400
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
Determination of the Electrochemically Effective Electrode Area Timothy E. Cummings and Philip J. Elving" The University of Michigan, Ann Arbor, Michigan 48 109
a useful relationship for evaluation of the effective electrode area that is not available because of shielding and orifice ill be referred to as the effective contact (this combined effect w contact area). A previously reported niethod ( 5 ) for evaluating the effective contact area was more complex in introducing correction for back pressure; the authors underemphasized the importance of the effective contact area correction by stating that it approximately equaled the orifice area and by failing to report the determined values. Because of the importance of knowing the true area for many purposes, eg., evaluations of diffusion coefficients and of the relation between polarographic limiting current and mercury column height, the effects of effective contact area and sphericity a t the D M E on measured parameters were systematically studied with the aim of determining the simplest set of equations which could, within a given tolerance of error, be employed. HMDE. For much work employing the hanging mercury drop electrode (HMDE), the electrochemically effective electrode area must be known. Regardless of which type of HMDE is employed, e.g., platinum contact or syringe, for precise work, the area must be experimentally evaluated. Determination of the HMDE area from cyclic peak current relations (6, 7 ) and experimental voltammograms for a reversible compound with a known diffusion coefficient, D , suffers from two problems. Since D is a function of temperature, solvent, and ionic strength, only D values determined in a solution of ionic strength sufficient for electrochemical work may be used. Furthermore, the literature is replete with contradictory D values. One intent of the present study is to present an internally consistent method for HMDE area evaluation using dc polarographic and cyclic voltammetric data obtainable in the same laboratory, thereby avoiding reliance on externally obtained values which may not have been obtained under identical conditions. The method has the advantages of the precision with which the DME effective area can be evaluated and the accuracy obtainable through comparison of measurements on the same solution.
The factors are discussed which affect diffusion controlled behavior in dc polarography at a controlled drop-time dropping mercury electrode (DME) and in cyclic voltammetry at a hanging mercury drop electrode (HMDE) with respect to the evaluation of the electrochemically effective area. The measurement of the latter in terms of capacity, the results obtained, and the difference in the effective area for faradaic and nonfaradaic processes are described. Based on publlshed values of the diffusion coefficient of Cd(I1) in 0.1 M KCI, the dc polarographic diffusion current at a controlled drop-time DME is found to obey the theory for diffusion to an expanding sphere; depletion effects are considerably reduced by convection resulting from use of a mechanical drop-knocker, and current-time behavior for single drops is very reproducible, even at times as short as 0.2 s. Contrary to published theory, shielding effects from the glass capillary decrease with time after drop-birth. An experimental technique for calibration of HMDE areas using the trioxalatoiron(111) species is described, which gives a precision of 2 to 4 % . Use of Cd(I1) for evaluation of HMDE areas is subject to errors due to trace adsorbates. Use of slow scan rates is recommended for precise HMDE area evaluation, and a mathematical procedure is detailed which accounts for the extant sphericlty effects.
DME. Mathematical theories for describing the polarographic diffusion current a t a dropping mercury electrode (DME) have been reviewed ( I ) . Because of both its simplicity and satisfactory description of the physical relations under normal conditions, the original Ilkovic equation (2)continues to be used, despite considerable advancement in the mathematical sophistication used to solve the DME boundary value problem. In a study of current-time behavior a t a DME ( 3 ) , the experimental data a t times shorter than one second showed a marked deviation from published theories. While it was, a t one time, difficult to use a DME having a short drop-time because of the necessarily large mercury flow-rates and the concomitant polarographic maxima induced by the rapid mercury flow, the mechanical drop-knocker has made work a t short drop-times feasible. Use of short drop-times has several advantages. A wider drop-time range increases the capability to study chemical kinetics. The current flow a t the end of a mechanically controlled drop-life can be made much smaller than for a natural drop-life, which reduces iR losses in solution, a fact of particular importance in ac polarography and cyclic voltammetry a t the DME. Furthermore, controlled drop-times are used in analysis to speed determinations and, in general, to avoid dependence of the natural drop-time and, hence, of the drop area on the applied potential. Until recently, it was generally assumed that the contact area between the mercury drop and the DME was small and that shielding effects from the glass capillary were minor; however, no reliable method was known for experimentally evaluating these effects. Recently, Mohilner et al. ( 4 ) , in connection with differential capacity measurement, reported 0003-2700/78/0350-0480$01 OO/O
EXPERIMENTAL Chemicals. Reagent grade CdC12-2.5H 2 0 (Baker) was dried (Merck), at 110 "C for several days. Reagent grade Fe2(S04)3.6H20 K2C204-H20 (Mallinckrodt) and KC1 were used without further purification. Mercury for electrodes was chemically purified and distilled. Water was suitably distilled. Instrumentation. All data were obtained using a jacketed, three-compartment cell thermostated at 25 rt 0.1 "C. The DME capillary was a 20.8-cm length of Corning Code No. 215670 marine barometer tubing. The mechanical drop-knocker was a solenoid with a metal pin attached to the solenoid plunger. The pin moved horizontally, striking the DME capillary with a force which was dependent on the electrically regulated solenoid current. The HMDE was a Metrohm E 410 Micro-Feeder. The potentiostat was a standard configuration, similar to one described (8). Triangular waveforms were supplied by a Wavetek Model 112 function generator. Potentials were monitored by a HewlettPackard Model 3440A digital voltmeter with a Model 3443A high gain/auto range unit. Data were recorded on a Houston Model 2000 x-y recorder.
D
1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
Procedures. Solutions were deaerated with purified nitrogen for 30 min; a nitrogen atmosphere was maintained in the electrochemical cell during experiments. Reported potentials are vs. an aqueous saturated calomel electrode. DC Polarographj. For 0.183 mM Cd(1Ij in 0.3 M KC1 solution, the potential was scanned at 4 mV/s, starting at -0.3 V. For all other solutions, the potential was held constant at a value on the diffusion plateau, -0.700 V for Cd(I1) and -0.350 V for Fe(IIIj, and the currents for 10 to 20 drops were recorded, using the time-base sweep on the recorder x-axis; an identical procedure used for background alone permitted background subtraction. To minimize long term stirring effects, the mechanical drop-knocker was adjusted to deliver the minimum striking force necessary to dislodge the drop. Cyclic Voltarnrnetrj. A drop corresponding to 10% of one rotation (two divisions) of the micro-feeder piston mechanism was used. The precision of thus setting the piston is about 170.A new drop was used for each cyclic voltammogram. THEORY Because most read-out instruments in current use respond sufficiently rapidly to measure the instantaneous polarographic current, the theory will be considered for such currents. Conversion for mean currents should be readily apparent. DC Polarography. The original Ilkovic equation (2), which does not account for sphericity effects a t the DME, is:
id
=
(1)
709 nD’ 2 C m 2 t’
where id is t h e maximum diffusion current in PA. n is the number of electrochemical equivalents per mole of species electrolyzed, D is its diffusion coefficient in cm2/s, C is its bulk solution concentration in mM, m is the mean mercury flow rate in mg/s, and t is the life-time of the drop in s. Derivations which accounted for sphericity effects (9-16) have produced, after truncating a series expression, equations of the following type, in which only the coefficient B differs: id
= 709 nD’ 2CmZ3t’ 6(1
+ BD’
2 t 1 ’ 6 / m 1 i 3 )( 2 )
In Matsuda’s solution (Is),which appears to be the most rigorous ( I ) , R is 36.3 for a freely hanging sphere and 23.5 when t h e shielding effect of the glass capillary is considered. Mohilner et al. ( 4 ) equated the electrochemically effective electrode area, A , to the difference between the area computed from drop volume assuming a spherical shape, A,, and the effective contact area of the drop, Ao. The accuracy of the spherical shape assumption has been shown to be sufficient (17-19). On substituting for A,, based on the mercury flow rate and drop-time, Mohilner et al. obtained
A
=
( 6 rniT’”/d)’ 3 t 2 ’ 3- A.
