Errors of Glass Electrodes in Certain Standard Buffer Solutions at High Discrimination

W. H. Beck, A. E. Bottom, and A. K. Covington Department of Physical Chemistry, School of Chemistry, University of Newcastle upon Tyne, England

Small errors of 0.005-0.020 in pH have been found when a representative selection of glass electrodes has been directly compared with the hydrogen electrode in cer- tain buffer solutions. The error increases with de- crease in the molality of the buffer constituents but appears to be independent of cation (Na+, K+, or NMe4+), of the presence of chloride, and of the total ionic strength. This observation is of importance when a discrimination of better than 0.02 is required in pH measurements. The error of 0.003-0.005 pH unit found in 0.025 equimolal disodium hydrogen phosphate- potassium dihydrogen phosphate buffer solution indicates its unsuitability as a primary standard for glass electrode measurements of the highest accuracy. The same is probably true of the phthalate buffer.

IN WORK REPORTED ELSEWHERE, a systematic study of the be- havior of representative commercial glass electrodes in acid ( 1 , 2 ) and alkaline solutions (3) has been made with particular reference to the time variation of the potential. In the course of this and other studies with glass electrodes it was observed that small errors of 0.005-0.020 pH unit were obtained in cer- tain buffer solutions. This paper reports a detailed appraisal at high discrimination of the performance of glass electrodes in buffer solutions of pH 1-9.2.

The only method of checking the hydrogen-ion response of glass electrodes, which does not involve assumption of values for activity coefficients or of the constancy of liquid junction potentials, is by direct comparison with the hydrogen gas elec- trode. The emf of the cell I :

I

is invariant of the pH and composition of the solution X if both glass and hydrogen electrodes are functioning perfectly as hydrogen-ion responsive electrodes. Precautions are neces- sary to ensure that the hydrogen gas electrode is functioning correctly-for example, that the solution X is not reduced at the platinum substrate. For this reason in the present work a third electrode has been introduced into cell I as a check on the hydrogen electrode. If solution X already contains chloride ion or chloride is added, then the silver-silver chloride elec- trode can be used as third electrode. Measurements between this and the hydrogen gas electrode, that is, measurements of cell I1 :

I1

Pt, Hz I X I glass electrode

Pt, Hz I X, C1- I AgCl I Ag

furnish values of paHycl, which is defined by (4):

PaHYCl = -log mH+YH’YCl- =

(E - E”)/k + log mcl- (1)

(1) W. H. Beck, J. Caudle, A. K. Covington, and W. F. K. Wynne-

(2) W. H. Beck, J. Caudle, and A. K. Covington, unpublished

(3) W. H. Beck, P. J. Buck, and A. K. Covington, unpublished

(4) R. G. Bates and R Gary, J. Res. Natl. Bur. Std., 65A, 495

Jones, Proc. Chem. SOC., 1963, p 110.

work, 1963.

work, 1966.

(1961).

where m refers to molality, y to activity coefficients, k = (RT In 1O)/F, and E” is the standard emf of cell 11. Using the Bates-Guggenheim convention (5) for ycl, paH, or pH (S) values have been established for certain buffer solutions (6) leading to the National Bureau of Standards pH scale.

Nearly all the work at the National Bureau of Standards, summarized by Bates (6), has involved the use of the hydrogen electrode in cell I1 and in the operational cell I11

Pt, Hzl X I Sat. KCll HgzCIzI Hg I11

which has been used for checking the internal consistency of the NBS pH scale which has five primary standards (7, 8). Very little work has been done in this connection with the glass electrode. Now that pH meters readable to 0.001 pH unit are available commercially, and with the definition of pH(S) values to the same precision following the adoption of the Bates-Guggenheim convention (5), a check on the reliabil- ity of glass electrodes at this discrimination becomes necessary. This is an entirely different problem from that of the interpre- tation of a measured pH in terms of hydrogen-ion activity or concentration, where the uncertainty even under favorable conditions remains at least i 0.02 pH unit (9,10).

