ANALYTICAL CHEMISTRY
1116 in this instance of 1.85. Results of some value, however, should still be available with a ratio of diffusion coefficients as low as about 1.4, but this should probably be considered the lower limit of feasibility of the method until further refinements of experimental technique have materially reduced the errors of measurement.
Heyrovskq, J., and Bures, M., Collection Czechoslov. Chem. Commum., 8, 446 (1936). (3) Lingane, J. J., Arca~.C H E M . ,15, 583 (1943). (4) MacNevin, TV. M., Baker, B. B., and McIver, R. D., Ibid., 25,
LITERATURE CITED
RECEIVED for review December 20, 1951. Accepted April 6, 1955. Presented before the Division of Analytical Chemistry a t the 126th Meeting of the AMERICANC H E M I C I L SOCIETY, ,\jew York, zi. Y..September 1954. Contribution 1304 from Department of Chemistry, Yale University.
iMeloche, V. W., and Shain, I., .4NAL. C H E M .26, , 471
(2)
274 (1953).
Meites, L., ANAL.CHEM.,27, 1116, (1955). (6) Meites, L., J . Am. Chem. Soc., 73, 4257 (1951). (5)
Cells, Apparatus, and Methodology for Precise Analysis by Coulometry at Controlled Potential LOUIS MEITES Sterling Chemistry Laboratory, Yale University, N e w Haven, Conn.
The failure of controlled potential coulometric analysis to be used in the analytical laboratory has been due primarily to the lack of an accurate and precise directreading current integrator. The construction and operation of such an instrument are discussed, together with two cells suitable for rapid controlled potential electrolyses, and the general methodology of precise analysis by coulometry at controlled potential is outlined. Determinations of cupric copper, in amounts varying from 2 to 600 mg., were accurate and precise to within & O . l % . An extrapolation technique is described which decreases the electrolysis time required to only 20 to 30 minutes.
I
N principle, coulometry a t controlled potential with a mercury
cathode, as developed by Hickling ( 3 )and Lingane ( 1 1 ) ,among others, has numerous advantages over ordinary electrogravimetric procedures, but in the past it has suffered from one crippling disadvantage. The advantages-the ease with which so many separations can be accomplished, the fact that a potentiostat relieves the operator for other duties throughout the whole duration of the electrolysis, and the elimination of all the operations involved in weighing a metal deposit (to say nothing of the fact that coulometric procedures need not involve the deposition of a solid metal)-have been expounded in a recent monograph by Lingane (4). The crippling disadvantage has been the lack of a precise, accurate, and simple instrument for integrating the electrolysis current. The silver coulometer employed by Szebelledy and Somogyi ( 1 6 ) merely substitutes the operations of washing, drying, and weighing the silver deposited in the coulometer for the very same operations on the metal deposited in the electrolysis cell. I n using Lingane’s gas coulometer (11), liquid levels must be adjusted before, during, and after the electrolysis, the volume, temperature, and pressure of the gas evolved must be measured, and finally the volume of gas must be corrected to standard conditions. Moreover, it is now known that the hydrogenoxygen coulometer gives seriously erroneous results with low currents (16). The seeming complexity of the coulometric measurements, coupled with the fact that the precision of the available data has been “not too impressive” (IO), has greatly retarded the adoption of controlled potential coulometric analysis as a standard technique of chemical analysis. Lingane wrote (9) that “the development of a direct-reading instrument, capable of integrating current-time curves with a precision and accuracy of the
order of O . l % , would be a boon to controlled potential coulometric analysis.” This paper describes an instrument which fulfills these specifications, together with some details of the manner in which it may be used in practical analysis. APPARATUS
The potentiostat and integrator used in this work were designed in collaboration with Julian h1. Sturtevant. The operating characteristics of the potentiostat are as follows: range of direct current output voltages available, 0 to 10 and 0 t o 28 volts on the low and high ranges, respectively; direct current electrolysis current available, 10 amperes a t 28 volts; alternating current ripple component of direct current output, less than 0.5% (peakto-peak) of direct current voltage per ampere; range of direct current control potentials available, A 3 volts; sensitivity of potential control, better than 1 5 mv. under all conditions thus far investigated. Although these characteristics are generally superior to those of most previously described instruments, they have (with the exception of the attainable voltage and current) relatively little influence on its use in coulometric procedures. A description of this potentiostat, which is to be manufactured by Analytical Instruments, Inc., Bristol, Conn., will be published elsewhere. A schematic diagram of the circuit of the integrator is shown in Figure 1. The electrolysis current is passed through one of the three standard resistors connected to the input selector switch, and the voltage developed is added algebraically to the opposing output of a direct current tachometer generator. The resulting voltage is converted to BO-cycle alternating current, is amplified, and is used to drive a tTyo-phase servo motor. This turns the generator a t a speed which produces a generator output practically equal to the zR drop through the input resistor. A five-dial revolution counter attached t o the gear train is turned simultaneously a t a rate proportional t o the rate of revolution of the generator shaft: thus the counting rate a t any instant is proportional t o the electrolysis current. Accordingly, the total number of counts recorded during an electrolysis is proportional t o the quantity of electricity used. This arrangement is very similar t o that of the voltage integrator described by Buzzell and Sturtevant (1). The three input resistors are provided to permit selection of an over-all sensitivity which gives ?.suitablv large number of counts for any coulometric analysis. 