Che mica I St rip ping An a I ysis Determination of Cerium(lV), Permanganate, and Iron(lll) in the Micromolar Concentration Range STANLEY BRUCKENSTEIN and JOHN W. BIXLER’ School o f Chemistry, University of Minnesota, Minneapolis, Minn. Oxidants such as Ce(lV) and MnOc in 1 N H2S01, or Fe(lll) in 1M HCI, will oxidize silver from a rotating platinum electrode. By depositing known amounts of silver upon the electrode and determining the time variation of potential of the electrode, the time required to oxidize the silver can b e determined. This time is inversely proportional to the concentration of oxidant in solution. The lower limits of applicability were Ce(lV) 10-6M, Mn04- 5 X 107M,and Fe+3 2 X 10-6M. The oxidation of silver metal by these oxidants was found to be mass transfer-controlled.
T
paper reports the development of an analytical method suitable for the quantitative analysis of dilute solutions of oxidizing agents. Few convenient electrochemical methods of analysis are applicable to very dilute solutions of oxidants. The coulometric titration of submicrogram quantities of manganese (as permanganate) has been reported (3). Also, coulostatic analysis (4) has been successfully applied to certain systems. When conventional voltammetry is used, the residual current of the supporting electrolyte is an appreciable portion of the total current when the concentration of the species being studied is of the order of 10-5M or lower. Chemical stripping analysis is partially based upon the principles of anodic stripping analysis. The plating and anodic stripping of silver have been described ( I ) . If a rotating platinum electrode (RPE), plated with a known amount of silver, is rotated in a dilute solution of an oxidizing agent, the following reaction will take place: HIS
n Ag
+ Ox $ n Ag+ + Red
(1)
where Ox is the oxidant, Red is the reduced form of the oxidant, and n is the number of electrons involved in the reduction of the oxidant. The rate of 1 Present address, Department of Chemistry, Lake Forest College, Lake Forest, Ill.
786
o
ANALYTICAL CHEMISTRY
Reaction 1 is proportional to the oxidant concentration in the bulk of the solution, if the heterogeneous chemical reaction is rapid compared to mass transfer. Chemical stripping analysis is a direct method for determining the concentration of an oxidant, since the time required to remove a given amount of plated silver chemically is readily related to the oxidant concentration used. I n this study silver was chemically stripped with two strong oxidants, ceric cerium and permanganate. In each case, the relationship between the rate of chemical stripping and oxidant concentration was established. The factors which determine the lower limits of applicability were evaluated. Similar studies with the weaker oxidant ferric iron in 1 V HC1 are also described. The only case involving chemical stripping previously noted in the literature was reported by Bruckenstein and Xagai (2) in work involving the use of the mercury-plated rotating platinum electrode. They continued to plate mercury during the deposition of lead and thallium, the dissolution process involving the oxidation of the amalgam by Hg(I1). THEORY
The limiting current observed for a solution of an oxidant in the presence of supporting electrolyte is related to its bulk concentration in solution, Cox, by Equation 2, when the electrode reaction Ox
+ ne- S Red
is rapid compared to the rate of mass transfer of oxidant to the R P E surface, (iJOx is the limiting current, corrected for residual current, and Cox is the bulk oxidant concentration. kox depends upon the electrode geometry, speed of electrode rotation, number of electrons involved in the electrode reaction, and diffusion coefficient of the oxidant. Chemical Stripping Process. Consider t h e situation described above, in which a silver-plated electrode is
rotated in a n oxidant solution and Reaction 1 occurs. If the rate of Reaction 1 is governed by mass transfer, this rate can be calculated, using a Nernst diffusion layer treatment and is
dN/dt
=
AD -
6
(Cox - Coox)
(3)
where d.V,’dt (moles per second) is the rate of silver oxidation, A is the electrode area, D is the diffusion coefficient of the oxidant, 6 is the diffusion layer thickness, and Coax is the oxidant concentration a t the R P E surface. A steady-state value of Cooxis established rapidly a t the R P E surface, and d,V’ldt becomes constant. r n d e r these conditions, Equation 3 may be written as: AN/A t
=
AD
- (Cox - Coox)
6
(4)
where A.V represents the number of moles of silver undergoing oxidation during the finite time interval At. Since i = nFd.I‘/dt, and assuming Cox >> C o o x , as is’the case when Reaction 1 proceeds quantitatively, it follows that
