V O L U M E 23, NO, 9, S E P T E M B E R 1 9 5 1
1223
-4CKNOWLEDGMENT
The author& wish to express their gratitude to the Atomic Eiiergy Commission a n d to the Research Corp. for grants-in-aitl which supprted t,hi. research. LITERATURE CITED (1j Albright, C., mLtciTer's thesis, The Pennsylvania State ('olic~uc~. 1950. (2) DeFord, D. D., nritl Aiidersen, D. L., J . Am. Chew. Sac., 72, ,3918 (!950). (3) Elmng, P. J.. T~orc.ritha1.I., aiid G a m e r . M. K., Ibid.,73, 1717 (1951).
(4) l ~ ~ l v i i i 1' g., J . , and Tang, C. S., Ibid., 72,3244 (1950). ( 5 ) Furxnall, s.H., and Stone, K. G., Ibid., 70, 3055 ( 1 M ) . (6) Hodgmaii, c'. I)., ed., "Handbook of Chemistry m d Physics," 26th rd.. ('leveland, Ohio, Chemical Rubber Pllblishing Co., 1942.
( 7 ) l i o i i i y ~ t h y ,J . C ' . , Jfalloy, I:., and Elving, P. J., Ax.4~.CHEM., accepted for publication. (8)Stewart, 1'. E., aiid Boiiner, W. A , Ihid.,22,793 (1950). (9) Stone, K. G., J . F'lcctrochen?.,Sot., 97,63 (1950). 1)wember 1, 1950. No. 10 in a series on the polarographic behavior of organic roiripound.?. Previous papers have appeared in .IXALYTICAI, C H m i I s l i ~ Y .J. o i i r . i i n 1 a f t h e American Chemicnl S o c i e t y , etc. RECEIVI.IJ
Derivative Polarographic Titrations CH4HLES N. REILLEY, W. DONALD COOKEL,AND N. HOWELL F U R M l K Princeton University, Princeton, IT. J. ' h i s method of differential polarographic titrations
r e u l t e d from a s t u d j of t h e fundamentals of endpoint indication for coulometric titrations. From theoretical considerations it was predicted that if a pair of platinum electrodes are polarized by a small constant current, ca. 2 microamperes, the electrode w i l l give runtinirous e.m.f. readings corresponding to t h e slope of a polarographic curve a t its zerocurrent axic. If the systems are both reversible, differentiaY e.ni.f. peaks will be obtained a t the end point. and a aiiccession of differential end
I
STEFtEST in dvnvativc titrations has recently been revived
( 3 , 4 , I d , 1 6 ) K a t t and Otto (16) used a concvntmtioii cell cffcxct for potentiornetric titrations involving solutions of metals in liquid ammonia Delahny (3,.$)described an electrical method for differentiating the voltage-volume relationship, u-lug the diffcrentiation prop.rtit.6 of a condrnser ( I ) . This lattrr method has the dieadvantap of requiring a constant flow rat(, o f titrttting ngcnt and therefore of having no sustaincd mvter rc3:~dingfor :L 1
I'rcent address Coruell Univerjity, Ithacs, K. Y.
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givcsn v o l u ~ n cof ~ th(7 titr:iting agent. The origirid differential method :I> tlt.viwd ~ O (X2 ) employed a dual titmtion where one titration na? kept .;lightly in advance of the other. -i more practic:tl method dewloped by MacInnes and Jonea (10) utilized the concentration vo1t:igt~obtained by removal of a mll portion of thv titrated solution 1x.forrS w c h addition of reagent. Miiller ( 1 1 ) employcd a simihr cchtmie. These last two whernes require a change ot rclfewnce solution before each addition of reagrnt. Some dihsinlilar bimetallic electrode eyPtems give results t h a t simuhte these differential potentiomctric titr:ttions ( I , $ , 17). Delahay ( - 5 ) has n w n t I \ discushetl the Foulk and Bawden 3'dc~;d-stop''inc.chanisni (6) by coneideration of tht. Phaptv O f various polarization curves. ti polarized bimetallic system using two similar electrodes n as suggested by Willard and Fenwick (18). Van Same and Fenwick (16) discussed VOLTbDL the behavior of two platinum electrodes polarized by R 0.5-volt sourcc. The method de-rrihctl in this paper is a polarized system similar t o thnt (Jf Fenwick e l al., but cam is taken to polarize the electrodes with constant current. Tlie electrochemical phenomenon giving rise to the curves i c esplained in tern- of polarographic behavfor. I t is hoped that the esplanation will rliminatr the, hcretoforc empirical nature of the method and assist the analyst in Rpplying this technique to new situations
7-
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51
points w i l l be r r a l i m c i in t h e titration of a succession of substance&. If one of the systems is irreversible, the electrodes w i l l s h o w a sharp increase or decrease in e.1n.f. at the end point. The conclusions we= verified experinlentally. This method provides simplicitj of apparatus, con tinirous indication, sharper breakfi mer the conventional potentiometric metho d s in mine cahes, rapid attainment of stable readings, eliniinatioo of a reference half-cell, and ability to detect a siicce4on of end points simply and witho u t plotting.
