ANALYTICAL CHEMISTRY
1454 through the annular space, the heavier down and the lighter u p the extractor. At suitably chosen speeds of rotation of the rod, the two flowing phases are broken up into vortices. Any material in either of the two phases is now efficiently partitioned in the extractor. The flow of both solvents can be made continuous by leading one solvent, the heavier, in a t the top of the column and out a t the bottom, while the lighter phase flows in a reverse manner. Such extractors have been used mostly for stripping one component out of a large volume of solvent containing a mixture ( 5 ) . Fractionation of a material in this type of extractor can be brought about by cycling one of the phases-e.g., the heavier allowing it t,o pass down t'he extractor under gravity and then raising it by an external air-lift so that it is returned to the top of the extractor and recycled. The lighter phase can be passed up and through the extractor in the normal manner. After extraction has proceeded for some time the light phase can be modified so that new extracting conditions obtain, and another fraction of the mixture is separated. Such an apparatus has been used in this lahoratory in the fractionation of silicone polymers, the method being part.icularly useful for removing the lowest molecular weight polymers from the bulk of a fluid. The solvents which were convenient for this purpose are equilibrated phases from the threecomponent system methanol-carbon tetrachloride-cyclohexane. Methanol and cyclohexane are only partially miscible, the partit#ion coefficient of t,he silicone st,rongly favoring cyclohexane. Carbon t,etrachloride modifies the two phases so that they are made more similar. By dissolving the silicones initially in the heavier phase of the three-component system-that is, the phase which contains most of the cyclohexane and least, of the methanol-placing this phase in the extract,or, and then extracting \\\-it,hthe lighter phase, the extracted polymer was found to have a much loiwr viscosity than that remaining in the extractor. Procedure. A mixture (specific viscosity 0.28) of 3.8 ml. of Dow Corning TO2 and 3.2 ml. of Dow Corning 550 was dissolved
in the heavier phase of the solvent composed of 30 ml. of carbon tetrachloride, 50 nil. of methanol, and 100 ml. of cyclohexane. This gives two liquid layers of almost equal volume. This phase was continuously cycled in the rotary extractor as described and polymer was extracted from it by the flowing of the lighter phase through the extractor. After 100 ml. of the lighter phase had been collected it was analyzed and found to contain 4.1 ml. of polymer having a specific viscosity of 0.19, considerably lower than that of the initial mixture. A further extract of the remaining polymer with 100 ml. of the light phase obtained from equilibrating 50 ml. of carbon tetrachloride, 50 ml. of methanol, and 150 ml. of cyclohexane was shown to contain 0.5 ml. of a polymer having a specific viscosity of 0.26. The residual polymer in the extractor had a specific viscositv of 0.41. Thus, most of thp low molecular weight material had been removed from the mixture. The method is as simple to run as a chromatographic column, all phase separations being carried out automatically. The fractions can be collected on an automatic fraction collector. AS illustrated the mrthod can he used for large quantities of polymer. ACKhOWLEDGMENT
The authors would like to thank Midland Silicones Ltd., 49 Park Lane, London, for the supply of polymers. D. W, Bannister wishes to acknoxyledge his indebtedness to Courtauld's Scientific and Educational Trust for the a v a r d of a research scholarship. LITERATURE CITED
(1) A h , 11.
S.,Williams, R. J. P., and Tiselius, d..Acta Chem.
Scand., 6, 826 (1952). (2) Barry, A. J., J . A p p l . Phys., 17, 1020 (1946). (3) Claesson, S.,A r k i z Kemi, 1, KO.24 (1949). (4) Short, J. F., J . Chern. SOC.,1952, 1278. (5) Spence, R., and Streeton, R. J. W., Analyst, 77, 579 (1952). (6) Williams, R. J. P., Zbid.,77, 905 (1952). RECEIVED for review December 23, 1'253.
Accepted .June 15. 1954.
Maleic and Fumaric Acids Origin of Split Polarographic Waves and Analytical Significance PHILIP J. ELVING'
and
ISADORE ROSENTHALZ
The Pennsylvania State University, State College, f a .
Certain unexplained apparently anomalous effects in the polarographic behavior of maleic and fumaric acids constitute a potential source of error in analysis. These acids have been systematically investigated over the pH range of 0.7 to 12 at different levels of ionic strength and with different buffers. At about pH 5 , the original w-ave of each acid begins to decrease; simultaneously, a second more negative wave appears, whose height increases with pH until it alone remains. The total current for both waves is essentially equal to that for the single wave in the low pH region. Above pH 8, the second maleic acid wave begins to disappear and is practically nonexistent at pH 10. The relation of these wave-splitting phenomena to the kinetics of the acid-anion equilibrium and to the sigmoid relation between pH and Eli2 for each wave is discussed. A possible procedure is indicated for separating pH erects due to bond reduction from those due to acid-anion kinetics. The application of Herasymenko's equation to the data is examined; the indecisiveness of the agreement is discussed. The analytical implications and importance of environmental control in the case of
polarographic wave-splitting are discussed and recommendations are made for the modification and improvement of existing analytical procedures far maleic and fumaric acids.