AN At
-
kox nS
= - cox
In ordinary practice the amount of silver which is chemically stripped (A.V) corresponds exactly to the amount of silver which has been plated. If a constant amount of silver is always plated upon the RPE, the reciprocal of the chemical stripping time, l / t c j will be proportional to the concentration of the oxidant. In connection with studies involving experiments with different amounts of plated silver, it is convenient to relate AiV to time parameters associated with the plating of silver on the R P E and with the anodic stripping process used to determine the amount of silver that was plated. The amount of silver plated under a given set of conditions can be determined by electrically stripping the plated R P E at a constant anodic current until all the plated silver is re-
moved from the R P E . This quantity of silver has been shown to be ( 1 ) (QAg)P
= (Qds=
id, -
Qc’
(6)
where (QAe)pis the number of coulombs of silver plated, ( Q A g ) S is the number of coulombs of silver stripped anodically, i, is the constant stripping current, t, is the anodic stripping time, and QC’ is the amount of electricity required to charge the electrical double layer a t the RPE surface. If an identical silver plate is chemically stripped until all the plated silver is oxidized from the RPE, (QAgIc
=
koxCodc -
(7)
QC”
where is the number of coulombs of silver chemically stripped, t, is the chemical stripping time, and QC”is the number of coulombs required to charge the double layer during chemical stripping. If all of the plated silver is chemically stripped, Equations 6 and 7 yield
iota-
Qc’
=
koxCoxtc-
QC”
= koxC‘oxtc
in the presence of excess supporting electrolyte. The flux relationships among Ox, Red, and ,4g + yield kRedCoRed
=
kox(Cox -
coox) = kAg+CoAg+
(12)
from which it follows that
(8)
Since t, and t, are measured between almost the same potential limits, the double layer charging effect is very nearly the same in the electrical and chemical stripping processes. Therefore
i,t,
rate is probably controlled by mass transfer. The observed value of the slope could be larger than the calculated value of the slope if the chemical stripping of silver was mass transfer-controlled while the rate of the electrochemical reduction of the oxidant was not. Equilibrium Calculations. MINIM U M VALUESO F EQUILIBRIUM CONSTANTS. T h e equilibrium constant for reaction given by Equation 1 is defined a s :
Thus i,t,/t, is proportional to c o x . The constancy of A-V/At during chemical stripping has been tested by varying the amount of silver plated (i,t,/n%), while holding Cox constant. The rate of chemical stripping should be independent of the amount of silver stripped, providing all the assumptions made are valid. This has been found to be the experimental situation in our studies. An alternative method for testing the constancy of A N / A t for a given Cox is to interrupt the chemical stripping process, leaving silver on the R P E , and complete the removal of silver with a constant anodic current. An equation analogous to Equation 10 has been derived which describes this case (2). Equation 5 predicts that a plot of Cox us. A,v/At is linear with a slope of kox/nS and passes through the origin. h comparison of this slope with limiting current data may indicate if Reaction 1 is mass transfer-controlled. If the slope is smaller than the value of kox/n5 calculated from limiting current data, the rate-controlling step is controlled by a chemical step, rather than by mass transfer. If the slope is the same as or larger than the calculated value, the
Table I. Minimum Required Values of Equilibrium Constants for Quantitative Conversion of Ox to Red
K Gat Cox = n
10-4
10-5
10-6
10-2 10-3 10-4 10-0 10-6 10-10 a K (Cox - C O O x ) ~ + ~ / C O O x cox ; c o o x / c ~ o x = 100. 1 2
sumptions predict a constant potential during the stripping process. The potential before starting the stripping process is determined by the applied e.m.f.; a t the end of the stripping process the potential is not easily evaluated, since no redox systems exist in the system which determines the potential. I n practice the electrode attains a potential considerably more positive than the steady-state potential. The steady-state potential is calculated to be
E where k R e d is the proportionality constant between the concentration and limiting current of Red. Combining Equations 11, 12, and 13, yields
(9)
Substituting Equation 9 into Equation 5 yields
-
=
+ 0.0591 log-
E / A ~ + , A ~
kOX
+
kAg+
