EDWARD R. I)IW~K AN EDSEDWARD I,. KIXG [ C O N T R I R U T I O S FROM THE I~EPARTErlENTO F CHE>fISTRS, ~ . S I V E R S I T YO F \vISCONSIS
!
Moving Boundaries Formed by Strong Electrolyte Systems BY EDKARD B. DISMUKES AND EDWARD L. KING T< ECEIl'ED A I A R c r I 21,
l%:\
K\AI
67 1 1 1 ' 1 i l ' i l i '
to the relative mobility of the absent ion. JVheii the proper assignment of 1-u products to the phases has been made, the compositions of the intermediate phases can be d e t e r m h d . The manner in which this is done is described in a later paragraph. The predictions of the Dole theory have been tested experimentally by Longsworth.* However, studies of certain additional types of systems which have not been reported would appear to be of interest. X system (a) should form the moving boundary system (b) during electrolysis, if the mobilities have the relative magnitudes rAl1 > Y B j ~
>1rlc3 (a) A, C, R ( h ) A, C, R
(CY) (CY)
A, B,K ( 6 ) C, R ( p ) + A, B.R ( r i --+A , B, R ( 6 )
:: A ,
A total of four ion species permits the two moving boundaries, and the proper assignment of the T'cr products leads to the formulation above. I t is particularly important to observe that the fastest moving boundary is not the type which is useful for mobility measurements for the reason that no ion disappears across the boundary. I n a similar manner if 'YRI > / Y S /> p$, system (c) must develop into system (d). (c)
((1)
.4, R,S (a) - ,4,R, T ( 6 ) A , R, S ( e )t A , R.S (0)fA, R,T (*/) :: A , R, T ( 6 )
The fastest anion, I rKa > limits in mind, certain facts of practical interest may be deduced. I t would obviously be a happy circumstance to r ~ and i l r c l l > / r B r O a / > / r I O a i ; that is t o say, according to the nomenclature previouly used, A = K , B = Na, C = have the moving boundaries resolve rapidly and move a t the Li, R = C1, S = BrO, and T = 1 0 9 . Using the Dole theory same time as sharp boundaries. Another way of stating it is possible t o calculate the values of the quantities V Y ~ these conditions would be that Vra/VP?, U ~ / U Tand U Y / U P and VOr for system (e) and the values of VaP and VOY for are all considerably larger than unity; the conductance system ( f ) . The limiting ionic conductance values a t 0" ratios determine the boundary sharpening characteristics. listed by Lange: have been used to obtain values for the Of these ratios, u r / d is equal to a constant, r x J r ~ i , but relative mobilities, which are T K = 0.973, r K a = 0.621, V-41 VPY and U ~ / U Yare determined by the concentrations r ~ i= 0.467, = -0.18j, rBrOa = -0.741 and rc1 = of the two initial solutions. However, the limits which are -1.000. Y that imposed upon the products V r W and V Y ~ mean The values of boundary displacements have been calcuV Y ~VPr / and ~ / U Ycannot have maximum values indelated from theory, and they have been measured experi- pendently. If d / u Y is greater than unity, it may be seen mentally. The results for systems of the type (e) are listed that rNs = V b Y U Y < v Y 6 u Y < V Y 6 U 6 < 7 K . If VYs/V6Y in Table I and those for systems of the type ( f ) in Table 11. approaches an upper limit of rK/rpia, u6/uY must be diI t is necessary to point out that KC1 is omitted from the minished toward unity, its smallest favorable value. On CY solution of experiment 3 and from the 6 solution of experithe other hand, if ~ / U Yapproaches a maximum value of r K / r N a , V Y ~ / V P must Y be reduced toward unity, its miniTABLE I mum value. In a similar fashion for the chloride-bromateiodate system the least sharp a p boundary is to be expected Experiment 1 9 3 when the velocities of the boundaries have their greatest a CKCl 0,0407 0 0152 0 0198 difference; conversely, the sharpest a fi boundary should 6 occur when the rate of resolution of the boundaries is lowest. ,0149 .02T .0185 CNsCl Photographs of the moving boundary patterns of experia ,00092 ,00092 0 CKCI ments 1, 2, 4 and 5 exhibit the predicted effects regarding a sharpness. ,00964 ,00964 ,00964 CLiCl Discussion 8.77 12.23 VYs theory 14.09 8.75 12.23 exptl. 14.18 Gravitational Stability ; Concentration Changes 7.75 9.12 theory 11.31 across Moving Boundaries.