There are three methods of bringing about a change in the pH and composition of the solution X in contact with the glass and hydrogen electrodes:

(a) by addition of a small quantity of concentrated solution to the stirred solution X. This could be described as a titra- tion technique. To ensure that the hydrogen gas electrode responds quickly, the added solution must be presaturated with hydrogen gas.

(b) by a flow system and taps, so that either of two (or more) solutions can be made to flow over the glass electrode surface. Separate reference electrodes must be provided in each solu- tion flow-line.

(c) by transfer of the glass electrode between two solutions each containing a pre-equilibrated reference electrode.

Although techniques (a) and (b) are preferable in that fea- tures associated with the removal of the glass electrode from solution-and the disruption of high resistance electrical cir- cuits thereby, are avoided-technique (c) has been adopted here because it is that used in all (except on-line) pH measure- ments. Use of technique (b) is essential when the true speed

( 5 ) R. G. Bates and E. A. Guggenheim, Pure Appf. Chem., 1 , 163

(6) R. G. Bates, “Determination of pH,” Wiley, New York, 1964,

(7) R. G. Bates, G. D. Pinching, and E. R. Smith, J . Res. Natl. Bur. Srd., 45, 1418 (1950).

(8) M. Paabo and R. G. Bates, unpublished work quoted in ref. (6) P 87.

(9) G. Mattock and D. Band in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., Arnold, London; Dekker, New York, 1967, p 38.

(10) “Specification for pH Scale,” British Standards Institution Specification 1649, 1961.

(1960).

pp. 75-88.

VOL. 40, NO. 3, MARCH 1968 501

Table I. Details of Glass Electrodes Used Tfm Elec- trode No.

1

3

4

6

19

22

23

24

25 27 28 29

30

31

32

Manufacturer Electronic Instruments,

Richmond, England Radiometer, Denmark

Electronic Instruments

Corning Instruments, Medfield, Mass.

Corning Instruments, Medfield, Mass

Jena Glaswerk, Mainz,

Electronic Instruments

Jena Glaswerk, Mainz,

Radiometer, Denmark Electronic Instruments Electronic Instruments Sargent-Jena, Chicago,

Radiometer, Denmark

Germany

Germany

111.

Beckman, Fullerton,

Sargent-Jena, Chicago, Calif.

Ill.

Type No. GFH33

242C

GHS33

476020

476020

HA9401

GG33

N9000

202c GG33 GG33

15c 202B

41263

HTA

U530050-

530056-10

Description and comments

Flat headed, 0-1 1

Flat headed, 0-12

All purpose, 0-14

Triple purpose but with 0 . h HCl filling 0-14 pH

Triple purpose, 0-

pH, 0"-50" C

pH, 10"-60" C

pH, 10"-140" C

14 pH, -5"- loo0 c

High alkaline, 1-14 DH, 0"-70' C

Standard, 1-10 pH,

Large bulb (30 mm) (obsolete)

(see above) (see above)

70" C

C

15"-80" C

10"-45"C

0-12 pH, 0"-60" C

1-14 pH, - 10"-

0-14 pH, 20"-60"

Type E2 0-14 pH,

High temperature, high alkaline 1- 14 pH, 20"-120° c

of response of the glass electrode to a stepwise change in p H is being studied (11-13).

Mattock (14) considers that a discrimination to 0.002 pH unit is possible with a glass electrode cell only if very great care is taken in all aspects of the measurement. Covington and Prue (15) have demonstrated how even higher precision can be obtained with low resistance (< 1 megohm) electrodes and Zielen (16) has carried out some similar studies with high re- sistance electrodes. Additional problems are encountered (1-3) with high resistance electrodes. One factor of prime importance in technique (c) is the method of treatment of the electrode between immersion in the two solutions, Inter- mediate swabbing with cotton waste or tissue (16,17), washing with distilled water and wiping dry (1 7), or washing with the second solution (15) have been advocated. Only the last technique has been found satisfactory in the present studies.