0.0591 log Cox (15) using the Nernst equation and Equais the formal tion 12, where EfApfIAg potential of the silver ion-silver couple. EXPERIMENTAL
From Equation 14 it is seen that even with very unfavorable equilibrium constants, quantitative conversion of Ox to Red can occur a t the RPE surface. Assuming that kox = k,,+ = kRed, minimum values of K required to reduce Coox to 1/101 Cox are given in Table I for two values of n. Thus, at C = 10-6M the standard reduction potential of the couple Ox ne- + Red could be 0.236 volt more negative than the silver ion-silver couple and still have quantitative oxidation. I n practice, chemical kinetic considerations will probably prevent attaining the thermodynamically predicted limits. We have studied three oxidants, Ce(IV) and M n 0 4 - in 1N H2S04 and Fe(II1) in 1M HC1. Using experimentally determined values of EfAg+.Ag = 4-0.553 volt us. SCE in lllr H2S04and 0.226 volt us. SCE in 1,M HC1, the equilibrium constants (Equation l ) for the reaction of silver with the indicated oxidant are: Ce(IV) ~ 1 0 1 0 , M n 0 4 - -106O, and Fe(II1) -106. In all cases quantitative surface reaction is predicted. POTENTIAL-TIME CURVES. I n the idealized chemical stripping example discussed above, it was assumed that steady-state surface concentrations were established virtually instantaneously, and depletion of Ox was negligible during the experiment. These as-
+
Water. Triply distilled water, previously deionized, was used to prepare all solutions. T h e second distillation was made from basic permanganate solution. Supporting Electrolytes. All chemicals used in preparing the supporting electrolytes were used without further purification. I n each case, the solutions were prepared by diluting concentrated analytical reagent grade acid with triply distilled water. Standard Solutions. A standard stock 0.100.11 XgiYOs solution was prepared by weighing dried analytical reagent silver nitrate and dissolving the crystals in triply distilled water. A standard stock 0.0246-V Ce(1V) solution in 131 HC10, was prepared from G. F. Smith Chemical Co. (KH4)*Ce(NOJ6. A 0.0912N Ce(1V) solution in 2N H&04 was also prepared from the material. Both solutions were standardized against standard sodium oxalate (6). A stock K M n 0 4 solution was prepared and found to be 0.1349N when standardized against sodium oxalate ( 7 )* A solution approximately 0.lN in Fe(II1) was prepared by dissolving analytical reagent Fe(KH4) (SO& 12H20 in 1N HzS04. A standard solution of 0.1015N Fe(II1) in lA7 HC1 was prepared from analytical reagent FeC13 6 H 2 0 . The latter solution \vas standardized by reduction n i t h Sn(I1) and titration with standard permanganate solution ( 5 ) . VOL. 37, NO. 7, JUNE 1965
787
' 0
20
60
40
CC,,,",
Chemical stripping with Ce(lV) in 1N H z S 0 4
Figure 1 .
Coulombs of silver used ranged from 1 3 0 RPE 1
X
Table II. Average Experimental Values of AN/Af [Ce + 4 ] Av. A N / A t precision f0.6 9.12 X 8 . 4 5 X lo-" f1.2 4.56 X 4.18 X IO-" 11.5 1.82 X 10-5 1.69 X f2.6 9.12 X 8.15 X 10-l* f0.8 4.56 X 10-6 3.80 X lo-'* f4.9 1.82 X 10-8 1 . 3 7 X
9.12
x 10-7
5.57
x
10-13
Nitrogen. A11 solutions were deaerated with Linde prepurified nitrogen. Prior to use, the nitrogen was passed through a n active copper furnace ( 8 ) to remove traces of oxygen, and then through a presaturator containing triply distilled water to minimize solution evaporation in the cells. Apparatus. The apparatus used, including the constant current source, d.c. amplifier, cells, transfer chamber, and rotated platinum electrodes has been described ( 1 ) . Two rotated platinum electrodes were employed in these studies. Both had projected platinum surface areas of about 0.15 sq. em., and are referred to as R P E 1 and R P E 2 . Three 1-mv. potentiometric recorders were employed. -1Bristol Dynamaster recording millivolt potentiometer equipped with an Insco gear changer, giving chart, speeds varying from 0.125 to 2.00 inches per second, was used. A Texas Instrument Model PWS recorder with chart speeds of 0.75 to 12 inches per minute (or per hour) and a Fisher Model PWS recorder with chart speeds of 0.50 to 8.00 inches per minute (or per hour) were also employed. A11 current-voltage curves were recorded with a Leeds and Northrup Electrochemograph Type E. Treatment of RPE. Prior to each determination, the R P E was subjected t o Pret'reatment B (1). Experimental Technique. The chemical stripping experiments were carried out in the double cell with the transfer chamber previously described ( I ) . Fifty-milliliter portions of silver and oxidant solutions Kere placed in the cells and deaerated for 20 to 30 minutes. A portion of solution was 788
A0
80
'OB
ANALYTICAL CHEMISTRY
to 5 X
0.6
Figure
0.4
2.