--Gravitational stabil7.65 9.01 ity a t phase boundaries is a matter of practical exptl. 11.19 V y 6 / v @ Y theory 1.131 1.341 1.246 interest which the theory does not treat. In order 1.304 1,100 1.257 to run experiments successfully, i t is obviously u6/uy ment 6. This means that the electrolyte contributing the fastest ion of the charge type which produces the moving boundaries is absent from one of the initial solutions, and in each experiment both moving boundaries are of the type across which ions disappear. The moving boundary patterns in these two special cases are illustrated in the following manner (3) Li, C1 ( a ) : : Li, C1 ( 6 ) + Na, C1 ( y ) -+ K, Na, C1 (6) + (6) K, C1, BrO3 ( a ) t- K, BrOs K, IO3 (7) : : R , IO3 (6) -
(a)
(4) To b e described i n a forthcoming publication b y N. E. B o n n H. I>.M a r v i n and R. A. Alberty. ( 5 ) J , Lange, Z. physik C h r r r i . , A l 8 8 , 2 8 1 11941).
important that convection from unfavorable density gradients should not disturb the boundaries. If one wishes to investigate a certain type of system, the choice of ion components depends not only upon relative mobilities which would produce the desired type of pattern during the passage of current but upon relative contributions to solution density which would permit a gravitationally stable system. For example, some other ion with the same mobility as BrOa- could not be used successfully in place of BrOs- if i t gave a contribution to density so much smaller than that of BrOathat the P solution of (f) should become less dense t h a n the a solution.
4' 00
EDWA4RD D.
DISMUKES AND EDWARD L. KISG
The equation which defines the apparent molal ~ ~ o l u mofe a solute may be rearranged to the form ld = ~-(.lIs- do&,) ' 1000, where 4~ is the apparent tiiolal volume of the solute, -112 is the molecular weight of the solute, L is the concentration of the solute in moles per liter, (1'0 is the density of pure scllvent, and A d is the increment in density of the s Jlution over that of the pure solvent. For water the solvent, the equation becomes A d = ( -- +y) ' 1000 as an a1)I)rOxirnatioii. Furthermore, for a dilute S C h t l ~ J I lwhich contains more than one solute, the d ~ ~ ] ~ r o ~ i ~Ad ~ i= ~ ~Tc, t i jo1i1, i'i,i i
1000 is assumed to be valid. This equation is useful in predicting the densities of the various phases in a moving boundary experiment. The authors found i t more convenient to estimate in advance by this calculation rather than by the tediousness of t r i J and error experimentation whether or not a certain system would have the required density cliaracteristics. The concentrations of the intermediate phases, which are necessary in making the ca1cuLitions of the densities, mere calculated using equation 38 of the paper by Dole l
TTOI.
$1
mobility opposite in sign to t h a t of V , ca/cb is greater than unity, and it approaches the value of u a / d as the mobility becomes infinitely large in absolute value. This last statement means that tlic total concentration of ions in equivalents per unit volume is always greater ahead of a moving boundary than behind it. I n this sense, the likelihood of having stable density gradients in ascending boundary patterns is unfavorably prejudiced. Of course, the ultimate prediction about the density of a given phase depends not only upon concentrations but upon the particular density increments. Iriasniuch as the y 6 boundary in (e) is a moving boundary across which no ion disappears, it is interesting to see how the concentrations change in crossing it. The compositions of all the phases for experiment 1 (an experiment of type (e)) are given i r i 'I'ablc 111. Since YK is larger than I'isu6 and I - ? ? U T ,it iiiust follow that c&/c& > 1. On the other h m d , r\% is less than V 6 u 8 and T'"&T, and it follows that < 1. For the chloride-bromateiodate system, chloride is more concentrated in the a solution than in the 3!, solution but, converselv, bromate is less concentrated. TABLE 111 PHASECOMPOSITIONS FOR MOVINGBOUNDARY SYSTEMIT EIPERIME\T1, WHICHAREPROVIDED BY THE DOLETHEORY I'iictbe
Q
iu
J.lrPuQ = 0
Ch(I
0 00092
C\~CI
(J
,00964
LI I C i
-4
-2
0
0
i
4
7.
