Diffusion Coefficients of Ferri- and Ferrocyanide Ions in Aqueous Media, Using Twin-Electrode Thin-layer Electrochemistry S. J. Konopka and Bruce McDuffie Department of Chemistry, State Uniuersity of New York at Bingharnton, Binghamton, N . Y. 13901
The diffusion coefficients, Do and DR, of the species ferri- and ferrocyanide, respectively, in aqueous KCI media were determined by twin-electrode thin-layer electrochemistry using a micrometer-type thin-layer cell. The values obtained for Do and DR at 2 5 O C in LOOM KC1 were 0.726 (10.011) X and 0.667(10.014) X cm2/sec, respectively, covering a concentration range from 0.61 to 6.36m.M in total electroactive species. Identical values within experimental uncertainty were found in 0.10M KCI medium. Criteria for the reliability of this absolute method for measuring the D values of a soluble, stable redox pair are presented, and comparisons of D values with those obtained by other workers are made.
VARIOUSMETHODS have been devised for determining the diffusion coefficients (D values) of species in solution, such as the use of the calibrated diaphragm cell (1-3), radiochemical tracers (4, 5), electrical conductance (6), and optical methods (7). For electroactive species in an excess of supporting electrolyte, electrochemical methods often have been used. Such methods, for the most part relative methods requiring calibration with a substance of known D value, have included Cottrell-type (8-13), chronopotentiometric (12, 14, 1 9 , and rotating disk (16) measurements at platinum electrodes, and polarographic measurements at the dropping mercury electrode (11, 17). Results by these electrochemical methods may differ from one another by 10-20z (13, 77). Macero and Rulfs (13) have attributed these differences largely t o uncertainties in the effective electrode area and to the necessity for using a suitable reference ion. Thin-layer steady-state methods are characterized by rnathematical simplicity and relative freedom from time-dependent (1) J. H. Northrup and M. L. Anson, J . Physiol. Chem., 10, 523
(1929). (2) R. H. Stokes, J. Amer. Chern. SOC.,72,763 (1950). (3) C. L.Rulfs, ibid., 76, 2071 (1954). (4) J. H. Wang and F. M. Polestra, ibid., p 1584. (5) T. A,, Miller, B. Prater, J. K. Lee, and R. N. Adams, ibid., 87, 121 (1965). (6) H. S. Harned and R. L. Nuttall, ibid., 69, 736 (1947). (7) G. Kegeler and L. J. Cosling, ibid., p 2916. (8) H. A. Laitinen and I. M. Kolthoff, ibid., 61, 3344 (1939). (9) H. A. Laitinen and I. M. Kolthoff, J . Phys. Chem., 45, 1061 (1941). (10) I. M. Kolthoff and J. J. Lingane, “Polarography,” 2nd ed., Interscience, New York, N. Y., 1952, pp 409-411. (11) M. von Stackelberg, M. Pilgram, and V. Toome, 2.Elektrockem., 57, 342 (1953). (12) P. J. Lingane, ANAL.CHEM.,36, 1723 (1964). (13) D. J. Macero and C. L. Rulfs, J. Amer. Chern. SOC.,81, 2942 (1959). (14) C . N. Reilley, G. W. Everett, and R. H. Johns, ANAL.CHEM., 27,483 (1955). (15) D. M. Oglesby, S. V. Omang, and C. N. Reilley, ibid., 37, 1312 (1965). (16) A. J. Arvia, J. C. Bazan, and J. S. W. Carrozza, Electrochim. Acta, 13,81(1968). (17) L. Meites, “Polarographic Techniques,” 2nd ed., Interscience, New York, N.Y., 1965, pp 145-150. 1 -
~
I -
experimental problems (18-21). The twin-electrode thinlayer method proposed by Anderson and Reilley (19) for measuring the D values of a redox couple is an absolute method based on measurement of the limiting steady-state current, is,, followed by coulometric analysis of the thin layer. The i,, between closely spaced twin working electrodes is given by the equation:
where n is the number of electrons transferred in the redox reaction, F is the value of the Faraday, A is the projected electrode area, C is the total concentration of electroactive species in the thin layer, 1 is the thickness of solution between the two working electrodes, and Doand D R are the diffusion coefficients of the oxidized and reduced species, respectively (19,22).
