VOLTAMMETRY n'ITH STATION.4RT MICROELECTRODE
1061
VOLTAMMETRY WITH STATIOX'ARY MICROELECTRODES OF PLATISULI WIRE1 H. A . L A I T I S E S 2 AND I. M. KOLTHOFF School of Chemzutry, Znstztute of Technology, Universzty of Minnesota, Mznneapolas, Mannesota Receaved December 16, 1940
We introduce the word voltammetry to designate the part of electrochemistry which deals quite generally with the determination and interpretation of current-voltage (c.-v.) curves. When working with the dropping-mercury electrode, the words polarography (self-registering apparatus) or polarometry (manual apparatus), which were introduced by Prof. J. Heyrovsky in Prague and which are in common use, are synonymous with voltammetry. In the present paper we deal nith the use of a platinum-wire microelectrode as an indicator electrode in voltammetry. By indicator electrode we mean that the potential of the electrode varies with the E.M.F. applied to the electrolysis cell, and the current is determined entirely by the phenomena occurring a t the particular electrode. Quite generally, a depolarized electrode is used as a reference electrode, the potential of the latter remaining practically constant when small currents flow through the cell. Various investigators have reported current-voltage curves with welldefined regions of diffusion current, obtained in electrolysis experiments using stationary electrodes in unstirred solutions. As early as 1897, Salomon (17) described current-voltage curves with solutions of silver, mercurous, and cupric ions, using stationary electrodes of the respective metals. Although definite diffusion currents were observed, the conditions of diffusion near the electrodes were not well defined, and the curves are difficult to interpret. Glasstone and Reynolds (3, 6) found a proportionality between the diffusion current and concentration for the electroreduction of potassium ferricyanide, ferric alum, potassium permanganate, quinone, cadmium ions, and cupric ions, and for the electrooxidation of potassium ferrocyanide, ferrous ions, iodine, hydroquinone, and hydroxylamine. These experiments were performed using a small platinum-wire electrode in unstirred oxygen-free solutions at room temperature without temperature control. Wilson and Youtz (18) studied the oxidation of ferrous iron 1 This article is based upon a thesis submitted by H. A . Laitinen t o the Graduate Faculty of the University of Minnesota in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1940 * Present address: Department of Chemistry, University of Illinois, Urbana, Illinois.
1062
H. A. LAITINEK .4ND I. M . KOLTHOFF
to ferric iron, using a cylindrical carbon anode of relatively large area separated by means of a porous cup from the cathode, which was a large hollow carbon cylinder. The concentration of ferrous ions was high (0.03 31 to 0.25 M), and the diffusion currents consequently were much greater than those of Glasstone and Reynolds. Even in this case, the diffusion current was found to be approximately proportional to the concentration of ferrous iron. The measurements reported in the literature are, however, accurate only to about =k5 per cent in the best cases and are not comparable in accuracy with those made with the dropping-mercury electrode. For analytical purposes, an accuracy of hO.5 to =k1 per cent in the current readings is desirable. It was the purpose of the present study to determine the reproducibility of diffusion currents obtained under well-defined diffusion conditions near a platinum-wire microelectrode and to check the proportionality between diffusion current and concentration with a view to possible analytical applications. In a previous study (9) it was mentioned that the diffusion current obtained with the above microelectrode was well reproducible if the current measurement was made after the steady state had been reached. EXPERIMEKTAL
Apparatus The electrical circuit was the same as that used previously (9). I n most experiments, the current was measured by determining the potential drop across the standard 9999-ohm resistance in series with the cell. The walltype galvanometer gave exactly the same results and map be preferred, since the approach to the steady current state may be followed directly and any fluctuations in the current are immediately apparent. A microammeter may also be used for the current meawrements. A \Yeston model 430 meter with a 30-microampere v a l e having divisions of 0.2 microampere was found to be convenient. The platinum-wire microelectrode cell and reference electrode of the type described previously (9, 10) nere uwally used with a large saturated calomel electrode (S.C.E.) or 0.1 S cilver-dver chloride electrode (iigC1) as an esteinal reference electrode. In -ome experiment-, a large pool of mercury \\as used as the second electioly-iq electrode, and the potential of the micioelectrode was determined for each applied E.M.F. against a third reference electrode (S.C.E.) outside of the electrolysis cell. In all figures, the potential of the microelectrode, ieferred to either of the t n o reference electrodes, is plotted against the cuirent. current due to a cathodic (reduction) process a t the microelectrode i. plotted upward as a positive current on the ordinate, while an anodic (o-dation) process at the microelectrode is represented by a negative cmrent plotted donnuard. The
VOLTAMMETRY WITH STBTIONARY MICROELECTRODE
1063
potential is always plotted on the abscissa, with increasing negative values to the right and increasing positive values to the left.