11 ith the particular motor, generator, and gear train used, the maximum rate of revolution of the generator shaft correspondq to an output of about 1 volt. Bccordingly, the 1-ohm input resistor is used in electrolyses in which the initial current may be as large as 1 ampere. If the initial current exceeds this value, the instrument cannot provide an accurate integral unless the 0.1-ohm resistor is substituted; in this way the range of the instrument is extended t o maximum currents of 10 amperes, which is ample for any practical use. If, however, the initial current is less than 0.1 ampere, the use of the 10-ohm resistor is recommended t o increase the number of counts recorded, and also to reduce to a minimum the unavoidahle effects of friction a t very low counting rates.
V O L U M E 2 7 , NO. 7, J U L Y 1 9 5 5
1117
Figure 1.
Schematic diagram of current integrator
Converter. Brown converter Brown Instruments Division, Xfinneapolis-Honeywell Co., Philahelphia, P a . I n p u t transformer. Type 1-67B. Palnier Electric a n d Manufacturing Co., Wakefield, Mass. Output transformer. Type CG-16, United Transformer Corp., New Ynrk
Po&Yr-supply choke. 15 millihenries. 10 amperes
A typical calibration curve is shown in Figure 2. This was secured by applying various constant voltages t o a circuit comprising a precision resistor in series with the 10-ohm input resistor of t h e integrator, and measuring the iR drop across the external resistor with a carefully calibrated Rubicon potentiometer. The quantity of electricity flowing in each calibration was computed from t h e known steady current and the measured duration of the experiment. Table I. Effect of Input Resistor on Sensitivity of Current Integrator Input Resistor, Ohms
(I
-__ Nominal 1 0 1 0 01 0 001 0 0001
h'. J.
Generator. Type 363 Electric Indicator Co., Springdale, Conn. Rated output. 420 mi.. per 100 r.p.m. Gear ratios. Motor t o generator, 12 t o 1; motor t o counter, 48 t o 1
do
:I 0 100
. 0
e
0 0099 2
Sensitivitv. Jlicrofaradavs per Count"
Observed 1 1 00082 10 0 099995 100 0 0100033 1000 0 00099976 10000 0 000099195 1 microfaraday = 0.096493 coulomb
Power transformer. Stancor PC-8411, Chicago Standard Transformer Corp. Servo motor. Type F P E 25-11, Diehl Manufacturing Co.. Finderne,
~
Difference,
%
+O -0 +O -0 -0
082 005
03 02j 80;
0 0980
I
I 40
I
I
80
0
Current, milliamperes
Figure 2. Typical calibration curve
These data show that with the 10-ohm input resistor in serieq with the electrolysis cell, the sensitivity of the integrator is constant and equal t o 0.099995 microfaraday per count for input currents between 1.5 and 105 ma. Table I shows that, with the exception of the data secured with an input resistor of 10,000 ohms (which would be used only for integrating currents smaller than 100 H a . ) the sensitivity is changed by a factor of almoqt exactly 10 whenever the value of the input resistor is changed bja factor of 10. Consequently, the instrument on every range i; direct reading in an appropriate decimal multiple of 1 microfaraday per count; it reads directly in milliequivalents after proper location of t h e decimal point. This is a very considerable advantage in routine analytical work. Theeffect ofthedecreaseof sensitivity atverylow currents, whirh occurs with every input resistor when the zR drop across it falls below aliout 15 mv., is sufficiently small t o cause the integrated current to be in error by less than 0.2%, if the initial current i.; a t least one tenth of the rated maximum for the input resistor used. The stock solution of copper(I1) sulfate had been standardized
Secured with 10-ohm input resistor
repeatedly by a very precise iodometric method ( 1 4 ) , and had a known normality of better than &0.02%. Aliquots of this solution, taken with carefully calibrated pipets, were used to provide known amounts of copper. All other chemicals were ordinary reagent grade. CELLS
-4ccording t o the equation deduced by Lingane (6)for the current-time curve during a controlled potential electrolysis, the rate of such an electrolysis is directly proportional to the ratio of cathode area t o solution volume. I n a cell of cylindrical cross section, Lingane found (4)t h a t the value of k in the equation it
= i01O-kt
was generally about 0.037. Thus, 54 minutes are required t o drive R reaction 99% of the way t o completion in such a cell,
ANALYTICAL CHEMISTRY
1118 or 81 minutes to achieve 99.9% completion, and very much longer to secure the maximum possible degree of separation (8). This is a considerable drawback t o the use of coulometry a t controlled potential in the routine laboratory. I n the cells of Figures 3 and 4, the area t o volume ratio is increased b y using a conical working electrode compartment, with the result t h a t 99% completion can be attained within 24 minutes, and 99.9% completion within 35 minutes.