D values are calculated according to the following equations (19):
(3) where iss(c) and are the limiting steady-state currents at the cathode and anode, respectively, Qc is the charge required to reduce all of the oxidized species between the thinlayer electrodes once the condition of is, has been reached, and Qa is the charge required to oxidize all of the reduced species and in the thin layer at the iss condition. The values of will be equal if there is negligible electrolysis current along with the steady-state current. From Equations 2 and 3, it is evident that the D values can be determined independently of n, A , and C. From Equation 1 and Faraday’s law for the coulometry of thin layers of solution (23, 24), straight lines should be obtained if the experimental values of l / i s s ( cl)/,i s s ( u Qc, ) , and Qu are each plotted against the /-setting of the micrometer, giving the respective slopes, S l ~ c s sS( lcl)i ,s s ( aS,,, ) , and SQ&. Using (18) R. C. Bowers and A. M. Wilson, J. Amer. Chem. SOC.,80,2968
(1958). (19) L. B. Anderson and C . N. Reilley, J. Electroanal. Chem., 10, 295 (1965). (20) H. Dahms, ibid., 11, 62 (1966). (21) A. T. Hubbard and F. C . Anson, in “Electroanalytical Chemistry,” A. J. Bard, Ed., Vol. 4, Marcel Dekker, New York, N.Y., 1970, pp 129-210. (22) B. McDuffie, L. B. Anderson, and C. N. Reilley, ANAL. CHEM., 38, 883 (1966). (23) C. R. Christensen and F. C. Anson, ibid., 35, 205 (1963). (24) L. B. Anderson, B. McDuffie,and C. N. Reilley, J. Electroanal. Chem., 12, 477 (1966).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
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these slopes instead of absolute values, Equations 2 and 3 become :
Do
=
1
2(S1if,. &%J
(4)
Thus the D values are determined independently of a knowledge of the absolute layer thickness, although accurate measurement of increments in I are required for accurate determination of the various slopes. In the present study, the thin-layer method is critically evaluated using the ferri-ferrocyanide couple in aqueous KC1 as a model redox system. Several modifications in technique and procedure are introduced to develop the inherent potential of the method. EXPERIMENTAL
A micrometer-type thin-layer electrochemical cell with twin working electrodes, each of measured projected area 0.278 cm2, was used (15, 19). Before each set of measurements with a fresh portion of solution, the platinum surfaces were polished to a mirror-like consistency using gamma alumina on a Gama1 polishing cloth (Fisher Scientific eo., No. 12-282). The Teflon (Du Pont) collar and cup were flush with the electrode surfaces to minimize edge effects while still allowing the attainment of I-values as small as 30 microns. A microscope with a filar micrometer eyepiece (Gaertner No. mllO-A), was positioned horizontally about 6 inches from the micrometer scale of the cell and used to ensure reproducibility of micrometer settings within h0.05 micron (p). In each experiment, layer thicknesses were changed by increments equivalent to the smallest division of the micrometer scale, Le., 25.4 h 0.1 p , the accuracy of these increments being limited more by the tolerance in placement of scale lines on the micrometer barrel than by the reproducibility of setting the micrometer at a given line. Philbrick operational amplifiers were used (15, 19) to achieve potential control of the two working electrodes, and to measure and integrate current. All potentials were measured us. an SCE reference electrode which was in contact with the cell solution via a fiber-tip salt bridge containing the supporting electrolyte. The auxiliary electrode was a platinum wire ring. A dual pen recorder, Sargent model DSRG, was used to record current and coulometric data. Limiting potentials were obtained by the method of thinlayer steady-state voltammetry (TLSSV) as follows : The electrode for measurement of steady-state current was fixed at an extreme anodic or cathodic potential, and the other working electrode was scanned slowly (100 mV/min) from a potential of zero steady-state current to a potential giving the limiting steady-state current, is,, i.e., to a limiting cathodic or anodic potential, respectively. A sensitive x-y recorder was used to record steady-state current us. E curves. Reagent grade KC1 and distilled demineralized water were used to prepare a large quantity of 1.00M stock supporting electrolyte