(3)
where d is the density of Hg. A useful (and obvious) relationship is
Since the Ilkovic equation is linear in A, (incorporated in terms of m and t ) , one can correct for the effect of Ao, i.e., replace A, by A , by substitution of Equation 4 into Equation 1,which, upon further substitution for A,, yields 1, =
709 nD‘ 2Cm’ 3 t i 6(1 - 117.8 Ao/m2i3t2 3,
(5)
where A. is in cm2. Since the effective electrode area does not appear in the derivation of Equation 2 in places leading to the second term in the parentheses (at least not in a manner amenable to correction of A , for A o ) ,Equation 4 can be introduced into Equation 2 analogously to the substitution into Equation 1, so that
481
AC Polarography. Although Mohilner et al. ( 4 ) were solving for the differential capacitance, this approach is readily adaptable to ac polarographic current measurements, which can be used to determine the DME drop area in the absence of a faradaic process. Since the measured ac current, i,, equals the product of the ac current density, j,,, and the electrode area, substitution of Equation 3 for the electrode area relates i,, and jac:
j,(6 r n i ~ ’ ~ ~ / d-)j,,A, ~’~t~’~
=,i
(7)
Thus, at constant Edc,a plot of i, vs. t 2 i 3should be linear with d ) ~an” intercept, 2,equal a slope, U,equal to j, (6 r n ~ ~ i ~ / and to -jacAo.Values of U and 2 can be determined by leastsquares; if m is known, A. can then be evaluated from
A.
=
- Z ( 6 mn”2/d)2’3/U
(8)
Because of resistance in solution and through the DME, the measured ac currents must be corrected for iR loss (20j, which also results in a phase shift of the working electrode ac voltage, AEw, relative to the applied ac voltage, V. If the in-phase, io., and quadrature, igo0, components of the ac current are measured, the total ac current, i,, is given by
it= (iooz+
iqoo2)”2
Correction for the
iR loss is then
(9) made using Equation 10.
i, = it/sin[arctan(iq,o/i,o)]
(10)
Cyclic Voltammetry. Nicholson and Shain (7) have x ( a tij and ” @ ( a t ) ,for a tabulated the current functions, ~ ~ reversible charge-transfer for Equation 11, where ro is the HMDE radius and u is the scan rate.
i = 6.02 X 1 0 5 n 3 i z A D ” 2 C u ” 2 [ n ” 2 ~i(at) 0.16(DI ‘iron‘ ” u ” ’)$ ( a t ) ]
(11)
At fast c, the second term in brackets in Equation 11 becomes negligible and Equation 11 can be accurately approximated for the peak current by
i,= 2.687 X 105n”2AD”2C U ’ ~ ~
(12)
At slow is. the assumption made in obtaining Equation 12 is not valid. If D’/’ is not large and ro and c are not very small, i, will still appear 28.5 mV past El!* and Equation 11 can be written for i, as
i,
=
6.02 X 105n3’”D’i2Cv’’2 [0.4463 + 0.1203 D ‘”/r0 IZ “ * u 1 1 2]
(13)
For a rapidly diffusing species, a very small ro or a very slow c, the second term in brackets in Equation 11 causes a shift of E , to slightly more negative values (for a reduction), and different numerical values of =‘I2 at) and 4 ( a t ) are required
(7). HMDE Area Evaluation. Several relationships may be used to obtain the HMDE area. If Equation 1 satisfactorily describes the dc polarographic current and Equation 12 accurately describes the cyclic peak current, the area calculation is straightforward. Equation 15 is readily deduced from Equations 1, 12, and 14; the HMDE area is then evaluated using experimental values of ip/Cc’/2and I d .
Id = id/crnzi3 tlJ6 (i,/Cu1’2)/Id = 3.790 X 102nli2A
(14) (15)
In the event that Equation 5 is assumed to be valid, ZJ, defined by Equation 16, replaces I d in Equation 15.
I d’ = id / C ( M 2 ’ 3 tli6- 117.8 A o / t ” ) (16) id = 709 1 ~ 0 ’ ~ ~ C m 6 (~1+‘ ~BD1’2t116/m1/3)(l t‘ If sphericity effects a t the DME are important, it is nec117.8 A,/m2 3 t 23 , (6) essary to evaluate 0’”. Using Equation 2, Id is given by
482
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
Since. for a given capillary, m / h c is a constant, symbolized by K , multiplication of Equation 21 by K , yields Equation 22, where Kh, is replaced by in, which permits calculation of m for any values of h and t , once K is determined.
Table I. AC Polarographic Currents and Current Densitiesa
m = Kh 258.6 251.4 2.10 2.06 0.00903 228.3 258.6 251.6 2.22 2.15 0.00938 229.3 257.2 250.6 2.39 2.26 0.00986 229.5 257.0 250.8 2.54 2.37 0.01028 230.5 257.5 251.5 2.69 2.48 0.01069 231.9 257.4 251.6 2.85 2.59 0.01112 232.8 256.5 251.0 2.98 2.67 0.01147 232.8 Mean 230.7 257.5 251.2 0.78 0.41 Std dev 1.82 0.30 0.16 Re1 std dev, % 0.79 2.09 1.01 4.58 Range 0.40 1.98 0.81 Re1 range, % a 0.4 M K,C,O,; E d c = -0.090 v; h = 39.5 cm. Based on rn calculated from Equation 22 with mlh, = 0.01429 mg/cm s. A , = 0.00106 cm’, based on i,, vs. t”’. A , = 0.00083 cm’, based on ,i vs. (mt)’”.