A
LTHOUGH fumaric and maleic acids have been repeatedly studied polarographically, numerous questions on their electrochemical behavior still remain unanswered. The literature on their polarographic determination has been summarized by Warshowsky, Elving, and Mandel ( 2 1 ) , with the exception of a subsequent paper by Silverman (19). General summaries are given by Kolthoff and Lingane ( I S ) and by Elving and Teitelbaum ( 7 ) . The latter, using conditions similar to those of the present study, investigated the acids and their diethyl esters over the pH range 2 to 10. They ascribe many of the discrepancies between the work of different investigators to the use of noncomparable background solution compositions and to the lack of adequate buffering. They obtained a modified S-shaped curve when E1 2 was plotted against pH and observed an apparently 1 2
Present addiess, University of .\Iichigan. Ann Irbor, ,Mich Present address. Rohni & Haas Co , Philadelphia. Pa
V O L U M E 2 6 , NO. 9, S E P T E M B E R 1 9 5 4 Table I. Coniposition of Buffer Solutions Buffer No. 1 1'
2 2' 3
p H Range 0 0-2 0 0-2 2 2-7 8" 2 2-7 8 h 4 0-5 7 4 0-5 7
Composition 1 0.U KC1 with added HC1 0 1.M KC1 with added HC1 h-azHPOd with added citric acid and KC1
1 , O M NaOAc with added HOAc 0.1-11NaOAc with added HOAc K H ~ P O I KzHPOa (Sorenson's buffer) 4 KH2POa KzHPOh .5 8 2-9 7 1.0.11 XHIC1 with added h'Hs 5' 8 2-9 7 0 . l M NHaCl with added N H I ci 8 2-9 9 0.05.V borax with added HC1 or NaOH, plus KC1 t o bring the ionic strength t o 1.0 7 12 0 0.2.M Pl'adIPOa with added NaOH a Buffer prepared according t o Britton ( 3 ) with KC1 added t o bring ionic strength t o 1.0. b At any one pH. this buffer contains twice the phosphate and citric acid of buffer 2 h u t the same amount of KCI.
3'
I'
5 8-6 5 6 0-6 7 a
++
split maleic acid wave a t t'hree p H values, the most significant being a t about p H 5.9. This splitting, which disappeared as the buffer concentration was increased, was tentatively thought t o be due to background and buffering effects. Rosenthal and Elving ( 1 6 ) found similar phenomena with fumaric acid-Le., its wave was split a t p H 5.9; this was recognized as characteristic of fumaric acid in well buffered solutions, and as not due to background effects. Consequently, a complete re-examination of maleic and fumaric acids was undertaken. After this work was completed, Hanus and Brdicka (9) published a study of these acids; the absence of reference to the work of Elvin,: and Teitelbaum ( 7 ) is undoubedly due to the relatively short time lapse between the papers. On the whole, the conclusions and data of this excellent paper (9) are felt to be essentially correct and to parallel in part the present work, rvhich, however, brings out aspects of the problem not considered by Hanus and Brdicka and also considerably extends their n.ork. The latter did not present their data in a fashion conducive to use by others; they did not give El 2 and f d values, but only the polarographic curves. EXPERIMENTAL
1455 maleic acid t o form the singly ionized anion, which, owing to its charge, diffuses a t a slower rate than the un-ionized acid. This effect, which has been noted with other acids ( 4 , 6, 15, 18), will operate regardless of whether the anion present in solution is reduced directly or through the prior formation of the undissociated acid. The wave is diffusion-controlled in this p H range. The second, much larger, drop is associated with the second ionization of maleic acid. I n the pH region 5.4 to 7.4 a second wave gradually appears as the original wave simultaneously disappears. For the latter, variations of i d (actually zl) with drop time and temperature approach the values for a kineticcontrolled process. With the second wave, hoa ever, the variation of zd with drop time shows definite adsorption characteristics in certain buffers, although the temperature coefficient throughout is that of a diffusion-controlled process. The split into waves is t o be associated with the acid-anion type of equilibrium encountered with pyruvic acid ( 1 , 2, 14). The species thought to be involved are the un-ionized acid and the singly charged anion. On this basis, the disappearance of the wave in the pH region 7 . 1 to 9.9 is attributed t o the equilibrium between the singly and doubly charged anions, with the second wave due to the latter occurring in the potential region beyond the background electrolyte discharge.
