ANALYTICAL CHEMISTRY
1662 other than sulfur is contributing t o the acidity of the absorbing solution. An examination of the points shown on Figure 3, forming the bases for curve 2, indicates that use of the milliammeter reading as the sole index of sulfur content is not entirely feasible if the limits of accuracy, as established by ASThl methods, are t o be maintained. Any extension of the technique in this direction would have involved complicatione and possible delay that would defeat the main purpose of this investigation-viz., to predict within reasonable tolerance the amount of sulfuric acid formed in the absorbing solution. ACKNOWLEDGMENT
The author appreciates the assistance of C. S. Tegge of the l’h>,\ics Sertion on electrical problems, technicians G . L. Coolidge,
T. S. Scott, E. Szurek, and W. A. Tettemer of the Inspection Section, and I;,. T. Scafe, supervisor of the Inspection Section, in the editing of this pager. LITERATURE CITED
(1) Ani. SOC.Testing hfaterials, Committee D-2, “Proposed Method of Test for Sulfur in Petroleum Products by the Carbon
Dioxide-Oxygen Lamp Method,” -4ppendix VI, November 1949.
Am. SOC.Testing 1Iatei.ials. “Sulfur in Petroleum Products by the Lamp Gravimetric Method (Tentative).” (3) Edgar, Graham, and Calingaert, George, IND. ENG. CHEM., AN.4L. ED.,2, 104 (1930).
(2)
R E C E K E DA P R I L12. 1931.
Sensitive End-Point Procedure for Coulometric Titrations W. DOKiLD COOKE’, C. N. REILLEY,
~ N D N. HOWELL FURMAN Princeton Cniversity, Princeton, N . J .
The development of techniques in the field of coulometric titrations has provided a method for the addition of extremely small quantities of titrating agents. As minute electrical currents can be accurately measured, these methods allow the addition of quantities as small as 10-’2, and possibly even lo-’’ equivalent of titrating agent. The usefulness of the titration is, however, limited by the sensitivity of the end-point detection. A modified amperometric procedure extends the range of coulometric titrations. The method has been applied to the titration of ferrous ion with electrically generated ceric sulfate. A sensitivity of 0.001 microgram of ferrous ion per milliliter of solution has been realized and titrations have been carried out at concentrations as low as 0.01 microgram per ml. The effect of interfering substances in the reigents is minimized.
I
S IIECEKT years coulometric procedures have become an
hcreasingly important method of analysis. The so-called coulometric titrations have been applied to a wide variety of oxidimetric and acidimetric systems, in both the macro and micro range. Although the methods can be applied t o accurate determinations of macro samples ( I ) , the greatest ad- ’ vantage over conventional procedures seems to be in the field of microtitrimetry. Amounts of titrating agents can be added coulometrically which would be difficult, if not impossible, by conventional methods. The addition of 10-12 equivalent has been accomplished by the procedures outlined here. It appears that quantities of titrating agent of the order of IO-’’ could be generated if the necessity arose. However, the limitation of this type of analysis lies not in the addition of reagent but in finding an end-point procedure of the desired sensitivity. In fact, it has heen stated that the determination of the end point is one of the major problems in microtitrimetry ( 7 ) . A search was made for an end-point procedure capable of high sensitivity, so that the range of coulometric analysis could be extended. It seemed that a method employing the measurement of diffusion currents would be most applicable t o this problem. Amperometric titrations employing the measurement of such currents have been applied t o oxidation-reduction titrations ( 2 , s ) . With systems in which both the oxidant and reductant yield a diffusion current, the titration curve obtained is of the type shown in Figure 4. I n such systems as the titration of ferric ion with titanous solution, a voltage is impressed upon the indicator electrode, so that the diffusion current for the reduction of ferric ion is set up a t the start of the titration. As the ferric ion concentration is decreased linearly, the current decreases in a similar fashion and reaches zero a t the end point. When the end point is passed, a diffusion current caused by the oxidation of the titanous 1
PI‘.