Materials All chemicals and reagents were of “analytical reagent” quality, and conductivity water was used in the preparation of all solutions. The quinone \vas a product of the Eastman Kodak Company; it was resublimed freshly and dried in a desiccator a t room temperature. Each solution was prepared freshly by weighing the dry quinone and standardizing the solution by iodometric titration with sodium thiosulfate. The dilute solutioils were freshly prepared at frequent intervals from 0.01 -11 or 0.1 -11 stock solutions.
Technique of measurements The attainment of a steady current state depends upon reaching a state of uniform and reproducible convection in the solution immediately surrounding the microelectrode. It is therefore necessary to perform the experiments in a solution maintained at a constant temperature to avoid thermal convection, and under conditions to prevent any niechanical disturbances such as vibrations from the thermostat stirring motor. The following experiments were run with the cell in a water thermostat regulated to =t0.01O , with the stirrer mounted on wall brackets to prevent vibration. The absence of mechanical disturbances was shown by measuring the diffusion current both with the thermostat stirrer in operation and with it shut off. Identical results were obtained in all cases, whether the stirrer L ~ B Sin operation or not. In most cases, it was necessary to remove the dissolved oxygen of the air from the solutions, since oxygen i.; reduced to hydrogen peroxide on a platinum electrode a t sufficiently negative potentials (see figure 6). In certain cases, such as the oxidation of ferrocyanide or ferrous ions, the removal of dissolved oxygen was unnecessary, since the entire currentvoltage curve occurred in a region of potentials so positive that the reduction of oxygen could not interfere. Commercial tank nitrogen was found to be sufficiently free of oxygen to be used without purification. hstreani of nitrogen was bubbled through the cell solution for about 30 min. ; then it n-as shut off and the solution was allowed to stand until stirring had ceased before the current-voltage curve was determined. .It each value of the applied E.M.F., the electrolysis was allowed to proceed until the current had reached a steady value. In most cases, 2 to 3 min. of waiting was found to be sufficient, although, in certain cases of irreversible electrode reaction, a considerably longer time was required for a steady current state. The applied E.M.F. was carefully and slowly increased to reach the next desired point on the curve, in order to cause a
1064
H. A. LAITINEN AND I. M. KOLTHOFF
minimum of disturbance of the diffusion state near the electrode and to prevent even a momentary discharge of gaseous hydrogen or oxygen on the electrode surface. The current-voltage curves were found to be entirely reproducible in either direction if care was taken to prevent the formation of gas bubbles on the electrode surfacea.
The deposition of metal ions Typical current-voltage curves obtained in the deposition of silver, c o p per, thallous, and lead ions in 0.001 M solutions in 0.1 N potassium chloride (0.1 N potassium nitrate in the case of silver) are shown plotted in figure 1.
POTENTIAL OF MICROELECTRODE, VOLTS (vs. S.CE.)
FIQ.1. Electrolysis of 0.001 M metal ion solutions in 0.1 N solutions of indifferent electrolytes. Curve I, silver; curve 11, copper; curve 111, lead; curve IV, thallium.
A region of constant diffusion current was obtained in each case, followed by a rising current due to evolution of hydrogen. The difference in hydrogen overvoltage on the various freshly deposited metal surfaces is clearly indicated by the differences in the potentials a t which the final unlimited rise in current occurs. It may be mentioned that the nature of the curve of hydrogen evolution is determined not only by the hydrogen-ion concentration and the hydrogen overvoltage of the metal surface, but also by the buffer capacity of the medium, since the discharge of hydrogen ions results a In the case of deposition of metal on a platinum surface, the metal will, of courm, go into solution a t any potential more positive than the null potential of the metal in the solution of its ions, and to this extent the current-voltage curve depends on the direction of change of the applied E . M . F .
1065
VOLTAMMETRY WITH STATIONARY mCROELECTRODE
in a region of comparatively alkaline solution near the electrode surface, unless the solution is well buffered. To test the proportionality between diffusion current and concentration, various concentrations of thallous chloride in 0.1 N potassium chloride I2 10
2
8
W
P
.u4 .4
2
0
-0.5 -0.6
-07
-0.8 - 0 9
-1.0
POTENTIAL OF MICROELECTRODE,
-1.1
-12
-1.3
VOLTS (vs S.C.E.)