I .6
The experimental conditions, procedures, and apparatus have 16). Although various capillaries were used, been described (i, t o simplify comprehension of the data all i d and Z ( i d / C m 2 ' 3 t l ' 6 ) values were exprePsed in terms of a single set of capillary characteristics for each acid. Temperature w t s maintained to 1 0 . 1 O C.; temperature coefficients vxre calrulateti by means of the compound interest formula. 3I:ileic acid was prepared by subliniation of maleic anhydride (Eastman Kodak white label) followed by repeated recrj-stallization from n-ater. Fumaric acid (Eimer and Amend Pure) was recrystallized three times from 1-11hydrochloric acid. Buffer solutions (Tahle I ) were diluted by'107, with the reducible acid stock solution. BEHAVIOR O F MALEIC ACID
In general, the results of Elving and Teit.elbaum ( 7 ) tvere substantiated, except that the more negative of the two waves reported for maleic acid at pH 4.5 is believed to be a hydrogen wave. The effects of background composition a t pH 5.9 were verified-i.e., there are two Ti-aves in 0.1M acetate buffer which gradually merge as the acetate concentration is increased until a t 1 . O X acetate there appears to be only one wave. The effects due t,o ionic st,rength or buffer capacity on the merging of the two waves are negligible compared to those due to the increase in acetate concentrat'ion. The data are summarized in Figure 1. Current Change with pH. I values show a slight drop of 4.5C;; over the pH range 0.i to 5.4,followed by a much larger drop of 14% over pH 5.4 t o 7.1. From p H 7.1 to 9.9, i d decreases almost t o zero. In all these pH ranges there are deviations from the general trend due to specific buffer action-e.g., with acetate buffers. The effect of the latter is attributed t,o interaction of buffer component with the reducible species, since dilution of the buffer or substitution of a phosphate buffer causes i d t o increase. The first over-all drop in i d can be attributed to the ionization of
PH Figure 1. 3laleic 4cid Relations of El,, and I (id/Cmz/it1'6) t o p H a t 25' C. and ionic strength of 1.O.V.
Lines reyresent E l l 2 ; circles and crosses represent I values for first and second waves, respectii-el,
Nature of Current-Controlling Process. The second nave has unusual current characteristics. The temperature coefficient of the current throughout the pH range is that associated a i t h diffusion or kinetic control of the current-producing process. The variation with drop time-Le., with head or height of mercury, h-in some p H regions approaches that postulated for an adsorption-controlled current-producing process. Because the
1456
ANALYTICAL CHEMISTRY
variation with h is not so clearly understood as that with .temperature, it is not necessary t o conclude that absorption is an effective current-controlling process. The variation of current with h seems t o change, as perhaps might be expected if a d s o r p tion were operative, with temperature range and nature of the background solution. The first wave tends toward kinetic control, as indicated by the variations over the pH range of the temperature coefficient of i and drop-time effects. The effect of temperature on E, 2 is also unusual. At p H 0.7 and 2.3 there is no effect; a t pH 6.0 and 7.1 the reduction is more difficult at higher temperatures, while a t p H 8.9 it is slightly easier at higher temperatures.
especially with regard to pyruvic and phenylglyoxylic acids ( I , 2 , 1 4 ) ; the essential details of the equations developed also apply t o dibasic acids. If pK, for the second dissociation of the dibasic acid is close to the pH region where separate waves appear for undissociated acid and its singly charged anion, then the dissociation of the latter to give the doubly charged anion must be taken into account, because the rate of formation of undissociated acid depends on the concentration of the singly charged anions which is diminished by their dissociation. T h e equation developed for dibasic acids (g), relating currents, and recombination rate of the singly charged anion to give the undissociated acid, is
BEHAVIOR OF FUMARIC ACID
The behavior of fumaric acid (Figure 2) is very similar to that of maleic, except that the second wave, which appears a t a lower p H than with maleic, does not apparently diminish until above p H 10. The second wave can be seen most clearly a t p H 5.9 in buffers 3 and 4'. I n buffer 3', it merges B-ith the background discharge, and tends to do likewise in all buffers studied a t other p H values. This explains why Brdicka and Hanus were unable to find the second fumaric wave; they used 0.1M acetate buffers in which this wave is not separated from the background discharge. The drop in current, attributed with maleic acid to the formation of the doubly charged anion as the diffusing species, is not found with fumaric acid t o such a large extent. This may be associated with the difference in dipole moments of the two isomers-i.e., the doubly charged maleate anion would be more highly hydrated because of its larger dipole. The effect of temperature on El/*is similar to that found with maleic in that where two waves appear--i.e., pH 5.4 and 5.7-the reduction appears t o be easier at loner temperatures. The second wave cannot be seen a t 0 " because of interference by the background discharge. The height and temperature coefficients of z for fumaric acid behave like those for maleic, except that in the alkaline region the fumarate wave does not take on kinetic characteristics. I n this region a t 25" with an ionic strength of 1.0, the h coefficient is that expected for an adsorption process. The temperature coefficient a t all ionic strengths is that for diffusion control. If, however, the ionic strength is decreased t o 0.1, the h coefficient drops to a value characteristic of a diffusion-coiltrolled process. With a buffer of ionic strength 1.0, decreasing the temperature to 0 " also causes the height coefficient to tend toward a value characteristic of diffusion control.