- Mercurv
Figure 3. Cell for controlled potential electrolysis with mercury cathode and internal auxiliary electrode
The cell shomx in Figure 3 was designed for electrolvtic s e p i a tions with a mercury cathode at controlled potential and an internal auxiliary electrode, and may be used for coulometric analyses when a suitable anodic depolarizer can be found. It consists of a three-necked 125- or 250-ml. Erlenmeyer flask with a side tube carrying a stout piece of platinum wire and filled with mercury for electrical connection t o the potentiostat. The central neck of the flask carries a one-hole rubber stopper through which the stirrer shaft passes. Around this shaft is wound a helix of platinum or silver wire which serves as the auxiliary electrode and is connected to the potentiostat by means of a n alligator clip just above the stopper One of the off-center necks of the cell carries a commercial 5-inch fiber-tvpe saturated calomel electrode whose tip just trails in the mercury; the other neck is used for the addition of reagents during the electrolysis. Stopcocks are provided for emptying the cell completely and for removing a portion of the solution without interrupting the electrolysis. The more elaborate cell shown in Figure 4 is necessary for analyzing solutions-e.g , of copper(I1) in ammoniacal mediumfor \Thich a suitable auxiliary electrode-depolarizer combination is impossible t o find. Diaphragm cells for coulometry at controlled potential have been described by Lingane, Swain, and Fields ( f b ) and by Diehl(2). However, neither of these is wholly practical ( 7 ) ,for it is not simple to prevent bulk flow of the solution between the two compartments without unduly increasing the cell resistance. These difficulties are surmounted in the cell of Figure 4 by the use of a double diaphragm enclosing a central compartment filled with the supporting electrolyte present in the working electrode compartment. T h e latter is separated from the central compartment by a 20-mm. fine-porosity sintered disk, and the central compartment is separated from the auxiliary electrode compartment by a medium-porosity disk of equal size. The second disk does not appreciably increase the total cell resistance (which is usually of the order of 10 ohms), and serves only t o prevent convective mixing of the solutions in the central and auxiliary electrode compartments. Stoppering the central compartment reduces the rate of equalization of pressure across the diaphragms, and permits reducing the rate of flow of liquid into the working electrode compartment t o 1 ml. per hour 01 less. Even this negligible volume of solution is practically free from the products of the reaction a t the auxiliary electrode. Since not every potentiostat will tolerate the resistance (about 2500 ohms) of a commercial fiber-type calomel electrode in its
control circuit ( 6 ) , i t may be desirable to use some other type of reference electrode when working n i t h another potentiostat. These cells are available commercially from A4nalyticalInstruments, Inc., Bristol, Conn. EXPERIMEYTA L
ill1 except a few preliminary experiments were made with the double-diaphragm cell described, employing the following procedure. The entire cell was emptied and the central compartment n-as filled rrith the supporting electrolyte and n-as stoppered. More of the same solution was added to the working electrode compartment to cover the gas dispersion cylinder, through which a rapid stream of nitrogen or hydrogen was bubbled. The auxiliary electrode compartment finally was filled with the same solution t o a point about 3 em. higher than the level in the working electrode compartment. The stirrer was started, and 30 ml. of mercury was added t o the working electrode compartment with the potentiostat adjusted t o maintain the cathode potential constant a t the desired value. .4 stirrer speed should be selected so t h a t the surface of the mercury is in as rapid motion as possible without causing the formation of detached droplets of mercury. This stirrer speed, by minimizing the thickness of the diffusion layer, serves to increase the currents secured and thus the rate a t which the electrolysis proceeds. Pre-electrolyzing the supporting electrolyte alone for a few minutes served to remove not only residual traces of oxygen b u t also traces of reducible material contained in the chemicals