FIG.2. Electrolysis of various coiicentrations of thallous chloride in 0.1 A- potassium chloride. Curve I, blank; curve 11, O.ooO2 N TIC1; curve 111, 0.0006 N TICI; curve IV, 0.0012 N TICI; curve V, 0.002 N TICI. TABLE 1 R e l a t i o n between concentration of thallous chloride in 0.1 N p o t a s s i u m chloride a n d d i f f u s i o n current of t h a l l i u m (45°C.) 'd
C
Observed mollrmolu per liter
0 200 0 600 1.20 200
mrcrwmperea
1 50 3 77 6 57 11 15
I
Corrected mlcroamperu
1 24 3 24 6 48 10 53
(6.2) 5.40 5.40 5.26
--
5.35 (average)
were run. The current-voltage curves are shown plotted in figure 2, and the relation between diffusion current (corrected for the residual current given in each curve by the horizontal line preceding the thallium discharge curve) and concentration is shown in table 1.
1066
H. A. LAITINEN AND I. M. BOLTHOFF
It is seen that, except for the smallest concentration of thallous chloride, a satisfactory proportionality between diffusion current and concentration was obtained. T h e oxidation and reduction of systems of which the oxidized and reduced forms are soluble in the liquid phase Examples of this type of application are the oxidation of ferrocyanide and ferrous ions, and the reduction of ferricyanide and ferric ions, etc. Figure 3 shows a set of current-voltage curves obtained in the case of ferrous and ferric iron, both separately and in a mixture. A proportionality
1.2
1.0
08
06
0.4
0.2
0.0 -0.2
POTENTIAL OF MICROELECTRODE, VOLTS (vs S.C.E) FIG. 3. Electrolysis of ferrous chloride and ferric chloride in 0.5 N hydrochloric acid. Curve I, 0.002 M FeCla; curve 11, 0.001 111 FeCL, 0.001 kf FeCls; curve 111, 0.001 M FeClz.
between diffusion current and concentration was found, although only two concentrations of ferrous and ferric ions were investigated. X set of current-voltage curves for various concentrations of ferrocyanide ions in 0.5 N potassium chloride is shown in figure 4. The relation between the diffusion current and concentration is shown in table 2. A proportionality was found between diffusion current and concentration of ferrocyanide ions in 0.5 N potassium chloride solution. In 0.1 iV potassium chloride, 5 x 10-8 Ji potassium ferrocyanide gave a diffusion current which was 4 per cent higher than in 0.5 N potassium chloride, while iM potassiuni ferrocyanide, the effect of changing in the case of 1 X
VOLTAMMETRY WITH STATIONARY .MICROELECTRODE
1067
salt concentration was only 1.5 per cent. This apparent discrepancy is to be expected, since in the latter case the effect is to be attributed mainly to a decrease in the diffusion coefficient of the ferrocyanide ion with increasing
POTENTIAL OF MICROELECTRODE, VOLTS (vs. AgCI) FIG.4. Electrolysis of various concentrations of potassium ferrocyanide in 0.5 N potassium chloride. Curve I, blank; curve 11, 0.001 .lI KIFe(CiY)s; curve III,0.003 .TI IC4Fe(CS)6;curve IV, 0.005 .?I K,Fe(CS),.
TABLE 2 R e l a t i o n betu'een concentration of potassium .ferrocyanide in 0.5 X potassium chloride a n d diffusion current of ,ferrocyanide (25°C.) K millimoles per Itfer
1.00 2.00 3.00 5.00
micrwmperea
i
~
1.97,2.00*
4.05 6.15 10.15;10.53*
i
= id/C
microamperes
1.95 -1.03 6.13 10.13
(1.95) 2.02 2.06 2.03 __ 2.04 (average)
* In 0.1 N potassium chloride. salt concentration, while in the case of 5 X X potassium ferrocyanide in 0.1 N potassium chloride, an added supply of ferrocyanide ions is provided by migration.
1068
H, A. LA1TINT)N AND I. Ed. KOLTHOFF
Figure 5 shows typical current-voltage curves obtained for the electroreduction of potassium ferricyanide and the electrooxidation of potassium ferrocyanide in an excess of potassium chloride. The relation between diffusion current and concentration of ferricyanide ions is shown in table 3.