nhere D is the diffusion coefficient of the undissociated molecule; h , the drop time at the limiting current; zgos, the limiting current due to reduction of undissociated molecules formed by recombination of anions-Le., the first wave; znen, the limiting current due to the reduction of anions-Le., the second ivave; K 2 )the second dissociation constant of the acid; p , the effective thickness of the reaction layer; and k , the bimolecular rate constant for the recombination reaction of hydrogen ion and singly charged anion. The situation for the second dissociation is similar to that for monobasic acids, except for a correction for the decrease in the diffusion coefficient of the doubly charged anion:
D = Dl([H+l
+ a & ) / ( K + [€IT])(2)
Hanus and Brdicka evaluate 01 from the decrease in i d of the acid a t p H values where only the doubly charged anion exists; it is about 30% for maleic acid. There is assumed to be little prac-
*\ 1.0
-X-
U
-
A B 3
I
l
l
7
5
l
l
9
'
l I
l -1-
DISCUSSION
The general behavior over the p H range of each of the acids is attributable to the operations of (1) the acid-anion equilibria involving a dibasic acid and ( 2 ) the two S-shaped relations between pH and El 2 for the two acid-anion systems of a dibasic acid. There are pH-invariant regions in the E1 *-pH relationship corresponding to the regions a here substantially only undissociated acid, singly charged anion, and doubly charged anion exist with regions of increasing (in a negative sense) E1 z between these plateaus. The magnitude and location of these flats will be determined by the relative K, values, and relative rates of associae tion-dissociation and of electron transfer. The split ~ a v phenomena, as previously indicated, are due to the rates of acidanion interconversion, which are slow enough to permit the waves of both the acid and its corresponding anion to be simultaneously observed polarographically. Hanus and Brdicka (9) explain the character of the split wave and the variation of i d with pH as being due to kinetic factors involving the recombination of the more difficultlyreducibleanions with hydrogen ions to give the undissociated acids or the singly charged anions, which are then reduced. The theory of this type of kinetic-controlled current has been frequently discussed,
I .4 -%2
I
1
0.8
0.6
L
I I
I
I 3
I
I
5
I
I
7
I
I 9
I
I
I
I1
PH
Figure 2.
Fumaric Acid
Relations,of Ell2 and I ( i d / C n 2 / , 3 t l / 6 )t o pH a t 2 5 O C. a n d ionic strength of 1.OM. Lines represent E L I Z ;circles and croases represent I valuesfor first and second waves, respectively
V O L U M E 26, N O . 9, S E P T E M B E R 1 9 5 4 tical difference between the diffusion rates of the acid and the singly charged anion. This assumption does not appear valid in the light of the present data as well as of t h a t of the alphahalo acids ( 4 , 6, 16, 18), where the change from undissociated acid to anion results in a 5 t o 10% reduction in id. By means of Equations 1 and 2 the shape of the curves of i d us. p H is accounted for in a generally satisfactory manner, but Hanus and Brdicka do not consider the nature of Eli2 variation with pH, the analytical implications, the effect of background conditions on apparent wave character, and the nature of temperature effect,s. A further unexplained point is why the recombination rate of the doubly charged fumarate anion with hydrogen ion is so much faster than that of maleate. As the slolvness of this rate is assumed t o cause the disappearance of the second maleic wave and such a process does not start with fumaric until beyond pH 10, the second recombination rate for fumaric acid must be assumed to be several orders of magnitude greater than that of maleic.