solution, which was diluted to 0.100Mas necessary. Weighed amounts of reagent grade K3Fe(CN)6or &Fe(CN)G. 3HzQ were added to dry flasks and diluted to volume with supporting electrolyte to obtain the desired concentration of electroactive species. Solutions containing electroactive species were used the same day as prepared. All solutions were deaerated with presaturated nitrogen prior to use and kept under a blanket of nitrogen during experiments (15). Experiments were conducted at 25.0 h 0.1 "Gin a constant temperature room, the temperature of the air and solutions being monitored with a calibrated thermistor probe. Resistance Method for Calibration of Micrometer. The micrometer cell was calibrated for linearity and for I-zero ( i e , , the setting corresponding to zero solution thickness 1742
e
between the electrodes) by measuring the resistance, R, of a IO-jM NaC1Q4 solution at various micrometer settings as follows: a 5 kHz alternating current signal of 5 V rms amplitude was passed to ground through a bridge circuit containing in one arm, a 100-K resistor followed by a variable resistor and variable capacitor in series, and in the other arm, a 100-K resistor, and the twin electrode cell. The bridge was balanced to within i.0.5 mV using a Tektronix Model 502-A oscilloscope with differential input channels as a null detector. With this arrangement, R values from 800 to 2400 ohms were measured with a precision of 2 ~ 0 . 5 x . Assuming a direct proportionality between R and I , the least squares best straight line corresponding to the R data at the various settings was determined by a computer program. The relative standard deviation of the slope constituted the check for linearity of the micrometer scale, and the zeroresistance intercept gave the setting corresponding to Izero, with its standard deviation. (See Figure 2 and discussion below.) Determination of Electrode Configuration. Cottrell-type chronoamperometric experiments were performed to establish the optimum electrode configuration, in view of solution density considerations (8). With a deaerated ferricyanideKCl solution in the cell, the top electrode was set at the limiting anodic potential and adjusted so the solution layer thickness was 0.2 inch. After the background current became constant, the top electrode was stepped to the limiting reduction potential and its i-t curve recorded, the other twin electrode being at ambient potential. The layer was flushed out, by raising and lowering the upper electrode several times, and the same procedure was followed at the bottom electrode. Then a ferrocyanide solution was put in the cell and analogous i-t curves for oxidation were recorded at the two electrodes, with the same solution thickness. The results (see Figure 1,a and b) are interpreted below. Procedure for D Value Determinations. is+) and Qa were measured first, as follows : the micrometer was carefully adjusted to obtain the thickest desired layer, Le., an I-value in the range 80-100 p . The upper electrode was set at the limiting anodic potential to pre-oxidize the solution layer, the other thin-layer electrode being at ambient potential. After 15 seconds, the bottom electrode (for the ferri-ferrocyanide system) was adjusted to the limiting cathodic potential, which initiated the limiting steady-state current, measured at the anode as The current was allowed to flow for 1 minute, enabling its constancy to be observed. The cathode was then disconnected and simultaneously integration of the electrolysis current at the anode was begun. The Qa curve was recorded for 90 seconds, after which the cell was returned to ambient potential. The solution between the electrodes was flushed out by raising and lowering the upper electrode, the micrometer was set to a layer precisely 0.001 inch thinner than the first, and i s s ( a ) and Qa were measured again. The process was repeated at successively thinner I settings. This first set of measurements at the various 1 values was discarded as a preconditioning set, then at least four sets after the first were run, at each of at least three I values. Immediately after the and Q. data were obtained, iss(e) and Q L were measured in an exactly analogous fashion by monitoring at the cathode and disconnecting the anode for coulometry. An identical sequence of 1-values was used. The procedure described above constitutes one experiment or run. To allow for edge effects, the value of Q for each Q-t curve was obtained by linear extrapolation of the coulometric curve to zero time using the tangent to the curve in the 60-75 second region. All data were corrected for background effects. The slopes of the llis,-l and Q-l lines were determined by a least squares computer program, which also gave the 1 intercepts and the relative standard deviations of the slopes and intercepts. Then Do and D R with their cumulative standard deviations were calculated from Equations 4 and 5.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