EXPERIMENTAL

Table I gives particulars of the commercial glass electrodes studied which are representative of those obtainable in Europe and the United States. Electrodes 25, 27, and 28

(11) A. Distkche and M. Dubuison, Rev. Sci. Znstr., 25, 869 (1954). (12) M. W. Geerlings, "Plant and Process Dynamic Character-

istics," Butterworths, London 1957, p 101. (13) G. A. Rechnitz in "Glass Electrodes for Hydrogen and Other

Cations," G. Eisenman, Ed. Arnold, London, Dekker, New York 1967, pp 339-42.

(14) G. Mattock in "The Glass Electrode," G. Eisenman, R. Bates, G. Mattock, and S. M. Friedman, Eds., Interscience, New York, 1966.

(15) A. K. Covington and J. E. Rue, J. Chem. SOC., 1955, p 3696. (16) A. J. Zielen, J. Phys. Chem., 67, 1474 (1963). (17) G. Mattock, "pH Measurement and Titration," Heywood,

London, 1961, pp. 249-51.

f-7 I !

Figure 1. Three-compartment cell used for comparison of glass electrodes directly with the hydrogen electrode (cell I) and for measurements of cell I1

were new for this work; others had been used previously in studies in this laboratory and numbers 29-32 elsewhere (18). All electrodes had originally been conditioned in disrilled water before use. When not in use they were stored in dis- tilled water. Electrodes were mounted in stoppers machined from 2-inch-diameter polyethylene rods to fit the ground- glass tapers (B45) on the electrode vessel (Figure 1). The stems of the electrodes were coated with paraffin wax to sup- press electrical leakage and render the surface hydrophobic, thus facilitating the washing procedure on transfer between solutions.

A three-compartment electrode vessel as shown in Figure 1 was used for measurements on cells I and 11. Taps which were lightly greased at the top and bottom of their barrels allowing electrical contact to be made by an annular film of solution, remained closed even during measurements, Six cells were placed side by side in an air thermostat giving temperature control a t 25.0' C in the solution to better than 0.05 O C. The inside of the thermostat was lined with grounded aluminum sheet. During measurement the potential of a cell was opposed by an almost equal voltage from a po- tentiometer (Tinsley and co . Ltd., Type 4025) so that a dif- ference of less than 10 mV was fed to the input of a vibrating condenser electrometer (Electronic Instruments Ltd., Type 1086A), amplified, and the output displayed on a Honeywell- Brown 10-inch potentiometric recorder. Careful attention to grounding and screening of the circuit wiring was required. A specially constructed screened, switch box containing a desiccant was used to facilitate introduction of the cell to be measured into the circuit. The hydrogen and silver-silver chloride electrodes, prepared by standard techniques (15, Is), were allowed 1 hour to reach equilibrium before commenc- ing work with glass electrodes. Wash solutions were stored in plastic wash bottles in the air thermostat. Optimum washing time was 10 seconds. Analytical grade reagents, where possible, and deionized water were used for the prepa- ration of the solutions.

Transfers were made from O.lm hydrochloric acid solution into one of a series of weak acid buffer systems and then back to O.lm HCl. In later experiments this solution was replaced by O.lm sulfuric acid in which case the mercury- mercurous sulfate electrode was used as third electrode (19, 20).

(18) A. K. Covington, M. Paabo, R. A. Robinson, and R. G. Bates,

(19) W. H. Beck, J. V. Dobson, and W. F. K. Wynne-Jones, Trans.

(20) A. K. Covington, J. V. Dobson, and Lord Wynne-Jones, Ibid.,

ANAL. CHEM., in press.

Faraday Soc., 56,1172 (1960).

61,2057 (1965).

502 0 ANALYTICAL CHEMISTRY

Table 11. Data on Buffer Solutions Added chloride

Buffer molality, molality, Ionic Emf of Buffer mole kg-l mole kg-1 strength (I) cell 11, mV

HCl 0.1000 0 0.1000 352.7 HzS04 0.1000 0 . . . 738.0" Potassium tetraoxalate 0.1000 0.1000 0.240 319.4

0.5000 0.1Ooo 0.177 388.6 0.1000 0.1OOo 0.118 417.3

Glycine-HCI (equimolal) 0.1000 0 0.100 435.4 0.5000 0.5000 0.100 437.3 0.0100 0.0900 0.100 437.2