1457 Kolthoff and Lingane have summarized (IS). Herasymenko’s development starts with the equation,
(3) where i is the current flowing a t applied potential E , K is essentially a n arbitrary constant (subsequently defined), and [R,] and [H+]are the concentrations of undissociated acid and hydrogen ion a t the electrode surface. T h e significance of Equation 3 and the assumptions inherent in it are best realized by examining the derivation ( I d ) of a similar but more general formula. Taking as the most probable reduction scheme,
+ 2e +R
2Hf 2H
FT*
2H RHZ
(4) (5)
a perfectly mobile equilibrium is assumed t o exist for the first reaction with the potential of the whole system determined by it,
YATURE O F E,/z-pH RELATIONSHIP
Relation between Acid and Ester. The data for the acids are plotted in Figures 1 and 2; qualitat,ively, the same types of curves are obtained. It is profitable to examine Figure 1 in the light of the behavior of the a-halo acidp (4,6, 1.5, 18) and esters ( 1 7 ) . These acids yield S-shaped curves when El)*is plotted against pH; there is initial pH-independence in the pH region where mainly undissociated acid existed, followed by a region of rapidly increasing El,?and then b y another region of pH-independence. T h e initial pH-independent region x a s taken t’o indicate the lack of influence of p H on the act,ual bond fission when secondary pH effects due to acid-anion interconversion were not involved. This was substantiated when the reduction of the esters of these acids was found t o be completely pH-independent (6, 1 7 ) Similar S-shaped relations between El;?and p H have been reported for other types of dissociatable compounds ( 4 , 8). With maleic acid, it may be assumed that the pH-dependence found with the ester ( 6 , 7 ) is due only to pH effects on t’he act’ual bond reduction and t,hat these bond p H effects are the same in the acid. Therefore, to obtain the pH effects due t o acid-anion kinetics the pH effects found with the corresponding ester-Le., Ell2 vs. p H slopes (not, actual El.2 values)-may be subtracted from those found with the acids. The curve thus obtained for maleic acid differs qualitatively from Figwe 1 only in that it is essentially pH-independent below p H 2.8 (values for E112 of diethyl maleate are taken from 6 and 7 ) , because El 2 of diethyl maleate is pH-independent above pH 6 and the slope of its El/*p H plot is equal t o that, for maleic acid in the p H region 0.7 t o 3.0. T h e situation ip similar for diethyl fumarate, escept that instead of a completely pH-independent region above pH 5.0, there is a region with a relatively small pH-dependence-Le., 0.025 volt per p H unit as compared to 0.14 volt a t lower pH. This slight pH-dependence decreases wit’h increasing pH-e.g., 0.015 volt a t pH 8-and may be responsible for the fact that in the region xhere both acid and anion waves exist, both waves appear to have a slight pH-dependence in contradistinction to the analogous maleic acid case. I n considering the effect, of p H on E , 2 of maleic and fumaric acids one can proceed by two alternative paths. T h e p H effects on bond reduction and those due to acid-anion kinetics can be treated separately, or one can attempt to develop an equation t h a t will deal with bot,h a t t,he same time. K i t h the former alternative it might be possible to segregate the complicating problems of p H effects on the bond reduction by the scheme suggested-Le., subtraction of El12-pH slopes. Equations Relating E l ! , to pH. T h e general trend in explaining the effects of p H on E112 for maleic and fumaric acids has been along the lines of Herasymenko (10, 1 1 ) and Vopicka (go), which
where [HI is the active concentration of hydrogen in the nascent state and K is defined as the ratio of the “solution tensions” of the two forms of hydrogen. The kinetics of Reaction 5 give
(7) where K’ is the rate constant in units such that it will directly give i, the current flow a t the electrode. Substituting for [HI2 in Equation 6 gives E = - - lR nT 2F
iK K‘ [R,] [ I I + ] 2
which is similar t o Herasymenko’s starting point. The latter’s main contribution was to assume that only the undissociated acid is reduced a t the electrode and to develop the pH-dependency of that form. I n connection with the latter effect, he assumed the dissociation equilibrium of the acid a t the electrode to be instantaneous. The final equation obtained, which is the one currently used, is
2 RT E = --ln[H-] F
- RT -ln([H+]2+Kl[HL] 2F
+KIK2)+K11 (8)