I
I
2
4
I 6
TIME, MIN
Figure 1. Effect of electrode configuration on currents in chronoamperornetric experiments a. Reduction of 3.6 mM ferricyanide, at potential of -0.05 b. Oxidation of 4 mM ferrocyanide, at potential of +OS0 V US. SCE v VS. SCE Curves A and B show response of top and bottom electrodes, respectively; layer thickness approximately 0.2 inch. Curve C is a theoretical curve for diffusion to an unshielded circular, planar electrode (26), of area 0.278 cm2,at stated concentrations
RESULTS AND DISCUSSION
Using a 1mM ferricyanide solution in 1M KCl, the TLSSV curve was Nernstian for a I-electron transfer reaction, scanning in either the anodic or cathodic direction, with a halfcurrent potential, E l , ~ ( , sof ) , $0.23 V, in agreement with the formal standard potential of this system (25). From the TLSSV curves, +OS0 and -0.05 V us. the SCE were limiting anodic and cathodic potentials, respectively. The same values were found in a 0.10M KC1 medium. Laitinen and Kolthoff (8) pointed out that in electrolysis at horizontal shielded planar electrodes, if the direction of diffusion was such that the less dense material (Le., ferricyanide) formed above the material of greater density (Le., ferrocyanide), agreement with theory for linear diffusion was obtained. If the direction of diffusion was reversed, producing a n inverse density gradient, large and irregular currents were obtained. Analogously, the experiment on determination of optimum electrode configuration was run using the unshielded electrodes of the thin-layer cell. For the reduction of ferricyanide (Figure la), the smaller current (curve B ) is obtained at the bottom electrode, while for oxidation of ferrocyanide (Figure lb), after about one minute, the smaller current (curve A ) is observed at the top electrode, in general agreement with Laitinen and Kolthoff's work. However, these smaller currents are higher than the theoretical values (curve C ) for diffusion to an unshielded planar circular electrode at short times (26), presumably because of some convective
stirring (8, 12). In the cases of electrode configurations giving rise to inverse density gradients (curve A , Figure la; curve B, Figure 16) the larger currents are observed, with a reproducible fluctuation in the ferrocyanide case such as the irregularities noted previously (8). The optimum electrode configuration is defined as that giving minimum current in the chronoamperometric experiments (in the present case, top electrode anode, bottom electrode cathode). Furthermore, it is assumed that convective stirring will be even less when the electrodes are very close together in the thin-layer experiments. To test this assumption, iss for the optimum electrode configuration was compared with the is, for the inverse configuration: values only about higher were found in the latter case; the sum of the coulometric slopes was unchanged, in accord with the concept of mass balance, but the slope ratio was changed significantly, giving rise to different D values. The closeness of the is, values confirms the recent work of Schmidt-Weinmar that convection is minimized in solution layers less than 200 p thick (27). Table I presents a comparison of I-zero values from the linear extrapolation of I / i s s ( c )and l/iss(a)data, illustrated in Figure 2. The agreement of Z-zeroes with each other and with the I-zero from resistance measurements (Figure 2 ) indicates the reproducibility of handling the cell, since it is taken apart after each experiment in order to repolish the electrodes. It has been observed that if nonlimiting potentials are used (e.g., the usual limiting potentials, but with electron transfer slowed
(25) Ref. 10, p 480. (26) 2. G. Soos and P. S. Lingane, J. Phys. Chem., 68, 3821 (1964).
(27) H. G. Schmidt-Weinmar,Bey. Bunsenges. Phys. Chem., 71, 97 (1967).