+ 3.1 K/(mt)’13
(22)
For h of 39.6 and 63.4 cm a t 2.10 s and 39.6 cm at 2.85 s, m
of 0.5225, 0.8694, and 0.5277 mg/s, respectively, were experimentally determined at open circuit; the corresponding h,, determined from Equation 21, were 36.6, 60.8, and 36.9 cm, respectively. T h e average m / h c or K , 0.01429 mg/cm s (relative average deviation of 0.06%), was used in Equation 22 to calculate rn at the various drop-times employed for the ac data (Table I) obtained a t an h of 39.5 cm. A plot of i, vs. (mt)’lYyielded a slope of 2.132 pA/mg“13 and an intercept cm2 is 22% less than of -0.2075 kA; the A. of 8.3 & 0.8 X that obtained from the i, vs. t 2 I 3 plot. Since i, is related to the differential capacity by drop-time independent terms except for the electrode area, the ratio of i, to the effective electrode area should be drop-time independent. Values of i,,/A,, and iac/(As- A,) for A. of 0.00106 and 0.00083 cm2 are shown in Table I. The results indicate Equation 17, which is a quadratic equation in D’12; hence, D112 that A = A, - 0.00083 cm2 is the best of the three values. For is given by Equation 18. either value of A,,, the precision of the mean iac/(As- A,) is I , = 709 nD’I2(1 BD’” t”6/m“3) (17) better than the precision of the data: however, using A. = O l t 2= [(l 4 Bt”61d/709nm1”3)1’2 - 11m1’3/2 0.00083 cm2, no systematic trend is observed between iac/(As - Ao) and t as is the case with the larger Ao. The importance Bt”6 (18) of using the correct A. is evident from the difference between If Equation 6 is employed, Id’ replaces Id in Equations 17 and the two mean values of & , / ( A s- .4,,). 18. The results in Table I indicate that the value of A,, deWhen sphericity effects a t the HMDE are negligible, D112 termined from m and t , is accurate to better than 0.5% over can be used with cyclic voltammetric results to evaluate A the time range of 2 to 3 s; for shorter times, the accuracy may directly from Equation 12. If u is sufficiently slow that be slightly poorer, depending on the validity of Equations 21 sphericity effects are not negligible, Equation 13 must be used. and 22. To simplify the calculation, advantage can be taken of the fact Several points must be made regarding the results just t h a t A equals 4rrO2;substitution of A’/2/27r1i2 for ro in presented and the work of Mohilner et al. ( 4 ) . Mohilner’s Equation 13 leads t o procedure was developed for evaluation of differential cai, = 6.02 X 105n3’2AD”2Cu”2[0.4463 pacitance data based on the slope of a plot of i,, vs. t 2 i S ;he 0.4 26 3 (D/A n u ) ] (19) was not interested in the value of A. based on the intercept. However, the intercept and slope of a straight line fit to data Since Equation 19 is a quadratic equation in A‘!’! are not independent, and differential capacitance (or current A = {[(0.1817 D/nu 2.966 X density) values based on intercept calculated contact area 2 C ” ~ ) Z,/n 3 / - 0,4263 corrections should agree with corresponding values calculated (D/nu) ]/0.8926}2 (20) from the slope of the plot. The values of i,,/(As - Ao),based on the slopes, were 0.1 pA/cm2 lower than the respective mean R E S U L T S A N D DISCUSSION: DC values in Table I in both cases, so that a plot, which yields POLAROGRAPHY an incorrect intercept calculated Ao, will also give incorrect Contact Area. A 0.4 M K2C2O4solution was employed for values based on slope evaluation. Because evaluation of m the contact area evaluation by ac polarography. A plot of i, at several values of h and/or t is tedious, it is desirable to avoid vs. t 2 / 3(Table I) yielded a slope of 1.422 ~ A / s ’ / and ~ an such a task whenever possible; as use of m values in calcuintercept of -0.2736 wA, giving an A. of 0.00106 cm2! based lations introduces the errors associated with evaluation of m, on m = 0.525 mg/s. An identical A. was obtained for the same e.g., precise back-pressure calculation. it is advisable to use capillary using 0.3 M KCI, suggesting that A. is independent Mohilner’s approach, Le., to obtain values of i, at long of the nature and concentration of the supporting electrolyte. drop-times, since m becomes relatively independent of t after Because of the short drop-times employed, back-pressure a few seconds. Since the linear least-squares method will effects can be significant; since A,, is evaluated by a long preferentially fit data at large values of t , the data a t long extrapolation, a nonconstant rn can result, in an erroneous Ao. drop-times should lead to proper evaluation of A. from a plot T o test the effect of variations in m on Ao, the data in Table of i, vs. P3.However, data at short drop-times, e.g., down I were analyzed as follows. Equation 7 indicates that a plot ~ ’ ~ be linear with a slope of j,, ( 6 ~ ’ / ’ / d ) ~ l ~ to 2 s, should also be used in the fit to prevent the need for of i, vs. ( ~ n t )should a long extrapolation to the intercept. The need to consider and an intercept of -jacAo, so that A. can be evaluated back-pressure effects on m a t the shorter drop-times confirms analogously to the method employing Equation 8. The the complex evaluation procedure of Nancollas and Vincent proposed method requires experimental evaluation of either (5). m as a function o f t at the column height, h, employed or the Cadmium(I1). Using the diaphragm method, Rulfs (22) relation between rn and the corrected column height, h,, since obtained 7.0 X 10% cm2/s for the diffusion coefficient of 1 niM h, is related to h and t through the back-pressure term, h b Cd(I1) in 0.1 M KCl; a later study (23) reported a weighted [given by 3.1/(mt)1/3(21),assuming the surface tension is 400 average of 7.0 & 0.13 X 10% cm2/s based on published results dyne/cm], Le., of four independent workers using different techniques. h,= h - 3 . l / ( ~ ~ t ) ” ~ (21) Because D for Cd(I1) in 0.1 M KC1 has been carefully eval-
+
+
’
I
’ ’’+
+
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
483
Table 11. Diffusion Coefficients for 1.012 mM Cd(I1) in 0.1 M KCP hc, cm
Idb
Dcd(rr)”2x I O 3 , cm/s”’
Id’
2.71h
36.5 41.1 46.9 50.9 53.8 55.9 58.7 60.8
4.15 4.15 4.16 4.15 4.16 4.15 4.15 4.14
4.59 4.57 4.56 4.54 4.54 4.53 4.52 4.51
2.93c 2.93 2.93 2.93 2.93 2.93 2.93 2.92
3.23d 3.23 3.19 3.17 3.16 3.15 3.15 3.13
2.5ge 2.59 2.61 2.61 2.62 2.62 2.62 2.62
2.6gf 2.69 2.71 2.71 2.72 2.71 2.72 2.72
2.829 2.82 2.81 2.81 2.81 2.80 2.80 2.79
51.71 2.72 2.72 2.72 272 2.72 2.72
Mean Std dev Re1 std dev, % Range Re1 range, %
4.15 0.004 0.10
4.55 0.028 0.61
2.93 0.003 0.10
3.18 0.037 1.16
2.61 0.015 0.57
2.71 0.011 0.41
2.81 0.012 0.42
2.72 0.003 0.11
0.014 0.34
0.084 1.85
0.010 0.34
0.100 3.17
0.040 1.54
0.030 1.11
0.030 1.07
0.009 0.33
a t = 2.1 s; m / h , = 0.01376 mg/cm s; literature value, 0“’ = 2.65 k 0.025 X cm/s”z ( 2 3 ) . Units are P A sl”/mM Expanding plarie model, Expanding plane model, Equation 1 (Ilkovic equation). mg2/3;Id’ is for A , = 0.00083 cm’. Equation 5, A , = 0.00083 cmz Ilkovic equation with contact area correction). e Expanding sphere model, Equation 2, B = 36.3 (Matsuda equation). Expanding sphere model, Equation 2, B = 23.5 (Matsuda equation accounting for shielding effect). g Expanding sphere model, Equation 6, B = 36.3, A , = 0.00083 cm’ (Matsuda equation with contact area correction). Expanding sphere model, Equation 6, B = 36.3, A , = 0.00047 cmz (Matsuda equation with contact area correction).