where K , and K? are the first and second dissociation constants ( R T / 2 F ) In [(id of the acid, and K l 1 is implied to be El 2 i)/i]. Herasymenko (10)calculated El’! values for maleic and fumaric acids up to p H 9, using Vopicka’s (20) experimental Eli2 value of -0.58 volt for the two acid. a t pH 0 or, rather, in I N hydrochloric acid. Significance of Herasymenko’s Equation. Estrapolat,ion of the present aut,hors’ data to p H 0 gives E, 2 values for maleic and fumaric acids of -0.51 and -0.53 volt, respectively. Use of these in Equation 8 gives values close in absolut,e amount to the present experimental results over pH ranges 0 to 5 and 0 t o 4, respectively. Hoivever, this agreement has little significance with respect to clarifying the behavior of the acids and testing t h e assumptions upon which Equat’ion 8 was dwived. For example, Herasymenko’s calculated values predict maleic t’o be more difficultly reducible t’han fumaric in the neighborhood of pH 1.5 t o 5 : use of the present El:: values at pH 0 in Equation 8 still gives a calculated crossover at, pH 4, which would require that maleic be more difficultly reducihle than fumaric. Erperimentally, this is not the case. From pH 0 to 4, the Eli?values of the acids differ by 20 mv., and fumaric is alwnys the more difficultly reducible; as p H increases, the difference is accentuated. Barring steric effects, the cis acid is experted to be more readily reduced than the trans form. Furthermore, over the p H region in which there is agreement between the calculated and experimen-
+
1458
ANALYTICAL CHEMISTRY
tal values, the plot of E L v s , p H gives rise t o essentially straight lines; a3 soon as the evperimental values differ from linearity, the agreement fails. This lack of agreement is ascribed b y Kolthoff and Lingane (13) t o the small concentration of undissociated acid a t higher p H values and t o the possible direct reduction of anions. A4s shown by the present data, the latter is to be associated only with the second wave. The important factor is not the equilibrium concentration of undissociated molecules a t the electrode, but rather the rate a t which equilibrium is attained. The derivation of Equation 8 assumes instantaneous attainment of dissociation equilibrium, which is contradicted by the existence of separate acid-anion waves. Since El/*becomes inore negative as the concentration of R, in Equation 3 decreases, the decrease in rate of equilibrium attainment should result in a sharper increase of Eli$with pH than is called for by the equilibrium concentration. This follows because the greatest value R, can have a t any one p H is the equilibrium value-Le., as fast as any R, is reduced it is replenished; as the rate of formation of R , slows down below that needed t o maintain equilibrium, [R,] will obviously be smaller than the calculated value. Such behavior can then partially explain the fact that in the region just before separate anion and acid waves appear, Herasymenko's equation gives values that are more positive than the experimental ones. It does not explain, however, why El/*does not vary with pH in the region where the two waves coexist. .4 more fundamental consideration is the fact that assumption of the reduction mechanism ( 1 2 ) of Equations 4 and 5 is not a prerequisite for obtaining Equation 3a, from which Herasymenko derived his equation. R e may assume, for example, that maleic acid, R, adds two electrons in a reversible manner t o give R:, which step determines the electrode potential:
R
+2
e ~ 2 R :
(9)
Then R: reacts irreversibly with hydrogen ions a t the electrode surface t o give the final reduction product RHn, with the current being defined by Equation 12: R:
+ 2 H + +RH,
(11)
R : may be assumed to be stabilized by adsorption on the elertrode and loose combination of the free electrons with the mercury. The difficulties here are certainly no greater than those involved in explaining the presence of nascent hydrogen. By proper substitution of Equation 12 in 10, an equation identical to 3a emerges. Thus, the basic issues concerning the mechanism of reduction and the potential-determining step remain unesplained, even if the equation did fit the dat,a, which, except for the trivial case where the data give a straight line, it does not. The purpose of the foregoing critical analysis is not to belittle the value of the equat,ions used to fit t,he data, but to point out that the problem is still practically unsolved. It' is felt that the method of reasoning backward from equations that fit the data to mechanisms consistent with the equations is unfruitful. Attempts should be made t o elucidate the mechanism by independent experiments of such factors as the steric course of the reaction, the effects of solvent and ionic strength, and t,he effect of substituents. Once the mechanism is clarified, it will then be necessary t o introduce the effects of the recombination rate of anion to form undissociated acid instead of using purely equilibrium concentrations as was done by Herasymenko. ANALYTICAL APPLICATIONS
I n the polarographic determination of maleic and fumaric acids, experimental conditions such as pH, ionic strengt,h, temperature,