Present address, Department of Chemistry, Cornel1 University, Ithaca,
Y,
ion is set up. A change in slope caused by the diffeience in diffusion coefficients is usually evident as the lines cross the zero axis. The circuit used with this type of procedure is shown in Figure 1. Reference cells of the correct voltage are sometimes substituted for the potentiometer, and no applied potential is necessary ( 4 ) . The choice of the potential to impress upon the indicator electrode is usually made from a study of the individual polarograms. I n Figure 2 are shown the polarograms of the ferric-ferrous and titanic-titanous procedures. For the voltage t o be impressed upon the indicator electrode, a value is chosen that will include the ferric ion and titanous ion plateaus. An analogous process was devised for the titration of ferrous sulfate with electrically generated ceric sulfate. The normal type of titration curve was obtained, but the results were not satisfactory at extreme dilutions. .4 precision of 5% wab ob-
REFERENCE ELECTRODE
Figure 1. Indicator Circuit
1663
V O L U M E 23, NO. 11, N O V E M B E R 1 9 5 1 tained in the titrations of 100-microgram samples of ferrous iron. The choice of the voltage to be impressed upon the indicator circuit was found t o be important. Different titration values were obtained when the applied voltage was varied For a change in potential of 50 mv., a difference in titer of 1 % was noted.
ceric. Because the current is zero, it must be assumed that t h e potential of the indicator electrode is the same a t the potential of the solution. I n Figure 4 the titration is carried out to zero current-that is, until the potential of the solution is the s a r n ~ as that of the indicator electrode, 0.95 volt. The titration might be considered similar to the type of titration proposed by Muller ( 6 ) ,in which a potentiometric titration is carried out to a predetermined potential. Whether a potentiometric or amperometric titration curve is obtained depends upon the resistance of the circuit. If a high resistance circuit is used, a potentiometric curve is obtained, and in a low resistance circuit, the diffusion currents are measured and an amperometric titration is obtained.
I-
I
\
Figure 2. Polarogranis of Ferric-Ferrousand Tit anic-Ti tanous Procedn res
For the amperometric titration of dilute solutions ( 5 micrograms per ml. or less), the applied voltage cannot be chosen by the method outlined in the previous paragraph and shown in Figure 2. The polarograms in Figure 2 are for equivalent amounts of ferric-ferrous and titanic-titanous ions. Obviously, such solutions cannot exist together because of the reaction between the titanous and ferric ions. A more applicable curve from which to choose the correct voltage would be a polarogram of the solution of ferric ion t i t r a t d just to the end point with the titanous solution. This type of polarogram for the ferrous-ceric titration is shown in Figure 3.
/'
I I
I
I
1
2
3
4
I 5
I
6
SECONDS
Figure i .
Titration Curves
For reasons that are somewhat obscure, high resistanw Indicator circuits-that is, potentiometric titrations-cannot hr applied to very dilute oxidation-reduction systems. Equilibrium is obtained slowly and the potential changes are diffuse in tht, vicinity of the end point. These difficulties are not present in amperometric titrations, and hence the latter type has been more widely applied t o very dilute solutions. However, this method suffers from poor reproducibility in microgram work ( 5 to 10 micrograms of iron), and the error involved in choosing the corlcct potential to impress upon the indicator electrode.
/
CC++'
Figure 3.
b
1.00
Polarogram of Solution at End Point
The potential of the solution i p the intersection of the polarogram and the zero current line-that is, point E. The correct indicator voltage in the amperometric titration of this system would be the voltage E. 4 n y other voltage would cause an ('rror, either in the positive or negative direction. For example, if E' were chosen for the indicator electrode voltage, when the actual end point %-as reached, a small current would still be flowing. Thus, when the solution was titrated further to zero current, a positive error would be obtained. The magnitude of the error introduced by the use of a voltage other than E for the reference voltage depends upon the slope of the polarogram at E . With the ferrous-ceric system, the slope of the curve a t this point is small, and an error of 1% is introduced by a voltage change of 50 mv. In other systems such as the amperometric titration of vanadate with ferrous sulfate, the slope of the polarogram is large a t E, and large errors are introduced by a small error in the choice of indicator electrode voltage. In the type of amperometric titration discussed above, the end point is taken as the point where one of the diffusion currents reaches zero, a8 shown in Figure 4 for the titration of ferrous with
I
E' TIME
Figure 3.