I
Table 111. Diffusion Coefficients for 0.212 mM Cd(I1) in 0.1 M KCP Dcd~II)”2 X l o 3 , cm/s’ hc, cm IJJ Id’b -
0
k Q
P
1 ,
1.5
Q 1 ,
.-v
. _W
36.5 41.1 46.9 50.9 53.6 55.9 58.7 60.8
4.09 4.08 4.08 4.08 4.09 4.08 4.08 4.08
4.53 4.50 4.47 4.47 4.47 4.45 4.44 4.44
2.55‘ 2.55 2.56 2.57 2.58 2.58 2.58 2.59
2.E15~ 2.65 2.66 2.67 2.67 2.67 2.67 2.68
2.7ge 2.79 2.78 2.79 2.80 2.79 2.79 2.79
Mean Std dev Re1 std dev, % Range Relrange, %
4.08 0.006 0.15 0.018 0.44
4.47 0.030 0.67 0.09 2.01
2.57 0.014 0.54 0.037 1.45
2.67 0.010 0.39 0.027 1.01
2.79 0.004 0.14 0.011 0.39
a t = 2.1 s, m l h , = 0.01376 mgicm s; literature value for c m / s ” 2( 2 3 ) . 1 mM Cd(II), D’ = 2.65 i 0.025 X Units are p A sliZ/mMmgZt3. Expanding sphere model, Equation 2, B = 36.3 (Matsuda equation). Expanding sphere model, Equation 2, B = 23.5 (Matsuda equation ac-
counting for shielding effect). e Expanding sphere model, Equation 6, B = 36.3, A , = 0.00083 cm’ (Matsuda equation with contact area correction). v/
4
12
8 hc>
I
crn”3
Figure 1. Variation of dc polarographic diffusion current with corrected mercury column-height, h, (calculated from hand mlh, using Equations 21 and 22; t = 2.10 s). (A) 1.012 mM Cd(I1) in 0.1 M KCI; mlh, = 0.01376 mglcm s. (B) 0.212 mM Cd(I1) in 0.1 M KCI; mlh, = 0.01376 mglcm s. (C) 0.183 mM Cd(I1) in 0.3 M KCI; mlh, = 0.01521 mglcm s and t = 2.07 s. (D) 0.341 mM Fe(II1) in 0.4 M K2C204;mlh, = 0.01429 mglcm s
uated, this system should serve as a good check on the contact area correction value for faradaic processes. T h e diffusion current for 1.012 m M Cd(I1) in 0.1 M KC1 was measured a t -0.700 V a t ten column heights, using a controlled 2.10-s drop-time. Similar measurements were made on 0.212 m M Cd(I1) in 0.1 M KCl and 0.183 m M Cd(I1) in 0.3 M KC1. Because t was controlled, only m was dependent on h,; the expanding plane model predicts that id should be linear with h:/3 and have a zero intercept. T h e latter re-
lationships are verified by curves A to (2 of Figure 1;however, when id is corrected for the effect of A,, on the electrode area, a nonzero intercept results (curves A to C of Figure 2 ) . If the polarographic diffusion current is best described by the form of Equation 2 or 6, id is not linear with h,2/3because of the spherical correction term, and a linear extrapolation of id vs. h: should have a nonzero intercept, a fact borne out by theoretically predicted ~ - h ; relations /~ (Figure 3). It is also obvious from Figure 3 that a positive value of A . alters the apparent intercept, which is a function of Ao, m/ho t , D, and the range of h, values at which data are fitted (the apparent linearity over the entire range of curve B of Figure 3 is merely a fortuitous consequence of the theoretical parameter values). The diffusion coefficient for Cd(I1) in 0.1 M KC1 was evaluated from the data in curves A to C of Figure 1, using various theoretical relationships (Tables I1 to IV); points deviating noticeably from the fitted line were not included. From the results in Table 11, the simple Ilkocic equation but the deviation from the gives the best precision for D1/’, reported value (23) is 10%. Equation 6 with B = 36.3 and
484
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
I c
i
I
1 4
i 8
I
1
I 12
16
B
/ /
’ /
I
i 4
8
:‘h,
1 12
C$
Figure 2. Variation of dc polarographic diffusion current (corrected for contact area effect) with corrected mercury column-height. Conditions and curve designations are as in Figure 1; A , = 0.00083 cm2
Table IV. Diffusion Coefficients for 0.183 mM Cd(I1) in 0.3 M KCln ~ ~ ’D,d(,,) b x i o 3 ,cm/s”* h,, cm Id 2.54c 2.63d 2.76e 36.6 4.05 4.44 2.54 2.64 2.74 43.6 4.04 4.38 48.3 4.02 4.34 2.54 2.63 2.12 2.65 2.74 50.9 4.04 4.35 2.56 2.64 2.72 53.9 4.02 4.32 2.55 4.03 4.37 2.55 2.64 2.74 Mean Std dev 0.012 0.049 0.010 0.007 0.014 0.28 0.50 Relstd dev, ?G 0.31 1.11 0.37
t = 2.07 s; m/h, = 0.01521 mg/cm s; literature value for 1 mM Cd(I1) in 0.1 M KCl, D”’ = 2.65 i 0.25 X lo-’
~ m / s ” ~ ( ( 2 3 ) . Units are LA s”*/mM rng”’. Expanding sphere model, Equation 2, B = 36.3 (Matsuda equation). Expanding sphere model, Equation 2, B = 23.5 (Matsuda equation accounting for shielding effects). e Expanding sphere model, Equation 6 , B = 36.3, A,, = 0.00083 cm’ (Matsuda equation with contact area correction).