and buffer nature are of vital importance. Analysis of mixtures of the acids is usually undertaken in 0.7M ammonium chlorideammonia buffer a t p H 8.2, under which conditions Warshowsky, Elving, and Mandel(21) found good separation between the maleic and fumaric waves, and id to be proportional to concentration. On the whole, these conditions still appear to be optimum, but certain factors that ordinarily need not be carefully controlled by the analyst are very important. Very precise pH control must be maintained. While i d for maleic acid varies by 10% as the pH is changed from 6.8 t,o 8.2 ( d l ) , the variation is much greater above pH 8.2; id decreases an average of 5% for each 0.1 increase in pH from 8.3 t o 8.9. p H 8.2 is considered optimum because it is near the probable lower limit of efficient buffering action for the ammonia system. I t is recommended that the final buffer concentration be 0.9JI instead of 0.7M, since the former value gives as good resolution of the two waves and a t the same time greater buffering capacity. The id of the fumaric wave is much less sensitive to pH variation with the buffers and pH ranges discussed; over pH range 8.2 t o 8.9, i d is constant to within 2Y0. The difficulties encountered with an ammonia buffer a t pH 8.9 ( 2 1 ) are believed due to the use of a mercury pool as a reference electrode. Csing a fritted disk-agar-saturated calomel reference electrode, no trouble was found in going out to pH 9.7. This makes it possible to determine small amounts of maleic acid, as the maleate wave decreases sharply with pH while that for fumarate changes very much less. I n fact, the maleate wave disappears a t p H 10 (borate buffer). However, with a borate buffer the fumarate wave is not so clearly defined as with an ammonia buffer. The latter buffer is consequently preferred, even though the maleate wave is still present to some extent a t pH 9.7. Khen it is desired to determine only one of the two acids, the pH restrict,ion needed for separation 110 longer holds. Care must be taken, however, not to use a pH range where the wave is split; this can be determined from esamination of Figures 1 and 2. Temperature must be carefully controlled, as the maleate wave begins to have kinetic characteristics a t pH 8.2: its temperature coefficient is 8% a t pH 8.9. The head of mercury a t which thr calibration is made must be maintained, since the variation of i d with h is different for both acids and in neit'her case can it h e predicted esactly, although, Lvith fumaric acid under the conditions used, i d seems to vary directly with h in the pH region 8.2 to 8.9. .It pH 8.2, i d is relatively insensitive to ionic strength changes where the ions are of a noncomplexing nature-i.e., 570 change in i d as the ionic strength changes from 0.1 to 0.9. At lower pH values-e.g., acetate system a t pH 4 to 5-id changes about 30y0 as the ionic strength changes from 0.1 to 0.9. Therefore, in determining either acid in such huffers, ionic strength must he carefully adjusted. ACKNOW LEDG.\IE\T
The authors wish to thank the .Itomic Energy Commission for support of the work described. LITERATURE CITED
Brdicka, R.. CoUrciiorz C z r c h o d o c . C'hem. C'ommuns., 12, 212 (1947). Brdicka, R., and Wiesner, K., IRid.. 12, 138 (1947). Britton, H. T. S., "Hydrogen Ionq," London, Chapman B- Hall, 1942. Elving, P. J.. Rosenthal, I., and Kramer, 31. K., J . A m . Chon. Soc., 73, 1717 (1551). Elving, P. J., Rosenthal, I.. and ZIartin, d.J., work in pr0gre.s. Elring, P. J., and T a n g . C . 8.. J . A n i . C h e m Soc., 74, 6109 (1952). Elvine;, P. J., and Teitelbaum, C., Ibid.. 71, 3516 (1949). Gergely, E., and Iredale, T., J . C h e m . Soc., 1951, 3502. Hanus, V., and Brdicka, R., ('hem. L i s t y , 44, 291 (1950). Herasyrnenko. P.. Collection Czechoslo?. C h e m . C'ommuns.. 9, 104 (1987).
V O L U M E 2 6 , NO. 9, S E P T E M B E R 1 9 5 4 Herasymenko, P., 2. Elektrochem., 34, 7 4 ( 1 9 2 8 ) . (12) Heyrovsk9, J., and IlkoriC, D., Collection Czechosloz. C hem.
(11)
(1.3) (14) (15)
(16)
Communs., 7, 198 (1935). Kolthoff, I. 11..and Lingane, J . J., "Polarography," pp. 374378, Kew T o r k , Interscience Publishers, 1941. Koutecky, J., and Rrdicka, R., Collection Czechosloa. Chem. Commztns.. 12. 337 (19471. Itosenthal, I., Albripht, C. H., and Elving, P. J., J . Electrochem. Soc., 99, 227 (1952). liosenthal, I., and Elving, P. J., J . A m . Chem. Soc., 73, 1880 (1951).
(17) Iloaenthal, I., Tang. C. S., and Elving, P. J., Ibid., 74, 6112 (1852).
1459 (18) Saito, E., Bull. soc. c h i m . Fiance, 1948, 4 0 4 . (19) Silverman, I.., Chemist-Analyst, 36, 5 7 ( 1 9 4 7 ) . (20) Vopicka, E.. Collection Czechoslov. Chem. Communs., 8 , 349 (1936). (21)
Warqhowsky, R.. Elving, P. J., and JZandel, J., A s ~ L CHEM., . 19, 161 ( 1 9 4 7 ) .
R E C E I V Efor D review July 22, 1962. Accepted June 26. 1954. Detailed tables of data covering the polarographic behavior of nialcic and fumaric ai,idr are available from the senior author. Abstracted from a thesis submitted by Isndore Rosenthal as part of the requirement for the P h . D . degree, The Pennsylvania State University, 1931.