Potassium hydrogen 0.1000 0.1000 0.206 520.9 phthalate 0.0500 0.1000 0.153 521.4

0.0100 0.1000 0.110 523.8 Disodium hydrogen 0.0500 0.1000 0.300 688.3

phosphate-potassium 0.0250 0.1Ooo 0.200 690.5 dihydrogen phosphate 0.0125 0.1000 0.150 692.0 (equimolal) 0,0025 0.1000 0.110 693.0

Tris-HC1 (equimolal) 0.1000 0 0.100 773.4 0,0500 0.0500 0.100 773.5 0.0100 0.0900 0.100 713.7

Borax 0.0500 0.1000 0.200 831.9 0.0100 0.1OOo 0.120 828.3 0.0050 0.1000 0.110 827.8

Against mercury-mercurous sulfate reference electrode.

PaHYCl 1 ,204

1.655 1.811 2.296 2.602 2.634 2.633 4.041 4.056 4.096 6.871 6.914 6.939 6.956 8.315 8.317 8.320 9.304 9.243 9.235

. . .

--log Y C l

0.109

0.144 0.131 0.116 0.109 0.109 0.109 0.138 0.126 0.113 0.154 0.137 0.125 0.113 0.109 0.109 0.109 0.137 0.116 0.113

. . .

PaH 1.095

1.511 1.680 2.180 2.493 2.525 2.524 3.909 3.930 3.983 6.123 6.177 6.814 6.843 8.206 8.208 8.211 9.167 9.127 9.122

. . .

RESULTS AND DISCUSSION

In Table I1 are collected data relevant to the buffer solutions employed. For the potassium tetraoxalate and potassium hydrogen phthalate, the ionic strength can be calculated from the known dissociation constants of the acids concerned (21, 22). For the equimolal phosphate buffer the actual ionic strength is found to be almost identical with the stoichiometric ionic strength. For glycine and Tris buffers there is no change in ionic strength on ionization. The fifth column shows the emf of cell 11. The standard emf of this cell was determined as recommended by measurement of 0.01m HCI (23) and found to be 222.3 mV in agreement with the value given by Bates and Bower (24). The paH values shown in the last column were derived from paHyC1 values given by Equation 1 using the Bates-Guggenheim convention (5 ) to obtain the values of -log ycl shown in the penultimate column. The paE values agree well with published data where direct comparison is possible.

Table I11 shows the error in pH units on transferring elec- trodes between 0 . h HCI and various buffer mixtures. The value tabulated refers to the change in emf expressed in pH units on change of solution in cell I from 0 . h HCl to the buffer solution of interest, which was identical with the change in emf on the reverse transfer. The time in which the reading became steady varied from electrode to electrode but was al- ways smaller for the change buffer to HCl than for HC1 to buffer. The sluggish response of some electrodes, which is partly associated with factors mentioned earlier, was described previously ( I ) as feature A. The error calculated from the steady emf readings was in all cases identical with that ob-

(21) V. E. Bower, R. G. Bates, and E. R. Smith, J . Res. Nail. Bur.

(22) W. J . Hamer and S . F. Acree, Zbid., 32, 215 (1944). (23) R. G. Bates et a / . , J . Chem. Phys., 25,361 (1956). (24) R. G . Bates and V. E Bower, J. Res. Nail. Bur. Std., 53,283

Std., 51, 189 (1953).

(1954).

tained by extrapolating to the time of transfer ignoring feature A (I, IS',]@.

It may be concluded that there is no error in the tetraoxalate or glycine-HC1 buffers-i.e., below pH 2.5. Above this pH, the error is approximately independent of pH. An error of 0.002 pH unit is considered to be within the experimental un- certainty (*O.lmV). Electrode No. 23 is an exception, but this electrode showed variable performance during the com- plete series of experiments. It had been extensively used in other work ( 3 ) and was presumably near the end of its useful life. It was noticeable that its performance improved after several weeks' storage in deionized water.