I2
a $
4
Le
f 0 20
-4
.-
-8
3
-I 2
-16
0.1
0.8 0.6
0.4 a2 0.0- a2 -0.4-0.6 -0.8-1.0
POTENTIAL OF MICROELECTRODE,
id
C Observed millirnole~pev liter
mimoamperes
1.00 2.00 5.00
2.25
I
1
VOLTS
(US.A@)
K Corrected
-
id/C
mimoamgarsd
2.20
2.20
2.26 12.01
2.39 2.28 (average)
The reduction of oxygen and of quinone and the oxidation of hydroquinone were chosen as examples of reactions a t the platinum microelectrode involving the oxidation or reduction of unionized solutes. Current-voltage curves for oxygen reduction in various buffer solutions
VOLTIMMETRY WITH STATIONARY MICROELECTRODE
1069
and in 0.01 ,V sodium hydroxide in 0.1 Ai potassium chloride saturated with air are shown in figure 6. It is striking that, although the electrode reaction
O2
+ 2e + 2Hf
-
H202
involves hydrogen ions, there is no pronounced pH effect on the potential at which oxygen reduction begins or on the shape of the current-voltage curve. The small differences in the shapes of the curves are probably to be attributed to specific effects of the ions constituting the various buffer systems. A similar behavior is found in the cme of the dropping-mercury electrode (II), where hydrogen ions do not appear to take part in the poten-
POTENTIAL OF MICROELECTRODE,
VOLTS
(US
AqCI)
FIG.6. Reduction of oxygen in various air-saturated solutions. 0 , phthalate buffer, pH 3.0; A , acetate buffer, pH 4.7; 0 ,borate buffer, pH 9.0; 0 , O . O l h' KaOH, 0.1 N KC1, pH 12.
tial-determining reaction, but changes in the shape of the reduction curve are found if two different buffer systems of the same pH are investigated. That the reduction product of oxygen on a platinum surface is hydrogen peroxide was shown by running an electrolysis experiment with two large platinum electrodes in a potassium nitrate solution in a cell with the anode and cathode compartments separated by an agar gel, and passing a current of 100 microamperes through the cell for 3 hr. Tank oxygen was bubbled through the cathode compartment during the electrolysis. The presence of hydrogen peroxide in both compartments was shown by adding a portion of each solution to an acidified solution of potassium iodide con-
1070
H. A. LAITINEN AND I. M. KOLTHOFF
taining soluble starch as an indicator. The presence of hydrogen peroxide in the cathode compartment was due to the reduction of oxygen. In the anode compartment, hydrogen peroxide 11 as probably formed by the oxidation of hydroxyl ions to free hydroxyl, OH, two molecules of which combined to form a molecule of hydrogen peroxide. This mechanism has been suggested by Klemenc (8) and by Glasstone and Hickling (4). A typical set of current-voltage curves for the reduction of quinone and the oxidation of hydroquinone in a phosphate buffer of pR 7.0 is shown in figure 7 . Although well-defined regiom of diffusion current were obtained
-6
1.0
I 0.8
I
1
I
0.6
04
02
POTENTIAL
OF
1
I
0.0 -0.2
MICROELECTRODE,
I
I
-0.4-0.6 VOLTS
(US
-C 3
A9CI)
FIG 7 Electrolysis of quinone and hydroquinone in phosphate buffer, pH 7.0 Curve I, 0 001 31 quinone, curve 11, 0 001 .I1 hydroquinone; curve 111,0.001.If hydroquinone, 0 00094 .If quinone.
for both the oxidation and the reduction process, the shapes of the curves Rho\\ decided abnormalities from those predicted theoretically.
Current-voltage cumes f o r evolution of hydrogen Since the potential region in which current-voltage curves can be obtained with platinum microelectrodes is always restricted in the negative potential direction by the evolution of hydrogen, the electrolysis of solutions of weak and strong acids in appropriate indifferent solutions 1% as investigated. Figure 8 shows current-voltage curves obtained in the electrolysis of 0.001 N hydrochloric acid in 0.1 S potassium chloride, using bright and
VOLT.UdMETRY WITH STATIONARY MICROELECTRODE
1071
platinized platinum microelectrodes of approximately the same geometrical area (projected area). Kell-defined diffusion current regions were obtained in both cases, but the diffusion current was not found to be proportional to the concentration of hydrochloric acid in either cace. The lack of proportionality in the caqe of the bright platinum electrode is shonn by the data given in table 4.