from which the supporting electrolyte was composited. The course of this pre-electrolysis was follolyed by using the integrator with a n input resistor ten times as large as that t o be used in the subsequent analysis. When the counting rate under these conditions had dropped to 0.1 count per minute or less (0.01 count per minute in the actual analysis), the electrolysis circuit was disconnected ( a switch for this purpose is provided on the Analytical Instruments, Inc., potentiostat) and the desired volume of cupric solution was added t o the cell. l17hen, after a minute or two, during which the appropriate input resistor of the integrator was connected into the circuit, the oxygen contained in the sample solution had been removed by the nitrogen stream, the integrator register was read to the nearest 0.1 count, the electrolysis circuit was reconnected, and the electrolysis was allowed to proceed without further attention. REF
-
Figure 4. Cell for controlled potential electrolysis with mercury cathode and external auxiliary electrode
When the total volume of solution in the cathode compartment was just sufficient to cover the sintered disk separating i t from the central compartment, the rate a t which the electrolysis proceeded was such t h a t 99.99% completion was reached in about 45 tp 50 minutes. After this length of time, the register was read again. Subtraction of the initial from the final register reading, followed by appropriate location of the decimal point, gave the number of milliequivalents of copper directly. Some data secured by this procedure in several different supporting electrolytes are shown in Table 11. The accuracy and precision of these data compare very favorably with those obtained in electrogravimetric work. Although each analysis consumed about 60 to 75 minutes, the operator’s attention was required during only a small fraction
1119
V O L U M E 27, NO. 7, J U L Y 1 9 5 5 Table 11.
Coulometric Determination of Copper
(Volume of solution was generally 100 to 150 ml., and of mercury cathode was 30 t o 35 rnl.) Supporting ECu s . Electrolyte, S.C.E., hleq. hleq. Error, 1 41 Volts n Taken Found 72 +0.29 2 9 476 9 503 0 50 -0.28 9 476 9 451 -0.02 7 103 7 105 -0.07 4 73‘1 1 733 +0.03 4 737 4 736 +O.l6 2 352 2 349 -0.04 1 4183 1 4178 0 7073 10.04 0 7070 -0.09 0 4672 0 1668 t0.07 0 2373 0 237.5 - 0 15 0 07546 0 07534 4 734 - 0 08 HCl -0 10 1 4 738 1 1745 1 1748 + O 03 9 198 +O 13 - 0 50 2 9 476 2 348 -0 04 2 349 “3 - 0 75 2 7 105 7 089 - 0 10 NHL I 0 7070 0 7068 -0 03 HClOa -0 50 2 18 96 18 96 +O 2 349 2 356 - 0 13 3Iean - 0 01 I O 09
Table 111. Extrapolation to Zero Current
the data in Table 111, which were secured during the electrolysis of a 1 M hydrochloric acid solution containing 6.482 meq of cupric copper. With the 1-ohm input resistor used, a total of 6482 counts should have been recorded. Sineteen and a half minutes after the beginning of the electrolysis-the time was chosen solely for symmetry in constructing the table, and, as is not true of the MacSevin and Baker technique, is of no importance in the calculations-when about 5% of the original amount of copper remained undeposited, the register was read and again was read exactly 1 minute later. During this 1-minute period 46 counts were recorded. This is practically equal to the instantaneous counting rate a t a register reading equal to the mean of the values at 19.5 and 20.5 minutes, or 35364. The measurements were repeated a t 24.5 and 25.5 minutes, and the counting rate then was found to be 24 counts per minute a t a register reading of 35529. Consequently 35529 minus 35364 ( = 165) counts were required to decrease the counting rate (which is proportional to the electrolysis current) from 46 t o 24 counts per minute. T o decrease the counting rate to zero, an additional (24/22) X 165 ( = 180) counts would be required. From this the final register reading would be 180 (=35709), which corresponds t o a expected to be 35529 total of 6479 counts and to an error of only -0.05%. The remaining data were treated in exactly the same way, with the results shown in the last column of Table 111. Results of this technique are accurate t o within a few counts with a saving u p to one half of the total time required for an analysis, and a controlled potential coulometric analysis may be carried out within about 0.5 hour and with an average precision of j=O.l%.