Errors were noted in the four remaining buffer solutions. These are dependent on the buffer component molality, in- creasing markedly as it is decreased. It is known that variable results can be obtained with the glass electrode in unbuffered solutions (25) and the effect may be related. The results were unaffected by stirring the solution. The errors are inde- pendent of total ionic strength and, it may be inferred, of cat- ion composition. To confirm this, potassium chloride added to the Tris-HC1 buffer system was replaced by tetramethyl ammonium chloride (Me4NCI). Apart from electrode No. 24 the errors obtained were closely similar. Like No. 23, elec- trode 24 was an old electrode which had been extensively used in other studies; its behavior can be attributed to a slight re- sponse to K+ at pH 8.2.

TO test the possibility that the errors were the result of carryover of hydrochloric acid into the buffer solution, the effect of which would be greatest the lower the concentration of the buffer, experiments were carried out in which the trans- fers were made from and to O.lm HzS04, with the results shown in Table IV. Sulfuric acid was chosen because Schwabe, Dahms, Nguyen, and Hoffmann (26) have shown,

(25) G. A. Perley, ANAL. CHEM., 21,559 (1949). (26) K. Schwabe, H. Dahms, Q. Nyugen, and G . Hoffmann, Z .

Elektrochem., 66, 304 (1962).

VOL. 40, NO. 3, MARCH 1968 503

Table 111. Transfer from O.lm HCl into Buffers Containing Chloride ( 0 . h Total) Errors in pH units

Buffer Electrode No. Buffer & chloride molality 1 3 4 6 19 22 23 24 25 27 29 30 Potassium te- 0.1 o.Oo0 o.Oo0 o.Oo0 . . .

0.01 . . . o.Oo0 . . . o.Oo0 o.Oo0 . . . . . . . . . . . . . . . . . . . . . Glycine + HCI 0 .1 O.Oo0 O.Oo0 O.Oo0 O.Oo0 O.Oo0 O.Oo0 0.012 O.Oo0 . . . . . . + KCI 0.05 0.002 O.Oo0 O.Oo0 O.Oo0 0.OOO O.Oo0 0.014 0.002 . . . . . . . . . . . .

Potassium hydro- 0.1 . . . 0,002 0.005 o.Oo0 o.Oo0 0.002 0.012 o.Oo0 0.002 0.005 0.002 gen phthalate 0.05 . . . 0.003 0.010 0.002 0.003 0.003 0.014 0.002 0.002 0.005 0.003

1:l Phosphates + 0.05 0.005 0.003 . . . . . . 0.004 0.003 0.003 0.022 0.002 0.003 0.007 . . .

0.0025 0.030 0.017 0.033 0.024 0.013 0,029 0.035 0.044 0.012 01022 o:oi7 ...

. . . . . . . . . traoxalate o.Oo0 * . . o.Oo0 o.Oo0 0:oao 0:002 o.Oo0 0.002 0 . . . + KCl

0.01 0.002 O.Oo0 O.Oo0 0.002 O.Oo0 O.Oo0 0.015 0.002 . . . . . . . . . . . .

+ KCI 0.01 . . . 0.007 0.015 0.007 0.007 0.008 0.020 0.005 . . . 0.005 0.010 0.007

KC1 0.025 0.005 0.003 0.010 0.006 0.003 0.005 0.010 0.022 0.003 0.007 0.007 , . . 0.0125 0.005 0.005 0.017 0.012 0.007 0.008 0.015 0.024 . . .

Tris +HCl + 0.1 o.Oo0 0.000 o.Oo0 O.Oo0 0 . m 0.002 0.012 0.002 . . . KCl 0.05 0.012 0.002 0.005 0.003 0.002 0.003 0.020 0.031 . . . . . . . . .

0.01 0.022 0.005 0.019 0.007 0.005 0.019 0.037 0.060 . . . . . . . . . . . . Tris +HCl + 0.1 0.002 O.Oo0 o.Oo0 o.Oo0 0.002 0.012 o.Oo0 . . . . . . . . .

Borax + KCI 0.05 0.002 0.003 0.002 . . . . . . . . . . . .

Me4NCl 0.05 0.008 0.002 0:&7 0.003 0.002 0.005 0.012 0.003 . . . . . . . . . . . . 0.01 0.015 0.002 0.025 . . . 0.008 0.022 0.029 0.017 . . . . . . . . . . . .