POTENTIAL
OF
MICROELECTRODE, VOLTS (us. S.C. E,)
FIG.8. Electrolysis of 0.001 N hydrochloric acid in 0.1 S potassium chloride. Curve I, platinized platinum electrode; curve 11, bright platinum electrode. TABLE 4 Relation between concentration of hydrochloric acid in 0.1 X potassium chloride and d i f u s i o n current of hydrogen i o n s c
id
ndlimoles per liter
niicroomperen
0. loo 0.500 1.00
1.70 8.00 13 5
l
K = idjC
17.0 16 0 13.5
The evolution of hydrogen on the platinum surface and the conqequent decrease in effective electrode area with increasing current probably account for the decreasing value of the diffusion current constant K nith increasing concentration of hydrochloric acid. A somewhat more steeply rising curve, occurring a t a potential about 0.1 volt more positive, was obtained with a platinized electrode than with the
1072
H. A, LAITINEN AND I. M. KOLTHOFF
bright electrode, clearly indicating a hydrogen overvoltage on the latter. This difference in potential, however, cannot be regarded as a quantitative measure of the overvoltage of the bright platinum electrode, since the platinized electrode has a zero overvoltage only a t the null point, Le., a t zero current. I n the electrolysis of a very weak acid, the diffusion current is determined by the rate of diffusion of the undissociated acid rather than by the diffusion of hydrogen ions. For a given concentration of solution, a weak acid should therefore give a much smaller diffusion current than a strong acid, since the diffusion coefficient of a weak acid molecule in general is much smaller than that of hydrogen ions. This behavior is illustrated in
POTENTIAL OF MICROELECTRODE, VOLTS FIG.9. Electrolysis of acetic acid in 0.1 N potassium chloride. Curve I, 0,001 N CHsCOOH; curve 11,O.OOlN CH,COOH, 0.1 N CHsCOONa; curve II1,O.l N KCl.
figure 9, which shows the current-voltage curves obtained in the electrolysis of 0.001 N acetic acid in 0.1 N potassium chloride, and in 0.1 N sodium acetate and 0.1 N potassium chloride. The diffusion currents obtained were 3.3 and 3.0 microamperes, respectively, as compared with 13.5 microamperes with the same concentration of hydrochloric acid. The current obtained in the presence of a large excess of sodium acetate may be taken as an indication of the rate of diffusion of undissociated acetic acid molecules, since under these conditions the acetic acid is present almost entirely in the undissociated form. The current of 3.3 microamperes obtained in the absence of sodium acetate is partly due to the diffusion of hydrogen ions from dissociated acetic acid.
1073
VOLTAMMETRY WITH STATIONARY MICROELECTRODE
T h e effect of temperature and indi$erent salt concentration o n the diffusion current The effect of temperature on the diffusion current of 0.001 IM lead chloride in 0.1 N potassium chloride and of 0.002 ill potassium ferrocyanide in 0.5 N potassium chloride is shown in table 5. The diffusion current of 1.00 X N silver nitrate in various concentrations of potassium nitrate was determined, using a microelectrode of approximately the same area as used previously. The results are given in table 6.
EFFECTIVE DIFFUSION LAYER THICKNEBS
id
Pb
1
'C.
microampcru,
1
20 25 30
4.13 5.50 6.55
;
i
Fe(CN);' microampees
3.30 4 05 1.97
I
Pb
I
0.251 mm'
,
1
Fe(CN);' mm.
0.270 0.250 0.226
TABLE 6 Effect of indifferent salt concentration o n d i f f u s i o n current of silver nitrate CONCENTRAIION OF I ( N 0 1
1
M
0.10 0.20 0.50
K mrcroampwee per millimole per lildr
I
1.00
3.80 3.85 3.95 4.20
DISCUSSION
Comparison of diffusion currents of various substances If it is assumed that the steady state of current is reached when a difTusion process occurs through a diffusion layer of constant effective thickness4 in all cases, it is possible to derive simple equations for the diffusion currents of various substances and for the shapes of the current-voltage curves. 4 The effective thickness of a diffusion layer is defined as the thickness of a hypothetical diffusion layer in which the concentration gradient of diffusing substance is constant throughout the layer and equal to that of the actual diffusion layer a t the electrode surface. The flux of diffusingmaterial, and therefore the current, is determined only by the concentration gradient a t the electrode surface and is therefore the same in the actual and the hypothetical cases.