%I
DISCUSSION
Figure 1. Typical Polarograms of a Solution of Ferrous Ion Being Titrated by Ceric Ion A. E.
Initial solution of ferrous ion Solution half titrated
C. D.
Solution at end point Solution after addition of excess d
o ion
Typical polarograms taken a t a platinum electrode in a stirred solution of a polarographically reversible system (ferric-ferrous) titrated by a reversible system (ceric-cerous) are shown in Fig-
ANALYTICAL CHEM STRY
1224
ure 1. A complete treatment of the theory underlying the shape of these polarograms is given by Kolthoff and Lingane (9). Figure 1, A , is typical of the initial solution of ferrous iron. B shows the polarogram of the solution when half titrated with ceric ion. C shows the polarogram a t the end point, and D shows the polarogram after excess ceric has been added. The slope of the polarographic curve as it crosses the zero current axis is seen to vary considerably during the titration and it is upon this variation that this method is based. Initially, the slope is very low, becoming larger upon addition of a small amount of reagent, then decreasing considerably in the vicinity of the end point, and again increasing rapidly upon addition of excess titrant. If the function dE/dI could be folloffed through a titration, the curve would have a shape not unlike that of the differential potentiometric titrations.
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Irreversible
A . Polarogram of solution containing no electrolytically active substance (solid line). Dotted line shows presence of an irreversible electrolytically active substance. B . Polarogram at end point of titration by iodine C. Polarogram of solution after addition of excess iodine
VOLTAGE
Figure 2.
Enlargement of Polarograms in Vicinity of Zero Current
How experimental attainment of such curves is reached, is shown in Figure 2, which is a n enlargement of the curves of Figure 1 in the vicinity of zero current. A platinum electrode when immersed in a solution assumes the potential of the solution, E,. If the potential of this electrode is decreased by an amount dE1, a reduction current, dI1, will flow. Similarly, if the potential of this electrode is increased above E, by an amount dE2, oxidation current d12 will result. Conversely, if a fixed amount of current (dI equals dI1 equals dI2) is forced through the solution by way of two identical platinum electrodes, one will assume a potential more positive, dE2, and one more negative, dE1, than that of solution E,. Thus the net potential, dEt, across the two electrodes will serve as an indication of dEt/dI, since the current, dI, is constant. The linearity of the voltage-current plot, discussed by Delahay (6) will break down a t high current densities as in region D (Figure 2). This has been observed by Myers and Swift (IS)for their polarized endpoint method. Irreversible systems may be treated in a similar manner by consideration of polarograms a t different points in a titration. A typical set is shown in Figure 3 for the titration of a nonreversible system such as thiosulfate-arsenite with iodine, the latter being reversible. In the original solution (Figure 3, A ) reduction of HaO+and oxidation of OH- may be thqonly electrode reactions for a solution containing some irreversible system. In this case the small amount of current (approximately 2 microamperes) will cause the derivative voltage t o increase until the hydronium ion is discharged a t one electrode and hydroxyl ion a t the other. The addition of any substance more easily discharged will lower this voltage. In some cases oxidation and/or reduction of the irreversible component may be possible, as indicated by the dotted lines in Figure 3, A . In any case, the slope is initially small; thus dE/dI is large. As the titration proceeds, the product(s) of the reagent-iodide for example-is formed, which may be oxidizable at the anode. I t is possible, too, that the products of
the irreversible system may be able to undergo reduction a t the cathode. At the end point (Figure 3, B ) the slope is still small, although the iodide is shown to give a wave. As the end point is passed (Figure 3, C) the slope suddenly increases. Thus up to and a t the end point, dE/dI is large, and a sudden drop of dE/dI occurs a t the end point (Figure 6). APPARATUS
The apparatus shown in Figure 4 is simple and easily set up.