Potential Change of Solution
I n the titration of ferrous iron with electrically generated ~ ~ i i sulfate, a method was found hg K hich both of these errors could t)e minimized. The amperometric titration may be considered as a titration to a predetermined potential. I n the titration studied, this voltage jqas chosen as 0.95 volt versus the hydrogen electrode. However, cerous sulfate solution from which the ceric ion was generated was found to have a potential of about 0.71 volt. I t was found that if the potential of the solution was increased to the reference potential before the addition of the unknown substance,
i *
1664
ANALYTICAL CHEMISTRY
much more accurate results could be obtained. Referring to Figure 5, the potential of the cerous solution at the beginning of the titration was in the vicinity of point A , 0.7 volt. The potential of the solution was raised by generating ceric ion until the reference voltage E (ca. 0.95 volt) was reached. The unknown ferrous solution was added which lowered the potential of the solution t o about point B. The ferrous sample was then titrated until the voltage was again a t the reference voltage as indicated by zero diffusion current. The use of this technique offered advantages over the conventional amperometric titration. The equilibrium voltage chosen thus became unimportant. Rather than the necessity of choobing the corrert referenre voltage within a few millivolts, wide latitude was allowed in the voltage impressed on the indicator electrode. As shown in Table I, any value between 0.85 and 1.00 volt gave the correct titration as long as the solution was brought up to the reference point, the unk n o ~ added, n and then titrated back to the reference voltage.
Table 11. Results of .Analyses Fe Taken, r
275,s
276,6
109 4
11.09 9.58 9.49 1.96 1 44 1.06 c.32 0.32 0.16 0.15 0.15 0.14
i l
ISOLATED ELECTRODE
)Il u
Figiire 6 .
Generator Circuit
A secorrd advantage of the method is that impurities in the reagents do not interfere in the titration-for example, any rrducing agent in the sulfuric acid is titrated in bringing the solution up to the reference potential before the unknown is added. A sensitive galvanometer (0.0005 microampere per mm.) was used to measure the diffusion currents. In this fashion it waa possible to detect very small differences in potential between the indicator and the solution. The voltage amplification was enormous-400 meters’ deflection per volt in the vicinity of the end point.
Table I.
Effect of Indicator Voltage on Titration
Indicator Voltage V8. Ha0 +H? 1.05 1.00 0.95 0.90 0.85 Q 75
Fe Found,? (Theory-109 4) 110 1 109.4 109.5 109.3 109 3 107 0
Fe Found,
Error,
70
Y
276.7 275.5 276.4 276.7 276.3 276,Z
2.600
0.2 0.3 0.2 0.3 0.5 0.3
2,600
0.4 1.2 2.4
0 330
2.5
0,0500
04 0.0
276.6 109.6 109.7 109.6 109.7 109.9 109.1 11.1.7
9.70 9.2ti 1.91 1 44 1.04
0.37 0.34
15 6
0.17
Ma.
0.03 0.11 0.14 0.03 0.18 0,l.i
n
276 R
Generating Current,
2 . GOO
0 0500
6
o,is
0 13
0.17 0 16
14
saturated solution of silver sulfate in 1 iV sulfuric acid was placed in the cathode compartment. The cathode reaction was then e A\g+-Ago and no hydrogen was evolved. A magnetic stirrer was used to stir the solutions, and the rate of stirring had no effect on the titrations, as the zero current was taken as the end point. The circuit shown in Figure 1 was used as the indicator system. A large stationary platinum-iridium indicator was used in preference to a rotating electrode. The area was about 2 sq. cm. The reference electrode was a mercurous sulfate half-cell with a agar-sulfate salt bridge. The galvanometer was equipped with an Ayrton shunt.