1074
H. A . LAITINES .kND I. M. KOLTHOFF
The total flux, f , of diffusing substance having a diffusion coefficient D through a diffusion layer of effective thickness I t o an electrode of area A is given by Fick's first law of diffusion, which becomes
f
=
AD
1 (C - CO)
-
where C is the concentration of diffusing material in the bulk of the solution and COis the concentration a t the electrode surface. The current due to the electrode reaction is i = nF*f =
AD
- nF(C 1
-
CO)
(2)
where n is the number of electrons involved in the electrode reaction, and F is the faraday. When a diffusion current is reached, Co becomes vanishingly small and equation 2 becomes
For a given electrode, and assuming that 1 is a constant in all cases, we have id
=
knDC
(4)
Equation 4 predicts a proportionality betn een diffusion current and concentration, and should hold only if the effective diffusion layer thickneis i5 a constant independent of the concentration of diffusing material. Several esamples of such a proportionality found experimentally have been given above. For various electrode reactions, the diffusion current a t the same equivalent concentration of diffusing substance should be proportional to the diffusion coefficients. -4 comparison of the calculated and experimental values of the diffusion current constant (the diffusion current of a solution containing 1 millimole per liter of electroactive substance) for various ions a t 25°C. in solutions containing 0.1 S indiffrrent electrolyte is given in table i . The diffusion coefficients of the various ions were calculated from the equivalent ionic conductances by the method given previously (9). It is seen from table i that there is a fair agreement ( f 5 per cent) betneen the observed diffusion current constants and those calculated from that of the thallous ion, assuming a proportionality between the diffusion current constant and the diffusion coefficient. These results indicate that the effective ciiffuiinn layer thickness is a t least approximately constant for various
VOLTAMMETRY WITH STATIOSARY AMMICROELECTRODE
1075
electrode processes. Although some uncertainty exists in the calculated values of the diffusion coefficients, this uncertainty appears to be less than the discrepancies between observed and calculated diffusion current constants in table 7 . A variation of the effective diffusion layer thickness from one electrode reaction to another is entirely possible, since the extent of the diffusion layer appears to be determined by convection currents in the solution near the electrode, caused by density changes resulting from changes in composition of the solution near the electrode. The magnitudes of the density changes depend upon the electrode reaction itself, and are indeed different even for different concentrations of the same diffusing substance. I n view of these considerations, the linear relationship between diffusion current and concentration holds surprisingly well. The exact nature of the convection TABLE 7 Relation between diffusion current and diffusioncoeficient K IN MICROAYPERES PER MILLIMOLE PER LITER SUBSTANCE
Tl+. . . . . . . . . . . . . . . . . . . . . . Agh. . . . . . . . . . . . . . . . . . . . . c u + + .. . . . . . . . . . . . . . . . . . . Pb+-. . . . . . . . . . . . . . . . . . . Fe ( C S )i3 ............... Fe (CK)i4. . . . . . . . . . . . . . . 02.. . . . . . . . . . . . . . . . . . . .
2.00 x 10-6 1.65 0.72 0.98 0.89 0.74 2.38'
Caloulated
Observed
(5.35) 4.41 3.85 5.24 2.38 1.98
5.35 4.24 3.92 5.48 2.28 2.04 12.8
Per cent difierence
-3.9 +1.8 +4.6 -4.2 +3.0
* Calculated from diffusion current. near the electrode surface is difficult to picture, but probably a very thin layer of liquid near the electrode surface is not in motion a t all, and it may be mainly in this layer that the concentration changes occur. Farther from the electrode is a layer of solution in which most of the convection occurs and the concentration of diffusing material approaches that in the bulk of the solution. The diffusion coefficient of oxygen was calculated by assuming that the effective diffusion layer thickness is the same for the deposition of thallium as for the reduction of oxygen. The solubility of oxygen in 0.1 N potassium chloride was assumed to be the same as in 0.1 N sodium chloride. The latter figure was calculated from the data of Randall and Failey (15) on the activity coefficients of dissolved gases. Assuming that the ratio log y / p , where y is the activity coefficient and pis the ionic strength, is contitant for various ionic strengths and is equal t o 0.132, we find y = 1.03 for I.( = 0.1. The solubility of oxygen in the air-saturated solution of 0.1 N potas-
1076
H. A. LAITINEN AND I. M. KOLTHOFF
sium chloride becomes 2.62 X M . The calculated value of the diffusion coefficient of oxygen, assuming that the reduction product is hydrogen cm2.sec-1. This value is not considered to be more peroxide, is 2.38 X accurate than 1 5 per cent, considering the individual differences in table 7 . The value found is in agreement with the value of Carlson (2), who reports a value of 1.98 X cm2.sec-1. in a 1 per cent (0.17 normal) sodium chloride solution a t HOC. Assuming a temperature coefficient of 3 per cent per degree (2), the value of Carlson becomes 2.39 x cm2.sec-1. a t 25OC. With the dropping-mercury electrode, C. S. Miller (11) in this laboratory found a value of 2.56 x cm2sec-1. a t 25OC.