Fig. 1.-The value of ca/cb for an ion of relative mobility r a function of relative mobility. (L~' and cb are the ion concentrations ahead of and behind the moving boundary.) The graph has been constructed for the case in which c"/cb = 1.25. The dashed horizontal line is at ?/ch = 1.23. The dashed vertical lines are at I = 1.00 and 123. ds
Figure 1 illustrates the manner in which the ratios of ion concentrations across moving boundaries depend upon the ion mobilities. The superscripts a and b denote phases ahead of and behind :t moving boundary, respectively. -4lthough the figure has been constructed for a particular case in which ua/ub = 1.25, the general features of the figures are the same for all cases in which ua/ub > 1, which is a necessary condition in order that a moving boundary is not rapidly destroyed by diffusion. It is seen that ca/cb is greater than unity for each ion having a mobility greater than V u a and that calcb is less than unity for each ion of the same sign as I/ having a mobility less than Vub. In the system, there can be no ion with a mobility lying between I'ua and b-ub, but if r = Vua the corresponding ion is absent behind the boundary, and if r = l'ub the corresponding ion is absent ahead o€ t h r houndarv. For w c h m r l every io11 haviiig 'i
? Y 6 VQ&P = 0 VP't'r't' = 0 621 VY6u6 = 0 916 VfiTu? = 0 467 VY6uY = 0 702
0 00346 0 .I2364
0.00661 ,0415
0
0.0407 ,0149 0
General Conclusions.-Fast moving boundaries of the type which has been described impose limitations on certain types of mobility measurements. Suppose that 111+?~is a metal ion which possesses acidic properties so that the presence of an appreciable concentration of hydrogen ion is needed to repress the formation of hydrolyzed species such as X(OH) tn--l.A mobility measurement of M+?z must then be carried out by forming an initial boundary in the following way H, A, X (a)- €1, M, X ( 6 )
Here HX is a strong acid, and A + is a slower cation than &I+". Due to the very high mobility of H', the passage of current must produce the type of a system
r-T, A, s
: : I T , A,
x(PI + €1, M,
s (y) ----f
I%,n1, s ( E )
The mobility of M f " is given by the equation WM = where v a y is the volume swept out by the Py boundary in ml. per coulomb and K is the specific conductance of the y solution. The difficulty here is that a conductance value for a solution not initially present is required. A sampling operation is thus necessary in order that the mobility of +" can be determined. llobility measurements on certain easily hydrolyzed anions would be complicated in a similar nianncr. For example, PO4' exists only in the prcwrici~o f high concentrations of hydroxide ion. t
l
h
~
,
ELECTROREDUCTION OF CXYGEN AND HYDROGEN PEROXIDE
Oct. 5 , 1952
4801
associated with the faster boundary. However, it is perfectly reasonable that a system may be set up initially with compositions so that both of the roots associated with the faster moving boundary have the same value. In this highly specialized case the concentration ratio ca/cb is equal to unity for every species present in a phase adjacent to the particular boundary. This can only mean that the boundary is not a real one and that the number of moving boundaries for the system is diminished by one. However, it is not felt that any practical use can be made of this fact as a means of avoiding the difficulties which have been sugP,,-=n, C1- ( C Y ) - HA, Na+, A-, C1- (7) gested. This is due to the fact that the lack of constancy of relative mobilities, even if accurate The uncharged weak acid type buffer is represented mobility data: for some particular concentration by HA, NaA, and the various negatively charged were available, would prevent a rigorous applicaprotein species are represented by PI-x1,P Z - ~. ~ . ., tion of the theory in order to determine the comPn-x*. If, as might be expected, chloride is the positions of end phases which would allow the fastest of these negatively charged species, there vanishing of the moving boundary across which no should be a moving boundary ahead of any boun- ion disappears. dary across which a protein constituent disapAcknowledgment.-The authors wish to express pears. However, this boundary may be so small that the optical system will not detect it. It their appreciation t o Professors J. W. Williams and might, nevertheless, change appreciably the con- R. A. Alberty for the use of the equipment which ductance upon which the protein mobility depends. was employed. One of us (E. B. D.) expresses The basis for all of the foregoing discussion has appreciation to the du Pont Company for a been the assumption that the Dole polynomials grant-in-aid. provide two unequal values for the Vu products MADISON,WISCONSIN