+
(Electrolysis of 6.482 meq. of Cu’+ in I50 ml. of 1M HCI E = 0.46 volt 1’s.S.C.E.; l i ~ g= 35 ml.) Register LITER4TURE CITED Elapsed Reading Extrapolated Time, ( 1 Count = Counts per Reading 0.001 Meq.) Minute hh. (1) Buzeell, A., and Sturtevant, J. >I., Rev. Sci. Instr., 19, 688 (19 4 8 ) . 0 29230,Z 20 35364 46 (2) Diehl, H., “Electrochemical Analysis with Graded Cathode 165 22 Potential Control,” p. 29, G. F. Smith Chemical Co., Colum26 3.5529 24 35529 (24/22)(165) bus, Ohio. 88.0 11.6 = 35709 0 (3) Hickling, A., T r a n s . F a r a d a y Soc , 38, 27 (1942). 30 36617.0 12.4 35617 0 4- ( 1 2 . 4 / 1 1 . 6 ) (4) Lingane, J. J., “Electroanalytical Chemistry,” Interscience, 45.5 6.0 (88.0) = 35711.1 New York, 1953. 35 3,j662.0 0.4 35662.0 (6.4/6.0)(45 6 ) (5) I b i d . , pp. 192-5. 22.8 2.9 = 35710.5 ( 6 ) Ibzd., pp. 263-4. 40 33684.8 3.3 35684.8 ( 3 . 3 / 2 , 9 )( 2 2 . 8 ) (7) I b i d . , pp. 269-72. 11.6 1.6 = 35710.7 ( 8 ) Ibid.. DD. 329-31. 4.3 3X98,3 1.7 35598 3 (1.7/1.6)~11.5~ i9) Ibid., 355. = 35710..1 (10) I b i d . , p. 359. 3Iean extrapolated value 35710 4 I0 . 5 ( 1 1 ) Lingane, J. J., J . Am. C‘hem. Soc., 6 7 , 1916 (1945). Expected final reading 33712 (12) Lingane, ,J. J., Swain, C. G., and Fields, M.,I h i d . , 65, 1348 Error, % -0.023 (1943). (13) MacSevin, W. M., and Baker, B., . ~ N A L .CHEX.,24, 986 (1952). (14) Meites, L., I b i d . , 24, 1618 (1952). (15) Page, J. A . , Ph.D. thesis, Harvard University, 1954. of this time, and washing, drying, and weighing of a solid elec(161 PzebellBdy, L., and Soniogyi, Z., Z . anal. Chem., 112, 313 (1938j.
+
+ + +
trode were entirely eliminated. Moreover, the total time required could be decreased considerablJ by employing an extrapolation method for estimating the last few per cent of the quantity of electricity consumed in an electrolysis. This technique, n hose theoretical foundation is identical with that of the MarSevin and Bahcr procedure ( 1 3 ) , is illustrated by
p:
RECEIVED for review October 1 1 , 1964. .4ccepted April 18, 195.5. Presented before the Division of Analytical Chemistry a t the 126th Meeting of the A h i ~ ~ r c CHEMICAL . 4 ~ QOCIETT, S e w York. September 1954. Contribution 1255 from Department of Clieniistry, Tale Uni\-ersity, N e x Haven, Conn.
High Frequency Combustion-Volumetric Determination of Carbon in Metals EDWARD L. SIMONS, JOHN E. FAGEL, JR., EARL W. BALIS, and LEONARD P. PEPKOWITZ G e n e r a l Electric Co., Schenectady,
N. Y.
An examination has been made of the variables present in the high frequency combustion-volumetric method for the determination of carbon in metals, and methods of controlling or correcting for them are discussed. The experimental work was done with the commercially available Lindberg equipment. The standard deviation for a single determination has been established as one division of the Lindberg gas buret scale, which corresponds to 0.005% carbon for a 1-gram sample when the gas is measured at 20” C. and 760 mm. of mercury.
T
HE convenience of high frequency induction heating devices for the determination of carbon in metals arises from the fact t h a t they permit rapid combustion of the sample in a total volume of oxygen (about 500 cc.) which is small in comparison with the volumes used in more conventional combustion equipment. It therefore becomes possible to substitute a rapid volumetric anal) sis of the combustion products for the gravimetric determination of carbon dioxide generally employed. A previous publication (6) described a precision determination of carbon in metals using a modified Lindberg high frequency