The thickness of the diffusion layer The effective diffusion layer thickness for thallous ions, calculated from equation 3, is 0.25 mm. This value is only one-half that reported by Wilson and Youtz (18), who calculate a value of 0.05 cm. obtained in measurements of the diffusion current of various concentrations of ferrous chloride in 1.5 M hydrochloric acid. The value of Wilson and Youtz is questionable, because of the large uncertainty in the value of the diffusion coefficient of the ferrous ion under the conditions of their experiments. Rloreover, their work was done using relatively large concentrations of ferrous chloride. The diffusion currents reported by Wilson and Youtz are of an entirely different order of magnitude from those obtained in the present work (0.038 to 0.35 ampere), and therefore a disagreement in the diffusion layer thickness may well be expected. Glasstone and Reynolds (3, 5) used the value of 0.05 cm. for the diffusion layer thickness given by Wilson and Youtz and also by Brunner (1) for the evaluation of their results on diffusion currents. The value of Brunner was obtained from measurements of rates of solution of solids in liquids in unstirred solutions, but can hardly be considered comparable except in order of magnitude to the value obtained in electrolysis experiments, because of the extreme difficulty in reproducing the conditions of convection. The results of Glasstone and Reynolds are not comparable in accuracy with those reported here, because they were reported reproducible only to & l o per cent, and only an average value of the diffusion coefficient of 1.2 cm2. per day (1.4 X om2.sec-I.) was used for all the diffusing substances. A glance a t the figures given in table 7 will indicate the magnitude of the errors caused by this assumption. Roller (16) criticizes the whole concept of a finite diffusion layer thickness and states that it has no physical significance. He cites examples of the widely varying values reported under various conditions of stirring, etc., and derives an expression for the rate of heterogeneous reactions a t solidsolution interfaces by considering both the rate of surface reaction and the rate of diffusion. I n cases in which the electrode reaction is slow and re quires an energy of activation, the speed of the reaction must be a function
VOLTAMMETRY WITH STATIONARY MICROELECTRODE
1077
of the electrode potential. Even in such cases, at regions of constant diffusion current the rate of diffusion must be slower than the rate of electrode reaction and must therefore determine the current. It is known that the rate of stirring has a large effect on the value of the diffusion current (13). This effect can be attributed entirely to a decrease in the effective thickness of the diffusion layer. The effect of temperature on the diffusion layer thickness is shown by the data presented in table 5, which gives the diffusion currents of lead and ferrocyanide ions at various temperatures, together with the calculated values of the diffusion layer thickness a t the various temperatures. The effective diffusion layer thickness as a function of temperature was calculated from equation 3, using the values of D calculated for each temperature from the equivalent ionic conductances of the lead and ferrocyanide ions a t infinite dilution, as given by Johnston (7) for the ferrocyanide ion and by Noyes and Falk (14) for the lead ion. For any temperature, t, the diffusion layer thickness, I,, is given by
and
The area, A , of the electrode was 0.071 cm*., found by calculation from the over-all dimensions, neglecting any surface irregularities. This procedure appears to be justified, since the same diffusion current was found for hydroquinone with a platinized platinum microelectrode as was obtained with the same electrode before plating with finely divided platinum. A p parently the effective electrode area is the projected area rather than the total area with surface irregularities. This result is not surprising when the relatively great extent of the diffusion layer is considered. The diffusion coefficient in general has a temperature coefficient of about 2.5 per cent per degree. Experimentally we found that the temperature coefficient of the diffusion current (table 5) is about 4 per cent per degree for lead and ferrocyanide ions. From these facts and equation 5 the value of I may be expected to decrease slightly with increasing temperature. A few values of 1 a t different temperatures are given in table 5. The temperature coefficient of the diffusion current of 4 per cent is considerably higher than that found with the dropping-mercury electrode (12), with which a temperature coefficient of about 2.5 per cent per degree is found. From an analytical point of view it is evident that the temperature must be carefully controlled when measuring diffusion currents with the platinum microelectrode.