0.0
0.2 E v s . S. C . E.
Current-voltage
curves
of
oxidants
All curves corrected for residual current A. 9.12 X 1 O - W Ce(lV) in 1N H&o4; i l = 9.8 PO., RPE 1 6. 1.35 X 10-%4 permanganate in 1N HnS04; ;l = 1 3.2 pa., RPE 2 C. 2.03 X 1 O-'M Fe(lll) in 1 M HCI; i l = 2 2 pa., RPE 2
used for one chemical stripping determination and then discarded. All work was done in a constant temperature bath a t 25' f 0.2' C. After pretreatment, the R P E was plated with silver for a specific length of time at 0 volt us. SCE, which is in the limiting current region for silver. The R P E was then stripped a t a constant current in the same cell to determine the amount of silver plated, pretreated, and replated under identical conditions. The R P E was moved through the chamber into position above the cell containing the oxidant. A potential more negative than the chemical stripping potential was applied to prevent silver oxidation as the RPE was lowered into the oxidant solution. Using Ce(1V) or permanganate, 0 volt us. SCE was applied, while with Fe(II1) in 1N HCI, 0.18 volt us. SCE was applied. After turning on the rotator and recorder, the chemical stripping step began when the applied potential was removed. A voltagetime curve of the chemical stripping process was recorded. The amount of silver plated depended on the oxidant concentration, and was kept sufficiently small so less than about 1% of the oxidant was reduced during the determination. Thus, it was unnecessary to correct for oxidant depletion. Using electrodes of the type equivalent described above, 3 X is the smallest amount of silver that can be accurately determined by anodic stripping; hence smaller amounts of silver could not be used in chemical stripping technique. RESULTS A N D DISCUSSION
Chemical Stripping with Ce(IV). Chemical stripping experiments were performed at different concentrations of Ce(IV) dissolved in 1N H2S04. The average values of A N / A t , calculated from Equation 10, are listed in Table 11. Amounts of plated silver were varied fourfold for each ceric concentration,
indicating the constancy of A.Y/At during chemical stripping. The data from Table I1 are plotted in Figure 1,'4. The slope of the line kc,t4 n5 is 9.29 X lo-' mole 'second-,ll. The lowest points are plotted on an expanded scale in Figure 1,B, which intersects the concentration axis a t 3 x 1 0 - 7 ~ Ce(IV), suggesting the presence of a low, constant concentration of reducing impurity(ies) in the solution. Xccording to the manufacturer's data, the I S H2S04 could contain as much as 1.6 X 10-6,V impurities reducible by Khln04. The average reproducibility was about k 2 % . The current-voltage curve of 9.12 x 10-5M Ce(IV) in 1-V H2SOa obtained with R P E 2 is shown in Figure 2,A. The limiting current is 9.8 pa., corrected for residual current, yielding a value of kce+4,'n5 = 1.12 x 10-6 ampere/M. Using R P E 2 , three chemical stripping experiments in 9.12 X 10-5M Ce(1V) gave an average value of A N / A t of 10.37 i 0.10 X lo-" mole per second. From the latter value, kCet4"n5 is calculated using Equation 5 to be 1.14 X mole/second-M. The latter value is indistinguishable from the value for kce+4/n5 calculated from limiting current data and indicates C ° C e + ~