A. = 0.00083 cm2 gives D’/’ values 4 to 6% higher than the published value. Matsuda’s relations predict D’12 in close agreement with that reported, being 1.5 to 3.8% low if a freely suspended sphere is assumed, and, in the case of a shielded sphere, within less than 1%for the two lower concentrations. Iron(II1). T h e Fe(III)/Fe(II) couple in high KzC204 concentration has been reported to be an uncomplicated, rapid electron-transfer couple at mercury (24-28). A recent investigation (8)of Fe(II1) reduction in 1M K2C204showed that the ac polarographic peak current was linear with the square root of frequency up to 15 kHz (upper limit of the study) and that the cyclic voltammetric cathodic-anodic peak potential separation was that expected for a simple reversible electron-transfer at scan rates up to 4000 V/s (fastest scan rate employed). Because of its reversible nature and noninvolvement of amalgam formation, the Fe(III)/Fe(II) couple
I
0
1
hc23 crn2’3 Figure 3. Theoretical relation of dc polarographic diffusion current to corrected mercury column height. Parameters: D = 7 X 10” cm2/s; C = 1 mM; n = 2; t = 2.10 s; mlh, = 0.014 mglcm s. (A) id relation defined by Equation 2 with 5 = 36.3. (B) id relation defined by Equation 6 with B = 36.3 and A , = 0.00083 cm2. Lines represent estimated linear relation of id to h,2’3 for h,2’3 L 1 1 ~ m ” ~
in K2C204should be excellent for evaluation of the effective DME and HMDE areas. The Fe(II1) dc polarographic id-hc relation was examined, analogously to the Cd(I1) study (curve D in Figures 1 and 2). Trioxalatoiron(II1) diffusion current constant and coefficient data are given in Table V. Lingane (28) reported an Idfor Fe(II1) in 0.2 M Na2Cz04 based on average currents which, when converted to the maximum current value, is 1.75 i 0.035, in agreement with the mean value of 1.75 f 0.011 in Table V, but 8% below the mean Id’of 1.90 f 0.09. Smith and Reinmuth (29) obtained cm2/s for D of Fe(II1) in 0.3 M K2Cz04+ 0.1 M 4.95 x H2C204+ 0.05 M KC1, based on the slope of a plot of ac polarographic peak current vs. frequency; the corresponding cm/s’/’, is in excellent agreement value of D1/’, 2.22 X with that of 2.23 X cm/s’/’ in Table V, based on the Matsuda equation for a freely suspended sphere. The latter agreement may reflect apparently identical definition of the electrode area as A,, and Smith and Reinmuth’s use (29) of Koutecky’s theory (16) to obtain the value of D by ac polarography. (Koutecky’s B of 39.5 is quite close to Matsuda’s B of 36.3.) The Apparent Area. It is well established that, a t a naturally dropping mercury electrode, the drop fall does not cause sufficient convection to homogenize the solution. Consequently, after the growth of the first drop under conditions of faradaic activity, there is some depletion of electroactive species in the solution region into which new drops grow, and the faradaic current for the first drop may be 10-20% larger than for succeeding drops (30). Thus, id for 1 mM Cd(I1) in 0.1 M KC1 would be expected to predict diffusion coefficients lower than those measured by nonpo-
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
485
Table V . Diffusion Coefficients for 0.341 mM Fe(II1) in 0.4 M K,C,O,‘
36.5 41.1 45.8 50.9 55.8 60.8
1.73 1.74 1.74 1.76 1.76 1.76
1.91
1.90 1.89 1.90 1.89 1.89
2.45‘ 2.45 2.46 2.48 2.48 2.48 2.47 0.016 0.65 0.038 1.54
2.20e 2.21 2.22 2.24 2.25 2.26
2.6gd 2.68 2.67 2.67 2.66 2.66
2.48g 2.40 2.40 2.40 2.41 2.41 2.40 0.005 0.20 0.013 0.54
2.28f 2.28 2.30 2.31 2.32 2.33
2.31h 2.31 2.32 2.34 2.34 2.34 2.33 0.015 0.64 0.035 1.50
2.30 0.022 0.97 0.057 2.47 Units are pA s’/’/mM mg2” ;Id‘ is a t = 2.1 s; m/h, = 0.01429 mg/cm s ; literature value, D1” = 2.22 X l o 3 cm/s’/2 (29). Expanding plane model, Equation 5, Expanding plane model, Equation 1 (Ilkovic equation). for A , = 0.00083 cm’. A , = 0.00083 cmz (Ilkovic equation with contact area correction). e Expanding sphere model, Equation 2, B = 36.3 (Matsuda equation). Expanding sphere model, Equation 2, B = 23.5 (Matsuda equation accounting for shielding effect). g Expanding sphere model, Equation 6 , B = 36.3, A , = 0.00083 cmz (Matsuda equation with contact area correction). Expanding sphere model, Equation 6, B = 36.3, A , = 0.00047 cmz (Matsuda equation with contact area correction). Mean Std dev Re1 std dev, % Range Re1 range, %
1.75 0.011 0.65 0.027 1.54
1.90 0.085 0.45 0.024 1.27
larographic techniques; since the results in Table I1 agree with or, in most cases, exceed the reported value, stirring due to the drop knocker must homogenize the solution and may even slightly enhance id because of convective effects extant at the drop fall. T o investigate the possible presence of stirring effects, the following procedure was used to examine the i-t profiles for single drops: (a) At E = 4.700 V, several drops were allowed to grow and fall a t a controlled 2.10-s drop-time; (b) the drop-knocker was shut off as a drop was dislodged so that the next drop grew and fell with a natural drop-time (this drop will be referred to as the first natural drop) and its i-t behavior was recorded; (c) i-t profiles of successive drops with natural drop-times were recorded (these will be referred to as the second natural drop, etc.). A similar procedure on the background solution permitted background subtraction. Some qualitative conclusions were immediately obvious. Comparison of i-t profiles for several controlled drops indicated very reproducible i-t behavior for t > 0.1 s (the recorder response time under the conditions employed). The i-t behavior of the first natural drop during its first 2.10 s was t h e same as t h a t of controlled drops, a rather obvious expectation. The i-t behaviors of the second and third natural drops were identical within experimental uncertainty for t < 9 s. At any given instant in the drop-life, the current for the first natural drop was larger than that for succeeding drops. Curve A of Figure 4 represents the current for the first natural drop to grow into relatively undepleted solution beyond the region traversed by a 2.10-s controlled drop. Although the second drop (curve C) grows into a region depleted by the previous drop, the extent of the depletion decreases with increasing distance from the capillary orifice and, with increasing time into the drop-life, the drop grows into a solution region for which diffusion has had additional time to reduce depletion due to the previous drop; hence, the depletion effect on the current decreases with time after drop-birth. T h e profound difference in current at short times between the first and second natural drops indicates that the mechanical drop-knocker introduces stirring effects which reduce or eliminate depletion due to the previous drop; however, the matter of whether such stirring merely homogenizes the solution or enhances the current, even 2.10 s after drop-birth, relative to theoretical prediction is unanswered. Although the behavior of the effective contact area corrected currents for the first natural drop (curve B of Figure 4) indicates that stirring influences the current even 2.5 s after drop-birth, this may be an artifact due to the effective contact area for faradaic processes being smaller than that determined by ac polaro-
2.23 0.025 1.11 0.064 2.87
2.67 0.012 0.45 0.034 1.27
0.7
P
2
-VI
0.51
1 ,
p
.
+ .= .-
V
ifc
0.3!
