taken from a well-shaken stannic oxide suspension produced by the standard nitric acid solution procedure may also be used directly. Tests of the method n-ith NBS No. 52 cast bronze and a commercially analyzed brass are summarized in Table 11. Although not capable of the higher accuracy attained by controlled potential coulogravimetric techniques, the sulfhydryl method is a rapid and simple method for the determination of copper in these alloys. The application of sulfhydryl generation to the determination of a n oxidizing agent is illustrated by the
The authors are grateful to the Sational Science Foundation and to 1Ierck and Co., Inc., for fellowships in 1956-7 and 1957-8. respectively, for Barry 1Iiller. LITERATURE CITED
(1) Bjerrum, J., Schwarzenbach, G., SillBn, L. G., “Stability Constants,” Part I, p. 8, Chemical Society, London, 19.57 -”-. .
(2) Kolthoff, I. XI., Barnum, C., J . Am. Chem. Soc. 63, 3061 (1940). ( 3 ) Kolthoff, I. ?*I., Lingane, J. J., “Polarography,” 2nd ed., p. 781, Interscience, New York, 1952. (4) Leussing, D. L., Kolthoff, I. M., J . Electrochem. SOC.100, 334 (1953). (5) Lingane, J. J., “Electroanalytical Chemistry,” 2nd ed., Chap. XX, Interscience, Sew York, 1958. (6) Miller, B., Hume, D. S . , A x . 4 ~ . CHEY.,in preparation. (7) Przybylowicz, E. P., Ph.D. thesis, Massachusetts Institute of Technology, 1956. (8) Przybylowicz, E. P., Rogers, L. B., Anal. Chim.Acta 18, 596 (1958). (9) Reilley, C. PIT., Cooke, W.D., Furman, x. H., .4N.4L. CHEM.23, 1030 (1951). (10) Reillev. C. K.. Porterfield. W. IT.* Zbid., 28,“443 (1956). 1) Reilley, C. S . , Schmid, R. W., Ibid., 30,947 (1958). 2) Schwarzenbach, G., “Compleximetric Titrations,” p. 101, hlethuen & Co., London, 1957. (13) Stricks, IT., Kolthoff, I. M., Heyndickx. -1..J . ilm. Chern. SOC.76, 1515 (1954). RECEIVEDfor review October 15, 1959. Bccepted January 7, 1960. Work supported in part by the U. S. Atomic Energy Commission under Contract AT(30-1)905.