2z
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
* 1743
OOlOC
I e500
OOOBC
0 0 06C
-
4
5 0.004C
Table I. Reproducibility of 1-Zero Measurements Data No. of plot Medium exptsa C-zerob av -f std dev l/i88(a) 1M KC1 10 0.136817 f 0.000018 0.1M KC1 3 0.136798 f 0.000003 l/i88(c) 1M KCI 10 0.136822 -f 0.000015 3 0.136822 =I=0.000032 O.1MKCl For concentrations of ferri- and ferrocyanide, see Table 11. * Micrometer setting in inches corresponding to solulion layer of zero thickness. Table TI. Dependence of Steady-State Current on Concentration C , mMa Sl,i (a) Kb 1.OOM KCI Medium 0.30 17.89 5.37 0.61c 8.69 5.38 1.10 4.89 5.36 1.10 4.98 5.48 1.36 3.93 5.32 1.55 3.40 5.26 5.02" 1.06 5.33 5.09 1.05 5.32 5 . 23d 1.04 5.45 6.36 0.85 5.43 av 5.37 stddev 0.07 (1.273 0.10M KC1 Medium 0.91 6.00 5.46 5.01d 1.06 5.32 5.09 1.07 5.45 av 5.41 88
0 002c
Figure 2. Comparison of methods for calibration of twin-electrodethin-layer cell l/i(ss) us. I data; 5.23 mM ferrocyanide in 1.QOMKCI. R us. Idata: 10-*MKaC104solution
by contamination of the electrode surfaces) the currents will be less than theoretical, and the I-intercept from the l/ibs DS. 1 plots will be at a much smaller micrometer setting than the I-zero obtained from the resistance measurements. Slight contamination will produce a shift in the I-intercepi several orders of magnitude greater than the standard deviation for the measurement. This effect can be tested easily by measuring the steady-state current at various E-settings without cleaning the electrodes, then cleaning the electrodes and repeating the measurements on another portion of the same solution. The currents in the first case will be much lower than those in the second case, resulting in widely varying 1-zeroes. According to Equation 1, is, is proportional to C. Alternatively using SI one obtains:
where the right hand term, hereafter designated K , is a calibration constant for a given redox system and twin-electrode cell, D, being defined as a weighted diffusion coefficient equal to ~DoDR/(& DR). Table I1 lists the values of K obtained for a range of concentrations in the two KCI media. The results indicate that the current is a true steady-state current in agreement with Equations 1 and 6. Since K is the same within experimental error in 1.00 as well as 0.1OM KC1, the value of D, is the same for the ferri-ferrocyanide system in both media. From mass balance considerations, the coulometric data should follow the relationship
+
(7)
Thus, to establish the reliability of the coulometric measurements, the quantity nFA was calculated from Equation 7 for each experiment. The average values so obtained, 2.71
1744
e
stddev 0.08 (1.5z) 100% ferricyanide except as otherwise noted.
K = [Sl/zss(a)] [C]. See text.
Equimolar ferri-ferrocyanide mixture. Ferrocyanide solution.
(10.05) X 10.' and 2.70 (10.04) x lo4 coulomb ern' mole-1 for 1.00 and 0.10M KCl, respectively, were within 1 of the value calculated from the measured electrode area. The individual diffusion coefficients found for the ferriand ferrocyanide species, with respective relative standard deviations, are presented in Table 111. Each D value, calculated from Equations 4 and 5, i s based on the slopes of two least squares data plots. The standard deviation, SD, of each D value is the square root of the sum Qf the squares of the relative standard deviations of the two slopes used. In 1M KC1 the value of S D ranged ~ from 0.5 tQ 2.0% and S Z I from 0.9 to 3.2z$ the averages being 1.4 and 1.6%, respectively. The agreement of these individual SD values with the standard deviations of the groups of D values, 1.5% and 2.1 %, respectively, indicates that there is no significant variance between experiments. Similar comparisons of standard deviations can be made using the O . I M KCI data. (The last two results in 1MKCl were obtained approximately 6 months after the other results, indicating the stability and reproducibility of the cell and the method over a period of time.) From Table III it is evident that the diffusion coefficients are independent of the total concentration of electroactive species, within the range of concentrations used, in accord with Fick's first law. Furthermore, the D values are independent of the initial concentration ratio of oxidized to reduced species. With this redox system, both Do and D R could be obtained
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
~
Table 111. Diffusion Coefficients of Ferri- and Ferrocyanide at 25 "C Concna DO X lo6 DR X lo6 rnM cm* sec-1 S D ~% , cmasec-l S D R , % 1.OOM KCl medium 0.61b 0.731 2.0 ... 0.731 1.9 0: kil 1.9 1.10 0.718 1.4 0.697 2.1 1.10 0.719 1.7 0.673 3.2 1.36 0.737 1.7 0.656 2.6 1.5.5 0.718 0.7 0.667 0.9 5.02b 0.705 1.6 0.666 1.0 5.09 0.721 0.8 0.668 1.2 5,230 0.741 1.9 0.641 1.1 6.36 0.730 0.5 0.668 1.0 4.47" 0.738 0.9 0.664 1.2 5.00 av 0.726 av 1.4 av 0.667 av 1.6 std devd 0.011 (1.5%) stddev 0.014(2.1%) 0.10M KC1 medium 0.739 1.7 0.681 2.1 0.717 0.7 0.656 1.6 0.703 1.2 0 660 1.3 av 0,666 av 1.7 av 0.720 av 1 . 2 std dev 0.013 (2.0%) std devd 0.018 ( 2 . 5 % ) 100% ferricyanide except as otherwise noted. b Equimolar ferri-ferrocyanide mixture. Ferrocyanide solution. d Standard deviation of the group of measurements, not standard deviation of the mean.