,ii i
,
I .o
,
1.3
416
,
, ,
I
1
26
Figure 4. DC polarographic current-time profiles for single drops. (A) First drop after drop-knocker shut-off: k = 1; 0.212 mM Cd(I1) in 0.1 M KCI; h = 49.7 cm; mlh, = 0.01376 mg/cm s. The small rectangles represent the data in curve A for k = 1 - 0.00047/A,. (B) Same as A except k = 1 - 0.00083/A,. (C) Second drop after drop-knocker shut-off; k = 1. ( D ) Same as C except k = 1 - 0.00083/AS. (E) Behavior predicted by Equation 2 for n = 2, C = 0.212 mM, D = 7 X cm2/s. B = 36.3, h = 49.7 cm, m l h , = 0.01376 mg cm/s and k = 1. (F) Same as E except B = 23.5. (G) Behavior predicted by Equation 1; parameters same as for E. The factor k is a means
of area correction graphic charging currents and/or a breakdown in the m/hc relationship a t short times. The latter seems unlikely, since the apparent effect is seen for drop areas which are intermediate between those for which the m/hc ratio was found to be constant. An alternative estimate of A. can be obtained from theoretical relationships between id, and m and t . To a first approximation, the contact area predicted by the Matsuda equation with shielding effects (Equation 2 with B = 23.5)
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978 30
I
I
Table VI. Area of the HMDE Based on dc Polarographic and Cyclic Voltammetric Data for 0.183 mM Cd(I1) in 0.3 M KCP A , cm’ u , VIS
I
0
I
I 0.3
I
1
I 0.6
I
I
I
0.9
Figure 5. Variation with scan rate of the cyclic voltammetric reduction peak current function for 0.183 mM Cd(I1) in 0.3 M KCI. (0)experimental values. (0)calculated planar current function values, based on the difference between the observed value and the spherical current function value calculated using A = 0.0144 cm2and ~ 2 =” 2.55 ~ X IO3 cm/s1’2. Dashed line is the predicted planar current function value based on the indicated values of A and 0”’.Uncertainties represent the standard deviation of 2 to 3 measurements
can be estimated as the difference between the sphericity terms (in the absence and presence of shielding effect correction) times the spherical electrode area, (36.3 - 23.5) D”2 t’I6 A,lm’13 or 12.8(6a1’2/d)2‘3 D1I2 t 5 I 6 m’f3;this approach indicates a n average effective electrode area for the data in Tables I1 and 111, which is 0.00047 cm’ smaller than the calculated spherical area (range of 0.00042 to 0.00050 cm’). Correction of points on curve A for a contact area of 0.00047 cm2 yields the results shown in Figure 4. Contact area corrected currents should obey relationships for a freely suspended drop and, indeed, the corrected curve A data do parallel the theoretical predictions (curve E) over the range of 0.5 to ca. 7.5 s; although these corrected id values lie above curve E, the deviation is well within the uncertainty of the D value for Cd(I1). The difference in apparent effective contact areas indicated by ac and dc polarography may result from several factors, e.g., an electrode may have different effective areas for faradaic and nonfaradaic processes. I t is well established that the faradaically effective area for solid planar electrodes, e.g., Pt and graphite, is t h e projected area, which more closely approximates the macroscopic rather than the microscopic area (31, 32) because the diffusion layer extends far beyond the surface roughness. This projected area phenomenon is precisely the reason why a spherical Hg electrode supports a larger current than a planar Hg electrode of the same geometric area, since the projected area for a spherical electrode is larger than its geometric area. Although the spherical term of Equation 2 accounts for the projection, the expression for a freely suspended sphere cannot properly account for the projection in the region of the neck or movement of the drop’s center of mass; the latter projection may partially compensate for the effective contact area determined by ac polarography. Because the ac polarographic charging current does not involve diffusion and because the double layer is very thin compared to the drop radius, the true, unprojected area is determined by the ac polarographic charging current method.
RESULTS AND DISCUSSION CYCLIC VOLTAMMETRY Cadmium(I1). To minimize problems associated with iR
0.091 0.128 0.182 0.365 0.730 Mean Std dev Re1 std dev, ‘70 Range Re1 range, %
0.0144b 0.0145 0.0147 0.0144 0.0142 0.0144 0.0002 1.3
0.0139c 0.0139 0.0142 0.0138 0.0137 0.0139 0.0002 1.3
0.0134d 0.0134 0.0137 0.0133 0.0132 0.0134 0.0002 1.4
0.013P 0.0135 0.0136 0.0132 0.0129 0.0134 0.0003 2.3
0.0126 0.0122 0.0119 0.0123 0.0003 2.3
0.0005 3.5
0.0005 3.6
0.0005
0.0007 5.2
0.0007 5.7
3.7
0.0125f 0.0124
Calculated from data in Figure 5 and Table IV. From Equation 20; D”’ = 2.546 X cm/s”’. From Equation 20; 0”’= 2.638 X cmls”’. From Equation 20; 0”’ = 2.735 X cm/s1/2. e From Equation 1 5 ; I , = 4.035 p A s”’/mM mgz’3. From Equation 1 5 ; I,+’ = 4.369 p A sl”/mM mg2’3. a
el 0
1
I
I
0.3
1
“ic.
1
I
0.6
I
1
1
0.9
(”/$
Figure 6. Variation with scan rate of the cyclic voltammetric reduction peak current function for 0.341 mM Fe(II1) in 0.4 M K2C204. ( 0 ) experimental values. (0)calculated planar current function values, based on the difference between the observed value and the spherical current function value calculated using A = 0.0151 cm2 and 0’” = 2.30 X lo3 cm/s”2. Dashed line is the predicted planar current function value based on the indicated values of A and 0 ’ ” . Uncertainties represent the standard deviation of 3 to 8 measurements
loss, cyclic voltammetric data were acquired on 0.183 mM Cd(I1) in 0.3 M KCl. T h e peak current function a t varying scan rate (Figure 5 ) clearly shows the effects of electrode sphericity, Le., it decreases with increasing u. Using the Table IV data and either Equation 15 or 20, the H M D E area was evaluated (Table VI); the results using Equation 15 show a trend with u due to sphericity. Even a t the fastest L’, where sphericity is relatively negligible (less than a 2% contribution), Equation 15 predicts an area ca. 10% smaller than that obtained from Equation 20 with the best estimate of D112. Subtraction of the spherical contribution from the observed current yields the planar current contribution, described by Equation 12 for a reversible system, for which ~ , / C U ’ / ~should be scan-rate independent. The results of such a subtraction (Figure 5 ) show that the calculated planar term is, indeed, essentially constant with no point deviating by more than 2% from the expected value. Iron(II1). Cyclic voltammetric peak current function data for 0.341 mM Fe(II1) in 0.4 M K2C204(Figure 6) were analyzed
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
Table VII. Area of the HMDE Based on dc Polarographic and Cyclic Voltammetric Data for 0.341 mM Fe(II1) in 0.4 M K,C,O,“ A , cmz
u , VIS
0.036 0.051 0.073 0.146 0.218 0.291 0.457 0.641 Mean Std dev Re1 std dev, % Meanf Std devf Re1 std dev, %f
0.0151b
0.0153 0.0152 0.0154 0.0146 0.0146 0.0156 0.0152 0.0151 0.0004 2.4 0.0153 0.0002 1.2
0.0144‘ 0.0146 0.0146 0.0147 0.0140 0.0140 0.0147 0.0145
0.0154d 0.0154 0.0152 0.0151 0.0142 0.0140 0.0149 0.0145
0.0142e 0.0142 0.0140 0.0139 0.0131 0.0130 0.0138 0.0134
0.0144 0.0003 2.0 0.0146 0.0001 0.8
0.0149 0.0005 3.5 0.0151 0.0003 2.3
0.0137 0.0005 3.5 0.0139 0.0003 2.2
Calculated from data in Figure 6 and Table V. From Equation 20; 0’” = 2.304 X cm/s”z. From Equation 20; D’”= 2.402 x cm/s”’. From Equation 1 5 ; 1, = 1.748 P A s’”/mM mg’”. e From Equation 1 5 , I d ’ = 1.895 9 A s”*/mM mg2’3. Based on six points not including values at u = 0.218 Vis and 0.291 Vis. a