0.01 . . . 0.003 . . . 0.010 0.005 . . . . . . . . . . . . . . . . . . . . . 0.005 . . . 0.010 . . . 0.031 0.012 ... 0.033 . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

- 31

. . .

. . .

. . . 0.002 0.003 0.007 0.003 0.003

o:oi4

. . .

. . .

. . .

. . .

32

O.Oo0 . . .

. . . 0.002 0.002 0.005 0.003 0.005

0.020 . . .

. . .

. . .

. . .

. . . ~ ~ ~~

Table IV. Transfers from O.lm H$04 to Buffers with and without Added Chloride Errors in pH Units

Buffer Molality of molality, addition, Electrode numbers

Buffer mole kg-1 mole kg-1 1 3 19 22 23 28 Potassium hydrogen 0.1Oo0 0 . . . O.Oo0 . . . . . . O.Oo0 0.OOO

phthalate 0.0500 0 . . . O.Oo0 . . . . . . O.Oo0 O.Oo0 0.0100 0 . . . O.Oo0 . . . . . . 0.005 0.002 0.0100 0.1 KCI . . . O.Oo0 . . . . . . 0.005 O.Oo0 0.0100 0.1 KC104 . . . O.Oo0 * . . . . . 0.002 O.Oo0 0.0500 0 .1 KCl 0.003 0.003 0.005 0.003 . . . . . . 0.0250 0.1 KCI 0.005 0.005 0.005 0.005 . . . . . .

Equimolal phosphates

0.0125 0 .1 KCI 0.0025 0.1 KCI

0.005 0.005 0.005 0.005 . . . . . . 0.020 0.020 0.012 0.010 0.014

0. 0025 0.1 KClOi . . . 0.010’ . . . . .. 0.014 0.007 0.0500 0 . . . O.Oo0 . . . . . . 0.002 0.002

. . . . . . . . . 0.004 0 O.Oo0\ E:::) 0.003)

0.0250 0.0031

0,0025 0 ... 0.010 ... ... 0.009 0.010

using radio tracers, that whereas chloride ion is absorbed on the glass surface from acid solution, sulfate and phosphate are not. I t was concluded that this explanation could not account for the observed errors, although some small contribution might arise from this source.

To check the unlikely possibility that the effect was due to the addition of chloride to the buffer systems, some transfers were made (Table IV) between 0.1~1 HzS04 and chloride free solutions or solutions to which O.lm KC104 was added. Electrode No. 28 was newly introduced for this experiment and had not been used previously in chloride-containing solutions. These experiments confirmed that there was no effect of chloride addition to the buffers nor of total ionic strength.

The observed errors could be important in certain pH mea- surements where high discrimination is important. The error is negligible provided the buffer concentration is high enough.

The buffer concentration selected for the NBS standard buffers is a compromise: too low a concentration will have poor buffer properties, too high a concentration presents difficulties in adopting a reliable value for the single ion activity coefficient of the chloride ion. The results of Tables I11 and IV suggest that the 0.025 equimolal phosphate buffer is too dilute for use as a primary standard when employing glass electrodes. A similar conclusion may be made about the phthalate buffer but more accurate tests are required to substantiate this.

The error may be significant in studies such as that of King and Prue (27) who have used cell 11, with a glass electrode re- placing the hydrogen electrode, to determine the pK values of benzoic, phenylacetic, and P-phenylpropionic acids. The technique involves making measurements at different buffer

(27) E. J . King and J. E. h u e , J . Chem. Soc., 1961, P 275.

504 ANALYTICAL CHEMISTRY

dilutions and extrapolating to obtain the thermodynamic dis- sociation constants. While their values for the first and last mentioned acids were in good agreement with other data, the value for phenylacetic acid was lower than previously reported (28, 29) values by 0.006. Recently, however, Smolyakov and Primanchuk (30) have reported a value from conductance measurements slightly lower than the result of King and Prue (27). Further studies are required of the possible effect of small errors of the glass electrodes on the extrapolation to obtain pK.