A small B battery of 45 volts (Burgess No. Z30-NX) is connected through an inexpensive l/c-watt, 22-megohm carbon radio resistor to two similar platinum wire electrodes. A high input resistance potentiometer (Beckman Model G) was used because the current through the solution was small (around 2 microamperes). A less sensitive potentiometer may be used by employ45V."B"BATTERY
22MEGOHMS
BECKMAN MODEL G
Figure 4. Apparatus for Derivative Polarographic Titration
V O L U M E 2 3 , NO. 9, S E P T E M B E R 1 9 5 1
1225
ing a l o n w value resistor (1megohm) and platinum foil electrodes. For most of the titrations, even the wire electrodes could be used with the higher current arrangement, but the sensitivity is decreased. A magnetic stirrer was used to pass the solution by the electrodes, as well as for mixing. EXPERIMENTAL
All the solutions titrated contained a supporting electrolyte of 3 A\7sulfuric acid, except the thiosulfate solution which contained 3 grams of potassium iodide per 100 ml. The net volume of solution was approximately 60 ml. The end points were followed potentiometrically with a platinum electrode-saturated calomel 0.26 volt 1's. standard hyelectrode pair (potential of calomel drogen) and differentially with ttvo other platinum wire electrodes (as in Figure 4)a t the same time.
The two results shot\n in Figure 6 are for the titration of thiosulfate in potassium iodide medium by means of 0.08 N and 0.008 N ceric sulfate as in the method of Furman and Wallace (7). The derivative method here gives very sharp breaks in coincidence with the smaller potentiometric breaks. The high derivative voltage a t the approach to the end point is due to the irreversibility of the thiosulfate-tetrathionate couple. The sudden decrease is due to the reversibility of the iodine-iodide couple as illustrated in Figure 3, C.
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35
34
Comparison of End Points
A s determined by potentiometric and differential polarographic methods A.' 0.09 N ferrous B . 0.009 N ferrous
The result for the titration of a polarographically reversible system with a reversible titrant is shown in Figure 5. In A and B where 0.1 and 0.01 X, respectively, ferrous ammonium sulfate are titrated, the sharp approach of the end points is due to the electrode reversibility of the ferrous-ferric couple as contrasted to the less steep decline after the end points due to the slight irreversibility of the cerous-ceric couple. The derivative end point coincides with the potentiometric end point and, in addition, can be directly determined without plotting.
Figure 7 shows the titration of a reversible system (ferrousferric) with an irreversible system (chromic-dichromate). Initially the derivative voltage is high, as might be expected from Figure 1, A , falling rapidly as the dichromate is added. At the end point, there is a sudden rise which remains past the end point because of the irreversibility of the chromic-dichromate couple (8).
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Figure 8. Titration of 0.09 N Ferrous Ammonium Sulfate and 0.2 N Vanadyl Sulfate by Ceric Sulfate Volume ratio, 1 to 25
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Figure 6. End Points for Thiosulfate Titration by Ceric Sulfate in Presence of Potassium Iodide
Figure 8 shom the results of a two-component system, ferrous and vanadyl sulfates, in ratio 1 to 25 ml. The first end point, due to ferrous exhaustion, is accompanied by a rapid rise in derivative voltage which remains high because of the irreversibility
ANALYTICAL CHEMISTRY
1226 of the vanadyl-metavanadate couple a t room temperatme.
LITERATURE CITED
Upon heating to 80” C. the derivative voltage decreases because the vanadyl-metavanadate couple is much more nearly reversible in hot solution, and also because of the increase in ionic mobility at higher temperatures. The second rise is attributed to the eshaust’ionof vanadyl ions and the rapid fall after the end point is due t,o the presence of the more nearly reversible cerous-ceric couple. In this latter case, the most satisfactory end point is the first sharp decrease due to the presence of the cerous-ceric couple. A ratio of ferrous t,o vanadyl of 10 t’o 10 ml. gave a check between potentiometric and derivative methods by 0.02 and 0.02 ml., respectively. A ratio of 20 ml. of ferrous to 1 ml. of vanadyl gave checks of 0.01 and 0.02 nil., respectively. Thr fvrrous was apprusimately 0.09 N a n d the vanadate 0.2 S. In a11 cases, the end-point readings become stable in 5 to 30 secon&, and in one case (ceric-vanadyl titration) Ptability was achieved five timei! faster with the derivative method. The approach of the end point is easily anticipated with practice. The advantages of thie unit are the simplicity, the sharper breaks afforded (as in iodine-thiosulfitte titrations), the elimination of plotting, the rapid at3tninmentof stable readings, the elimination of a reference half-cell (esp!cially advantageous for yniall volumes and high t e m p m t u r w l , and ability to detect a succwpion of c.nd point9 simply.