analogously to the cadmium data to determine the electrode area (Table VII) and to calculate the planar current function (Figure 6). As with Cd(II), a trend in the calculated area using Equation 15 indicates the effect of sphericity. If the data a t scan rates between 0.2 and 0.3 V/s are neglected, the standard deviations of the determined area are about 1% , the same as t h e Cd(I1) data; however, the mean areas determined using t h e two chemical systems differ by 0.0005 to 0.0015 cm2 or 5 to 12% of the area obtained using Fe(III), which always gives larger areas. E f f e c t of C h e m i c a l S y s t e m on D e t e r m i n e d H M D E Area. Because the uncertainties in the parameters associated with the calculation of U’/*and A are considerably below the level which could account for the 5 to 12% discrepancy in the areas determined using Cd(I1) and Fe(III), the difference is likely to be significant. In fact, although the F-test indicates no significant difference between the variances a t the 5 7 ~ uncertainty level, i.e., S,*/S2*is smaller than the value of F which would be exceeded by chance 5% of the time, there is a significant difference between the mean areas determined by Cd(I1) and Fe(II1) even a t the 99% confidence level. T h e probable source of the discrepancy is a difference in behavior of the chemical systems. Some often overlooked reports suggest that Cd(II)/Cd(Hg) is not a satisfactory model system. Delahay and Trachtenberg (33,34)showed that, when “normal care” is taken in chemical purification, small amounts of adsorbable impurities may be present, which can drastically alter the heterogeneous rate constant ( h s , h ) measured at a n H M D E but which have little effect on work at a DME. They observed a decrease of more than two orders-of-magnitude in t h e Cd(I1) hs,h when the exposure of the HMDE to the solution before measurement varied from a few minutes to two hours. Randles and Somerton (35,36) noted a change of over three orders-of-magnitude in hs,h upon variation in the concentration of added surfactant. T h e extreme sensitivity of h s , h t o adsorbed impurities is probably due to the close proximity of the Cd(I1) reduction potential to the potential-of-zero-charge. T h e cyclic voltammograms, from which the data in Figure 5 and Table VI were derived, showed a seemingly peculiar phenomenon. For a two-electron reduction, the difference between cathodic and anodic peak potentials, E, - E,, should be 0.030 V; the observed values, even a t = 0.09 V/s, were L)
487
0.02 V. However, the difference between E , ant1 the potential a t half peak height, Epc12, which should be 0.014 V, was 0.03 V, which, because of the observed value of E,, - E,,, cannot be due to iR loss in solution. In light of the reported effect of impurities on the cadmium behavior, the dra,ivn-outnature of the cathodic peak is probably the result of a small h s , h . However, regardless of the reason for the drawn-out nature of the Cd(I1) peaks, their deviation from the theoretically predicted behavior for a reversible system !suggests that HMDE areas calculated from Cd(I1) data, assuming reversible behavior, will be erroneous and, because of the drawn-out nature of the peaks, will be low. EVALUATION OF THEORIES AND PROCEDURES DC P o l a r o g r a p h y . The results clearly indicate that, for controlled 2-s drop-times, the Ilkovic equation does not accurately describe either the id-h, or i-t relations for a single drop. Application of Equation 5 and the effective contact area determined by ac polarography results in calculated diffusion coefficients for Cd(II), which are a t variance with previously reported results by over 40% (20% for U’,’2). The remarkably good agreement between the U values in Table 111, calculated using Equation 2 with R = 23.5, and the published value is a fortuitous consequence of t,he drop-time employed for data acquisition. as is obvious from the time (1.87 s) at which experimental curve .4of Figure 4 and curve F for the theoretical behavior predicted by Equation 2 with B = 23.5, cross, and by the fact that the difference between curves A and F a t 2.10 s is only 0.3%. It is evident from Figure 4 that, in the time range from 1 to 4 s, the experimental data (curve A I are within 3% of the theoretical prediction based on Equation 2 with R = 23.5 (curve F ) ; the same accuracy is obtained for B = 36.3 (curve E) in the range of 2.3 to greater than 12 s on the first drop with natural drop-time; however, use of long controlled drop-times may result in eventual development of depletion in the solution region encountered by the electrode surface near the end of its drop-life, since the stirring effects accompanying mechanical dislodgment may not completely homogenize the solution far from the capillary orifice. Within the range of 2 to 4 s, either form of the Matsuda equation will apparently give comparable accuracy. The change a t about 3.4 s in the value of R for Equation 2, which better describes the i--t relation, probably reflects the assumption used in Matsuda’s derivation (15), that the drop is spherical throughout its life. The assumed spherical shape defines a certain fraction of the drop for which (a) the drop is nearly contacting the glass capillary or (b:’the distance between drop and capillary is less than the expected diffusion layer thickness, so that supply of electroactive species to that region of the electrode is greatly reduced; based on Matsuda‘s theory, the fraction of the drop area suffering from one of these two phenomena increases during drop-life. Early in the drop-life, the shape probably is relatively spherical; however, the drop is actually pendant-shaped, particularly later in its life when the weight is relatively large. T h e pendant shape results in the major portion of the drop‘s mass---and, hence, area-being below the neck and, consequently, farther removed from the capillary than would be thfz case for a spherical shape, with concomitantly reduced shielding by the capillary. Thus, early in the drop-life, when the shape approaches spherical, the equation accounting for shielding more accurately describes the i--t behavior: later; as the mass increases and the drop neck stretches, the shielding effect diminishes and the i-t behavior is more nearly approximated by the equation for a freely suspended drop. For very accurate measurement of D , Le., 1 to 2 % accuracy, it is evident from the factors discussed in the previous paragraph and the fact that the Hg flow-rate influences the
488
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
time a t which the i-t behavior is more accurately described as that of a freely suspended drop, that calibration data should be obtained under the drop-time and Hg flow-rate conditions to be employed. For the purpose of calibration, the system of 1 mM Cd(I1) in 0.1 M KC1 appears to be excellent, since D for Cd(I1) under these conditions is accurately known. Considerable debate has recently centered on the questions of whether polarographic behavior at controlled drop-times of less than 1 s is accurately described by the Ilkovic equation and whether the back-pressure term in the calculation of h,-and, hence, m-is properly described by 3.1/ (mt)'I3. Canterford (37) has reviewed the various reports and has presented evidence which indicates that the Ilkovic equation does not properly describe the currents at short drop-times. The results of the present study also clearly indicate that use of a mechanical drop-knocker tends to diminish or eliminate the depletion effects, which, under conditions of natural drop-fall, counterbalance sphericity effects and permit the Ilkovic equation to describe accurately the i-h, relation. Cyclic Voltammetry. For accurate determination of the HMDE area using cyclic voltammetry or linear potential scan amperometry, a chart recorder is preferable to an oscilloscope as a read-out device because of the inherently greater accuracy of the former; however, because of the relatively slow response time of a recorder, it is generally not possible to employ scan rates exceeding 0.5 to 1 V/s; even with scan rates of ca. 0.5 V/s, low current axis sensitivities must be employed to prevent recorder response degradation, thus reducing the precision with which peak currents can be measured. (The danger associated with using too high a current axis sensitivity is exemplified by the points in Figure 6 for ul/' of 0.47 and 0.54 V1/'/sl/'.) Thus, one must evaluate the electrode area under conditions of slow scan rate, for which it is necessary t o use the cyclic voltammetric peak current equation which accounts for sphericity. T h e variability of the HMDE area, as indicated by the standard deviations for the peak current functions (Figures 5 and 6) is less than 3%. Because of the previously mentioned problems associated with the Cd(II)/Cd(Hg) system, this system should not be employed for H M D E area evaluation. The Fe(III)/Fe(II)
couple seems to be an excellent choice for such area evaluation.