Polarographic Determination of Zinc in Gold SAMUEL B. DEAL Tube Division, Radio Corp. o f America, Lancaster, P a .
The purpose of this investigation was the development of a method for the quantitative analysis of small amounts of zinc in gold. No spectrographic standards were available, and the solution technique of spectrographic analysis resulted in inconsistent results. Colorimetric methods available were nonspecific and too time-consuming. By the use of the polarographic technique, accurate results in the range of 0.001 to 1% zinc were obtained. This method of analysis can be used for the quantitative determination of zinc in gold as a routine procedure. 4 minimum of reagents and equipment is required. The niethod is simple and easil? carried out.
T
HIS paper describes the use of the polarographic method of analysis for the determination of small concentrations of zinc, ranging from 0,001 to 1%, in a zinc-gold alloy. I n this analysis, the first step is the separation of gold from the alloy by precipitation Tq-ith an aqueous solution of sulfur dioxide. IVhen the gold has been removed, the polarographic method can he used to determine the zinc concentration with a high degree of accuracy. TIlEORETIC4 L COKSIDERATIONS
Gold-Zinc Alloy. I n t8heanalysis of a gold-zinc alloy. preliminary separation of gold is necessary because t'he high diffusiqn current of gold would mask the diffusion current of the zinc. One of the simplest and most complete methods (8)for this preliminary separation is the precipitation of gold wit,h an aqueous s jlution of sulfur dioxide. This method of prec-ipitatim results in t,he complete removal of gold and eliminat,rs the necessity for a reyrecipitatim. EXPERIMENTAL PROCEDURE
Reagents. Four molar ammonium hydroxide plus 131 animonium chloride solution ( I ) containing 5 ml. per liter of a solution of methyl red and bromocresol green. Methyl red-bromocresol green solution composed of three parts of a 0.2% alcoholic solution of methyl red and two parts of a 0.2% alcoholic solution of bromocresol green. Saturated aqueous sulfur dioxide solution. Removal of Gold. A 1-gram sample of a gold-zinc alloy n-as dissolved in a freshly prepared mixture of 5 ml. of concentrated nitric acid and 15 ml. of concentrated hydrochloric acid. The sample was heated in the acid mixture on t,he hot plate until solution was complete; then i t \\-as evaporated to a low volume. The residue was transferred to the steam bath and evaporated to dryness. The resulting salts were dissolved in wirm water and diluted to approximately 60 ml. One milliliter of concentrated hydrochloric acid \vas stirred
into thc solution and 25 nil. of a saturated aqueous solution of sulfur dioxide were then added. The solution was stirred well, and left on the steam bath for approximately 1 hour to allow precipitation of gold. After 1 hour, additional 10 ml. of sulfur dioside were added, and the solution was left on the steam bath for 5 minutes longer. Y)
t
3 6C > 4 a
E 50 m
f 40 z
iI
5 30 8
F 20 w J
Figure 1. Current-Voltage Relationship of Sample Solution Prepared from Gold-Zinc Alloy
The solution and precipitate of metallic gold were transferrcd to a 100-mI. volumetric flask and diluted to the mark xvith distilled water. After thorough mixing, the gold was allowed t o Fettle. -150-ml. aliquot of the supernatant solution was transferred to a second 100-ml. volumetric flask. This aliquot in the second 100-ml. volumetric flask was diluted to the mark with 4.U ammonium hydroxide-ammonium chloride base solution rontaining methyl red-bromocresol green as maximum suppressor. Sample solution and base solution were thoroughly mixed and a portion was withdrawn for analysis. Analysis of the Sample. I n the analyeip, a capillary tuhe, having a bore of 0.05 mm., was used for the mercury-dropping electrode. Sitrogen was used for the removal of oxygen from the solution to be analyzed, and was also passed over the surface of the solution during analysis to prevent the entrance of oxygen. Galvanonirter readings were taken a t 0.05-volt intervals over a range from 0.90 to 1.66 volts. Potential values were not corrected to standard potentials. The sensitivity control of the Fisher electrodropode used in ohtaining polarographic measuremrnts ir-as set a t 2X during the entire series of analyseP. The current-voltage curve obtained by plotting the experimental values determined for the sample solution is given in Figure 1. Preparation of Calibration Curve. Three standard solutions containing 0.5, 1.0, and 1.5 mg. of zinc, respectively, were analyzed polarographically to obtain data for the preparation of a calibration curve. The current-voltage curves obtained for the three solutions are showii in Figure 2 . T h e residual current of a solution blank, containing all components with the exception of zinc, was used as a base line for graphical measurement of diffusion currents.