(1) Baker, H. H., and sftiller, R. H., Tram. Electmchet?~.Soc., 76, 75 (1939). (2) Cox,D. C., J . Am. C h e m Soc., 47, 2138 (1925). (3) Delahay, P.,AXAL.CHEhr., 20, 1212 (1948). (4) Delahay, P., Aiial. Chim.Acta, 1, 19 (1947) (5) Ibid., 4,636 (1950). (6) Foulk, C. W., and Bawden, 4.T., J . d m Chem. Soc , 48, 2045 (1926). (7) Furman, S. H., and Wallace, J. H., Jr., I M . , 53, 1283 (1931).
(8) Glasstone, S., and Hickling, A,, “Electrolytic Oxidation and Reduction,’’ p. 123, S e w York, D. Van Nostrand Co., 1936. (9) Kolthoff, I. M., and Lingane, J. J., “Polarography,” S e w York,
Interscience Publishers, 1941. (10) XIacInnes, D. H., and Jones. P. T., J . -4m. (1926).
C h .SOL, 48, 2831
(11) Muller, ’Erioh, “Eleknonietrische AIassanalyae,” 7th ed., Dresden, T. Steinkopff,1942. (12) Muller, R . H., A N A I .CHEM.,22, 72 (1950). (13) Myers, R. .J.. and Pwift, E. H.. ,J. A m . C h m . Soc.,70, 1047 (1 948). (14) Van Name, H. C,., and Fenwick, F., Ibid.. 47, 9 (1925). (15) Ibid., p. 19. (16) Watt, G. W.,and Otto, J. B., Jr.. J . Elecbodi~na.Soc., 98, 1 (1951). (17) Willard, €I. H., a n d Fenwick, F., (1922). (18) Ibid., p. 2516.
J. 87n. C 7 w n
Soc.,
44,2604
RECEIVEB February 28. 1951.
Three-Dimensional Model for Interpreting Electrometric Processes CHARLES 5. REILLEY, W. DONALD COOKE’, AND N. HOWELL FIiRMlN Princeton Unirersity, Princeton, N. J . Recent work on coulonietric procedures prompted inquiry into the common basis for many electrochemical methods. A description is given of a surface, plotted in three dimensions with current, per cent oxidized, and voltage as coordinates. This surface is presented as a unified basis for explaining and relating polarography,amperometry,potentiometry, and polarized end-point phenomena such as the “dead-stop” method. The equation for the surface under proper conditions is shown to give a quan-
I
S SONE recent work on coulometric titrations, the need arose
for more sensitive electronietric end-point, procedures, because the conventional methods did not, have the desired sensitivity for use in the microgram and submicrogram regions. In the search for applicable procedures the interrelationship of various electrometric procedures was studied. A relationship capable of unifying potentiometric, amperometric, polarographic. and other electrochemical methods was found. As s result of this study, t x o tv-o new end-point procedures have been developed: :t differential method (10)and an amperometric t.itration of high sensitivitp ( 8 ) . It is hoped that this unified explanation will prove advantageous in the clarification, development, and application of electronietric procedures to new situations. When a platinum electrode is placed in a solution containing a reversible couple such as ferric-ferrous or a dropping mercury electrode in hydroquinone-quinone, the properties concerning their interaction may be depicted on a graph of three dimensions: current, voltage, and per cent of the couple in the oxidized st’ate 1
Present address, Cornell University. Ithacit, S . Y.
titative explanation for these electrochemical procedures. This study has been instrumental In the development of a derivative polarographic end point and a sensitive end-point procedure for &metric microtitrations. This surface provides a fundamental picture of the relationship between the various electrochemical methods and should prove valuable in the application and understanding of existing techniques as well as in the development and extension of newer methods of electrometric analysis.
(see Figure 1 ) . The equation for the surface of this figure may be written for various stages of concentration polarization:
where z is the fraction of the total concentration, CO,in the reduced state and the other terms have their usual significance (7).
E Ea R T n F fred
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voltage of electrode
= standard oxidation-reduction potential = gas constant = absolute temperature =
electron change between oxidized and reduced forms
= faraday (96,500 coulombs) = activity coefficient of reduced state = diffusion constant for oxidized state such that
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