LITERATURE CITED (1) (2) (3) (4)
J. M. Markowitz and P. J. Elving, Chem. Rev., 58, 1047 (1958). D. Ilkovic, Collect. Czech. Chem. Commun., 6. 498 (1934). J. M. Markowitz and P. J. Elving. J . Am. Chem. Soc., 81, 3518 (1959). D. M. Mohilner, J. C. Kreuser, H. Nakadomari, and P. 0. Mohilner, J . Nectrochem. Soc., 123, 359 (1976).
(5) (8) (7) (8)
G. H. Nancollas and C. A. Vincent, Electrochim. Acta, IO, 97 (1965). W. H. Reinmuth, J . Am. Chem. Soc., 79, 6358 (1957). R. S. Nicholson and I. Shain, Anal. Chem., 36, 706 (1964). T. E. Cummings, M. A. Jensen, and P. J. Elving, to be submitted for publication. H. Strehlow and M. von Stackelberg, 2 . Nekfrochem., 54, 51 (1950). M. von Stackelberg, Z . Bekfrochem., 57, 338 (1953). M. von Stackelberg and V. Toome, 2. Nektrochem., 58, 228 (1954). T. Kambara and I. Tachi, "Proc. I . Internat. Polarograph. Congress", Vol. 1, Prirodovedeche Vydavatelstvi, Prague, 1951, p 126. T. Kambara and I. Tachi, Bull. Chem. Soc. Jpn., 23, 226 (1950). R. S. Sabrahmanya, Can. J . Chem., 40, 289 (1962). H. Matsuda, Bull. Chem. SOC. Jpn., 36, 342 (1953). J. Koutecky, Czech. J . Phys., 2, 50 (1953). W. M. MacNevin and E. W. Balis, J . Am. Chem. Soc., 65, 660 (1943). G. S. Smith, Trans. Faraday Soc., 47, 63 (1952). J. W. Perram, J. E. Hayter, and R. J. Hunter, J . Elecfroanal. Chem., 42, 291 (1973). D. E.Smith, in "Electroanalytical Chemistry", Vol. 1, A. J. Bard, Ed., Dekker, New York, N.Y., 1986. J. Hevrovskv and J. Kuta. "Princioles of Polaroaraohv", Academic Press, London, 1966, p 37. C. L. Rulfs, J . Am. Chem. Soc., 76, 2071 (1954). D. J. Macero and C. L. Rulfs, J . Elecfroanal. Chem., 7, 328 (1964). M. von Stackelbera and H. Frevhold. 2.Elektrochem.. 46. 120 (1940). J. J. Lingane, Cheh. Rev., 29, 1 (1941). J. E. E. Randles and D. W. Somerton. Trans. Faraday Soc., 48, 937 (1952) R deleeuwe, M Sluyters-Rehbach, and J H Sluyters, Hectrochim. Acta, 14 1183 (1969) J. J. Lingane, J : Am. Chem. Soc., 68, 2448 (1946). D. E. Smith and W. H. Reinmuth, Anal. Chem., 33, 482 (1961). J. Kuta and I. Smoler, in "Progress in Polarography", Voi. 1, P. Zuman and I . M. Kolthoff, Ed.. Interscience, New York, N.Y., 1962, p 43. P. J. Elving and D. L. Smith, "Analytical Chemistry 1962", Elsevier, Amsterdam, 1963, pp 204-213. C. N. Reilley, G. W. Everett, and R. H. Johns, Anal. C k m . , 27, 483 (1955). P. Delahay and I. Trachtenberg, J . Am. Chem. Soc., 80, 2094 (1958). P. Delahay, J . Chim. Phys., 54, 369 (1957). J. E. E. Randles and K. W. Somerton, Trans. Faraday Sm., 48, 951 (1952). J. E. E. Randles. Faraday Soc. Discuss., 1, 11 (1947). D.R . Canterford, J . Nectroanal. Chem., 77, 113 (1977).
(9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) 1241 i25j (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37)
RECEIVED for review October 21, 1977. Accepted December 7,1977. The authors thank the National Science Foundation, which helped support the work described.
Solvent Extractioa of Chromium(II1) by Salicylic, Thiosalicylic, and Phthalic acids Dennis G. Sebastian' and David C. Hilderbrand" Department of Chemistry, South Dakota State University, Brookings, South Dakota 57007
The use of salicylic, thiosalicylic, and phthalic acid complexing agents for the solvent extraction of Cr(II1) from aqueous solution was investigated. N-Butanol was used as the organic solvent. The extraction efficiency was optimized with respect i o pH, heating period, choice of buffer, and concentration of a salting-out agent. An extraction efficiency of greater than 97 YO was obtained using a mixed phthalic-thiosalicylic complexing system.
Quantitative solvent extraction of many first row transition metal elements can be readily achieved a t room temperature 'Present address, Agrico Chemical Co., South Pierce Chemical Works, B a r t o w , Fla. 33830. 0003-2700/78/0350-0488$01,00/0
using a variety of complexing agents. The solvent extraction of chromium is much more difficult with quantitative extraction occurring only after extraction at elevated temperature for a prolonged period of time. One cause of chromium's poor extractability is the lability of the hexaquochromium ion. The half-life of the exchange of water molecules has been reported as 40 h (I) and corresponding rate constants for the exchange reaction of 2 X lo-' (2) to 4.8 X 10* s-' ( I ) have been reported. By comparison the rate constants for exchange of hydrated copper(I1) and iron(II1) ions are 2 X lo8 s-l and 2.5 X IO25-l (2). Chromium(II1) was chosen as the oxidation state for extraction because of its stability compared to chromium(I1). Acetylacetone, thenoyltrifluoroacetone, hydroxyquinoline, diethyldithiocarbamate, and l-phenyl-3-methyl4-benzoylpyrazolone have previously been used to extract 1978 American Chemical Society