+
In potentiometric titrations, equilibrium voltages are reached rather slowly in dilute solutions. Holvever, with this indicator system, the currents reached equilibrjuni rapidly (less than 1 minute in the vicinity of the end point. In the titrations of quantities in the vicinity of 100 micrograms, the indicator current was of appreciable order of magnitude as compared to the generating current A negative error was thus introduced by thr oxidation of some of the ferrous ion a t the indicator electrode. To circumvent this difficulty, a resistance of the order of 100,000 ohms was placed in the indicator circuit. This resistance was removrd when the end point was approached. In the titration of quantities of material below 1 microgram, a drift in the indicator current was noted. This drift was of thr order of magnitude of 0.005 microampere per minute and limited the titrations to quantities not lrss than 0 1 microgram. ELECTRICAL CIRCUIT
TITRATION CELL
The cell used for the titration of samples greater than 100 micrograms haa been described (1). For samples smaller than this value, a 10-ml. cell of similar construction waa used. The reference electrode was a mercurous sulfate half-cell (0.62 volt) with a sulfate-agar bridge. The generator anode was a bright platinum-lO’% iridium electrode with an area about 2 sq. cm. The platinum-iridium alloy was preferred because of its rigidity compared to pure platinum. The cathode (2 s cm. in the large cell and 1 sq. cm. in the small cell) was isolate3 by means of an asbestos or agar plug. In previous work involving titrations of macro amounts of ferrous iron with electrically generated ceric .sulfate, hydrogen waa evolved a t the isolated cathode. In the microtitrations, however, the hydrogen gas interferes. The gas diffuses rapidly through the asbestos plug and ap reciably lowers the voltage of the solution. To circumvent tgis difficulty, a
.
A constant voltage circuit (6) was used as the source of the generating current. The desired value of the current was obtained by placing the appropriate resistances in series with the cell. With the arran ement sh0n.n in Figure 6 current could be controlled to better t i a n 0.1%. The electronic voltage supply used in this work is not necessary and five 45-volt B batteries could conveniently be used for generating currents. TIMER
A Standard Time Co. synchronous motor clock (S-6) was used
to measure the generation time.
REAGENTS
The standard ferrous ion solutions were prepared from primary standard ethylenediamine ferrous sulfate. Two standard solu-
1665
V O L U M E 23, N O . 11, N O V E M B E R 1 9 5 1 tions, 0.01 ,\- and 0.001 iV, were prepared by dissolving the appropriate quantity of the salt in oxygen-free water. The solutions were transferred under carbon dioxide to a storage vessel, and stored under carbon dioxide. A solution so prepared maintained its strength without appreciable change for 2 weeks. As it seemed inadvisable to prepare more dilute solutions, it was necessary to take very small volumes of the 0.001 N solution as samples for the smaller ranges of concentration. For this purpose, a l-ml. syringe with an attached capillary was used as a weight pipet. Samples as low as 10 mg. of solution could be weighed with an accuracy of 1%. Evaporation from the capilIarftip was negligible. A saturated solution (ea. 12%) of cerous sulfate u-as prepared from G. F. Smith Chemical Co. reagent grade cerous sulfate.
RESULTS
The results of the titrations carried out by the above procedure are shown in Table 11. ACKNOWLEDGMENT
The authors gratefully acknowledge the financial aid which made this work possible. The work was begun while one (W. D. C.) held a postdoctoral fellowship from the Atomic Energy Commission and the National Research Council. 4 subsequent fe1lowship from the Eugene Higgins Trust Fund enabled the study t o be continued and completed.