The results presented in Table I1 for the emf of cell I1 sug- gest a method for checking the performance of glass electrodes in cells without liquid junction without the necessity of using the hydrogen electrode. The difference between the emf given

(28) J. F. J. Dippy and F. R. Williams, J . Chem. SOC., 1934, p 161. (29) G. H. Jeffery and A. I. Vogel, Ibid., p 166. (30) V. S. Srnolyakov and M. P. Prirnanchuk, R u m J . Phys. Chem.,

40, 493 (1966).

in Table 11, column 5, for any two buffer solutions is the theoretical emf change for a perfect glass electrode transferred between two chloride-containing buffer solutions, each con- taining a silver-silver chloride reference electrode. Any deviation from this value amounts to an error of the glass electrode, which can be attributed to one of the solutions if there is good reason to believe that there is no error in the other. It would be advisable to choose the highest buffer molality given in Table 11. This method is considered supe- rior to methods involving cells with liquid junction. A some- what similar method but using high ionic strength solutions has been suggested recently by Light and Fletcher (31).

RECEIVED for review Oct. 23, 1967. Accepted Nov. 24, 1967. One of us (A.E.B.) thanks the Science Research Council for the award of a Research Studentship.

(31) T. S . Light and K. S. Fletcher, ANAL. CHEM., 39, 70 (1967).

Derivative Chronopotentiometry of Multicomponent Systems P. E. Sturrock, W. D. Anstine, and R. H. Gibson1 School of Chemistry, Georgia Institute of Technology, Atlanta, Ga. 30332

The theory and technique of derivative chronopotenti- ometry are extended to systems containing two or more electroactive species. Theoretical equations, appli- cable to reversible electrode processes, are derived and experimentally verified. As in most voltammetric methods, the sensitivity is limited by the double-layer charging current. The feasibility of standard addition procedures is shown, even in cases where the initial solution contains such a low concentration that a significant portion of the current is used in charging the double layer.

IN PREVIOUS PAPERS (1-3) the theory and instrumentation for derivative chronopotentiometry, as well as applications to systems of one electroactive species, have been reported. In this paper the relationships between the minimum of the dE/dt function and the transition times are derived for systems containing more than one electroactive species.

Delahay and Mamantov (4) reported the relationship be- tween concentrations and transition times for two consecutive electrode processes. Reilley, Everett, and Johns (5 ) ex- tended the relationship to multiple consecutive electrode processes. The potential-time relationships in such systems have not been reported previously but follow readily from application of the response function additivity principle of Murray and Reilley (6).

Carolina at Charlotte, Charlotte, N. C . Present address, Department of Chemistry, University of North

28205.

(1) P. E. Sturrock, J. Electroanal. Chem., 8, 425 (1964). (2) D. G. Peters and S . L. Burden, ANAL. CHEM., 38,530 (1966). (3) P. E. Sturrock, Gregg Privett, and A. R. Tarpley, J. Electro-

(4) Paul Delahay and Gleb Mamantov, ANAL. CHEM., 27, 478

( 5 ) C . N. Reilley, G. W. Everett, and R. H. Johns, Zbid., 27, 483

(6) R. W. Murray and C. N. Reilley, J. Electroanal. Chem., 3, 182

anal. Chem., 14, 303 (1967).

(1955).

(1955).

(1962).

Using this principle, the bulk concentration of the jth electroactive species, Co,j*, is given by Equation 1.

During thejth step of the chronopotentiogram-Le., for 3 j -1 c Tm > t > Tm

m = l m = l

[t"2 - (5 m - 1 T m ) ' / z ] ( 2 )

where Co,j and C,,5 are the surface concentrations of the oxidized and reduced forms of the jth electroactive component. The initial bulk concentration of the reduced form, C,,5* is assumed to be zero. Solving Equations 1 and 2 for Co,jr and C r , j and substituting into the Nernst equation gives the potential time relationship for the jth step of the chronopo- tentiogram.

Equation 3 is valid, provided the j th couple is reversible. However, reversibility of preceding electrochemical processes is not necessary.

Differentiating Equation 3,

X dE -RT - = - d t 2n5Ft1l2

VOL. 40, NO. 3, MARCH 1968

(4)

505