The high mobility of hydroxide ion would automatically lead to one of these fast moving boundaries in any suitably designed experiment to determine the mobility of POa’. I n addition to causing complications with strong electrolyte systems, moving boundaries across which no ion disappears may also complicate weak electrolyte and colloidal electrolyte systems. Consider the electrophoresis of a protein solution which has been dialyzed against a buffer containing an additional salt. I n a particular case, the initial boundary system may be described as HA, Na+, A-, P1-=2, P Z - ~ Z . ., ,
[CONTRIBUTION FROM
THE
SCHOOL OF CHEMISTRY OF
THE
UNIVERSITY OF MINNESOTA]
Oxygen Induced Electroreduction of Hydrogen Peroxide and Reduction of Oxygen at the Rotated Gold Wire Electrode BY
I. M. KOLTHOFF AND JOSEPH
JORDAN’
RECEIVED APRIL24, 1952 The electroreduction of oxygen was studied voltammetrically a t a rotated gold wire electrode in media of pH 4-13. Proportionality between diffusion current and concentration was found in an acetate buffer of PH 4, a phosphate buffer of pH 7 and in 0.1 M sodium hydroxide. The hydrogen overvoltage a t the rotated gold electrode was determined in various supporting electrolytes and was found t o be about 0.4 volt while the overvoltage at the rotated platinum electrode is negligible. Gold wire electrodes are more suitable than platinum for the amperometric determination of oxygen. Hydrogen peroxide greatly increases the limiting current of oxygen at the rotated platinum and gold electrodes. The electroreduction of oxygen induces the electroreduction of hydrogen peroxide a t potentials a t which the peroxide is not normally reduced. The exaltation of the oxygen wave by hydrogen peroxide and the induced electroreduction of the peroxide are accounted for by the sequence of reactions: 02 e02-; 01H~OZ.+OH02 OH’ ; OH’ e- -+OH-. Use of the exaltation can be made in the determination of very small concentrations of oxygen.
+
-+
+
+ +
+
I n a preliminary communication2i t was reported that the electroreduction of oxygen induces the reduction of hydrogen peroxide a t rotated and stationary platinum electrodes. The exaltation of the oxygen wave by hydrogen peroxide was described and a reaction mechanism was postulated, involving primarily a two-step reduction of O2 to 02--, with the intermediate formation of 02(anion of HOz). A chain reaction between 02(or HOz) and hydrogen peroxide, according to the Haber and Weiss mechanism3 accounts for the exaltation of the oxygen wave. I n the present paper are presented and discussed the results of a detailed study of the electroreduc-
tion of oxygen a t the rotated platinum and gold wire microelectrodes. The rotated gold wire electrode was found to be more suitable than platinum for the determination of oxygeii in the pH range between 4 and 13. The exaltation of the oxygen wave by hydrogen peroxide has been investigated as a function of pH, concentration of hydrogen peroxide and of oxygen, and temperature. With our gold electrode the exalted limiting current in loF3M hydrogen peroxide solution was found to be proportional to oxygen concentration in the loF7 to 10” M range. Analytical application of the exaltation to the determination of traces of oxygen is described.
(1) On leave from t h e Hebrew University, Jerusalem, Israel. (2) I. M. Kolthoff and J. Jordan, THISJOURNAL, 1 4 , 570 (1952). (3) F. H a b e r a n d J. Weiss, Naturwisscnchaflen, 10, 948 (1932); Proc. R o y . SOC.(London). 8147, 332 (1934).
Materials.-C.P. chemicals, and conductivity water (redistilled in an all-Pyrex still) were used throughout, Dilute
Experimental