PROCEDURE
A solution of the desired volume was made approximately 0.1 N in respect to cerous ion in 2 to 3 N sulfuric acid. These concentrations were not critical. Carbon dioxide was bubbled through the solution for a few minutes to remove any dissolved oxygen. As this solution had a potential of 0.71 volt, and the indicator electrode was set a t 0.95 volt, an oxidation diffusion current of the cerous ion was set up. The indicator current was adjusted to below 0.0005 microampere by generating ceric ion to raise the voltage of the solution. The timer waa reset to zero, and the unknown ferrous solution was added. Ceric ion was then generated until the current was again below 0.0005 microampere. Rather than titrating exactly to zero current in the preliminary adjustment, an arbitrary current value close to zero could be chosen as the reference point. If the sample was titrated just to the end point, additional samples could be added to the same solution.
LITERATURE CITED
(1) Furman, N. H., Cooke, IT.D., atid Reilley, C. Y., .INAL. CHEM,;
23, 945 (1951). (2) Heyrovsk?, J., “Polarographie,” p. 419, Vienna, Julius Springer,
1941. (3) Kolthoff, I. M., and Lingane, J. J., “Polarography,” p. 447, New York, IntersciencePublishers, 1941. (4) Ibid., p. 462. ( 6 ) Muller, Erich, “Electrometrische Massanalyse,” 6th Aufl., p. 90, Dresden, T. Steinkopff, 1942. (6) Reilley, C. N., Cooke, TV. D., and Furman, N. H., - ~ N A L . CHEX. 23, 1030 (1951). (7) West, P. TV., Ibid., 23,51 11951).
RECEIVED > l a r c h 17, 1931.
Coulometric Titration of Microgram Quantities of Vanadium in Uranium N. HOWELL FURMAN, CHARLES N. REILLEY, AND W. DONALD COOKE’ Princeton University, Princeton, X . J. This investigation was undertaken to test the application of the coulometric titration process to the estimation of milligram and microgram amounts of vanadium in the presence of macro quantities of uranium. With judicious choice of reagents for the prior reduction or oxidation of the substance that is to be determined, a high degree of accuracy may be attained. In the microgram range a sufficiently sensitive method of determining the end point must be adopted. By opposing a suitable potential to a cell composed of an indicator electrode and a reference electrode and titrating to zero current with a galvanometer of high sensitivity, indication is achieved that is capable of almost unlimited sensitivity. This procedure may be considered from the viewpoint of an amperometric or potentiometric titration. The galvanometer sensitivity is so chosen that no significant amount of material is used by the indicating process itself.
IN
RECENT years the determination of small quantities of vanadium has become increasingly important ( 2 , 4). 91though a coulometric procedure has been applied to macro quantities of vanadium (S),no work has yet appeared on application to micro quantities of vanadium. The coulometric method has its greatest advantages in the microgram region due to ease of addition of reagent, elimination of reagent impurities, and the fact that the addition of reagent does not dilute the solution ( 1 ) . Since the development of a sensitive end-point procedure ( I ) , the microgram vanadium titration seemed feasible in view of the work by Parks and hgazzi ( 4 )and Gale and Mosher (8). The principle of the “carrier ion” method of coulometric analysis is illustrated by Figure 1, A . 1
Present address, Cornel1 University, Ithaoa. N. Y.
The electrons are carried to or from the generator electrode with the help of an added intermediate ion. This carrier ion, converted a t the generator electrode to another valence state, then travels throughout the solution and reacts with the substance to be determined. If a platinum electrode in a solution containing ammonium metavanadate and sulfuric acid is subjected to a polarizing potential, a curve such as ABGHIQJ results. The wave a t B is attributed to the reduction of metavanadate to vanadyl ions, the wave at H to the reduction of vanadyl ions to vanadous ions, and the wave a t I to the reduction of hydronium ions If a current of value indicated by N is forced through the solution, the generator electrode will attain a potential indicated by K. As the supply of metavanadate ions becomes depleted during such an analysis, the voltage will drop to a value indicated by L in Figure 1, B. At this time the current is due in a small part to electrol.ytic reduction of metavanadate ions and to a larger extent to the reduction of vanadyl ions forming vanadous ions, which in being stirred through the solution will encounter and react with metavanadate ions to give vanadyl ions. Thus essentially the electrons are carried by the