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H. A. LAITINEN AND I. M. KOLTHOFF
The temperature coefficient found in the present investigation is in agreement with that reported by Wilson and Youtz (18), who state that the diffusion current is doubled for a 25-degree change in temperature. Glasstone and Reynolds (6) give a temperature coefficient of 10 per cent per degree, measured at lower temperatures (15" to 25°C.). This temperature coefficient is somewhat uncertain, owing to the inaccuracy of the measurements, and appears to be too high, even though at lower temperatures a somewhat higher temperature coefficient may be expected. I n table 6 the effect of varying concentration of potassium nitrate on the diffusion current of silver nitrate is given. The effect is quite marked and is probably not, or is only partly, due to a change of the diffusion coefficient with salt concentration. This matter will be discussed in detail in a subsequent paper, in connection with similar studies made with various types of electrodes. The results reported here indicate that the effective diffusion layer thickness is affected by the salt concentration of the solution. The shapes of the rising portions of the current-voltage curves and the analytiral application of the platinum wire microelectrode will also be discussed in future papers. SUMMARY
1. The term voltammetry is introduced to describe the determination and interpretation of current-voltage curves in electrolysis studies. 2. Current-voltage curves with definite and constant diffusion current regions are shown for the deposition of silver, copper, lead, and thallous ions, for the reduction of ferricyanide ions, ferric ions, quinone, and oxygen, and for the oxidation of ferrocyanide ions, ferrous ions, and hydroquinone. 3. The diffusion current was found to be proportional to the concentration of thallous, ferrocyanide, ferricyanide, ferrous, and ferric ions, usually to an accuracy of fl per cent. The proportionality between diffusion current and Concentration indicates the constancy of the effective diffusion layer thickness near the microelectrode. 4. The diffusion current was found to be proportional to the calculated diffusion coefficients of silver, copper, lead, thallous, ferricyanide, and ferrocyanide ions in 0.1 Ai indifferent salt solution, to an accuracy of f 5 per cent, indicating that the effective diffusion layer thickness is at least approximately constant for the various electrode processes. 5. The effective diffusion layer thickness was found to depend on the total salt concentration in solution. With increasing temperature from 20" to 30"C., the diffusion layer was found to become thinner. REFERENCES (1) BRUNNER, E.: Z . physik. Chem. 47, 56 (1904). (2) CARLSON, T.: J. Am. Chem. SOC.33, 1027 (1911). S.: Trans. Am. Electrochem. SOC.69, 277 (1931) (3) GLASSTONE,
VOLTAMMETRY WITH ROThTING MICROELECTRODE
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(4) GLASSTONE, S., AND HICKLING, A.: Chem. Rev. 26, 407 (1939). (5) GLASSTONE, S., A N D REYNOLDS, G. D.: Trans. Faraday SOC.28, 582 (1932). (6) GLASSTONE, S.,A N D REYNOLDS, G. D.: Trans. Faraday SOC.29, 399 (1933). (7) JOHNSTON, J . : J. Am. Chem. SOC.31, 1010 (1909). (8) KLEMENC, A.: Z. physik. Chem. Ala, 1 (1939). H.A.,AND KOLTHOFF,I. M.:J. .4m. Chem. SOC.61, 3344 (1939). (9) LAITINEN, (10) LINGANE, J . J . , A N D LAITINEN, H . A.: Ind. Eng. Chem., Anal. Ed. 11,504 (1939). (11) MILLER,C. S.:Ph.D. Thesis, University of Minnesota, 1940. V.:Collection Czechoslov. Chem. Commun. 1, 319 (1929). (12) NEJEDLEY, E. S.: 2. physik. Chem. 63, 235 (1905). (13) KERNST,W., AND MERRIAM, K . G.: J. Am. Chem. SOC.34, 454 (1912). (14) NOYES,A. A , , A N D FALK, (15) RANDALL, M., AND FAILEY, C. F.: Chem. Rev. 4, 271 (1927). (16) ROLLER,P.S.:J. Phys. Chern. 39, 221 (1935). E.:Z.physik. Chern. 24, 55 (1897);26, 365 (1898). (17) SALOMON, (23) WILSON,R. E.,A N D YOUTZ, M. A.: Ind. Eng. Chem. 16, 603 (1923).
VOLTAMMETRIC DETERMINATIONS A S D AhfPERO.METRIC TITRATIONS WITH A ROTATISG MICROELECTRODE OF PLATINUhI WIRE' H. A. LAITINEN'
School
0.f
AND
I. M. KOLTHOFF
Chemistry, Institute of Technology, University of Vinnesota, I\. inneapolis, Minnesota Recezved December 16, 1940
In a previous paper (12) it was shown that well-defined regions of diffusion current can be obtained in electroreduction and electrooxidation with stationary platinum-wire microelectrodes. From a practical viewpoint the measurements involve the disadvantage that it is necessary to wait for at least 2 min. at each value of the applied E x F . until a steady state of current is reached. This disadvantage can be eliminated by working with a rotating electrode. Naturally, diffusion currents measured with a. rotating electrode are much larger than those measured with a stationary electrode of the same dimensions. Thus it should be possible to determine electroreducible and electrooxidizable substances a t much smaller concentrations with a rotating electrode than with a stationary electrode. Many investigators have studied current-voltage curves obtained in electrolysis experiments, using either rotating platinum microelectrodes or This article is based upon a thesis submitted by H. A. Laitinen t o the Graduate Faculty of the University of Minnesota in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1940. ? Present address: Department of Chemistry, University of Illinois, Urbana,, Illinois.