0.91 5.010 5.09
Q
0
at a total concentration of electroactive species of 1mM or greater. At lower concentrations, the iss values were still reliable, but Q determinations became erratic. Electrode interferences may be responsible for erratic coulometric results at low concentrations. The D values obtained in 1M KC1 give Stoke's law radii ( 1 7 ) of 3.38 A and 3.68 A for the diffusing ferri- and ferrocyanide species, respectively. Both ions tend to ion pair with Kf (28, 29), and ferrocyanide appears to form an ion triplet to some extent (29). A small part of the observed difference in Stoke's law radii could be attributed to ion triplet formation in the ferrocyanide case, but a larger part of the differencemust have some other explanation, such as a greater extent of hydration of the ferrocyanide species over that of the ferricyanide. The calibration constant, K,can be used with n, F, and the measured value of A to calculate the quantity, D,. Since D w is defined as 2 D o D ~ / ( D o DE),it can be calculated from the experimentally determined values of Do and D R which have no dependence on C, A , or n. From the average values for the 1.00M KC1 medium (Table 11), D, = 0.694 X cm2 sec-1, whereas from the average D values (Table 111), D, = 0.695 X lod6 cm2 set-1. In 0.10M KC1 the corresponding values are 0.689 and 0.692 X 10'6 cmz secdl, respectively. This agreement demonstrates that the twinelectrode thin-layer method is an absolute method: Le., D values can be obtained for a soluble, stable redox pair without a knowledge of n, A , and C and without the use of a reference ion. In one exploratory experiment, from steady-state current ' cm2 sec-1 was obtained in data, a D, value of 0.709 X 106 0.1M KNOa. [This datum was obtained five years earlier in another laboratory using a 2mM ferri-ferrocyanide mixture in the same type of thin layer cell.] This result indicates little
+
(28) J. C. James and C. B. Monk, Trans. Faraday Soc., 46, 1041 (1950). (29) S.R. Cohen and R. A. Plane, 9. Phys. Chem., 61, 1096 (1957).
Comparison with Selected Literature Values for Ferri- and Ferrocyanide at 25 OC Do X loK DR X lo6 Method Medium cma sec-l cma sec-1 Ref Cottrell, absolute: 0.1MKCl 0.842 0.717 8 0.1MKCl 0.836 0.687 13 0.1MKCl 0.763 0.650 I1 O.liMKC1 . . . 0 670 12 Chronopotentiometric 0 . 1 M KC1 0.697 12 Pt, relative to Pb O.lMKC1 0:7i3 0.638 10 0.588 Rot. Pt disk 16 1.OMKC1 0.677 0.667 This work 1.OM KCl 0.726 Thin layer 0.67 This work 0.1MKC1 0.72 Thin layer
Table IV.
I
difference between KC1 and KNOI as supporting electrolytes. A comparison of results with those obtained by other methods is given in Table IV. The first set of results (8) may be high because of electromigration effects in the Cottrell experiment, since a 5mM electroactive species concentration was used with only a 0.1M supporting electrolyte concentration. [In our method, although these same concentrations were used in two experiments, no appreciable electromigration effect was observed.] The high value of Do in the next set (13) may be traced to the neglect of solution density effects; ferricyanide was reduced at an electrode where the direction of diffusion was upward, forming the heavier ferrocyanide and thus increased current due to convection. The remaining results show reasonable agreement except for the D values obtained using a rotating platinum disk electrode (16), where nonlimiting potentials may have been used. Effect of Nonparallelism of Electrodes. Although the working electrode faces are considered to be parallel to each other, nonparallelism could introduce errors in the steady-state current. .This problem was treated by Anderson and Reilley for square facing electrodes (19). For circular electrodes, graphical integration yields the following results (same notation as in keference 19): l/isswill be 6 . 4 z less than for perfectly parallel surfaces if I = 2q, 2.7 less if 1 = 3q, and 1.5 % less if 1 = 4q. [Corresponding decreases for the square electrode case (19) are 9%, 3.8%, and 2.1 respectively. From the micrometer setting a t which the cell "shorted" in the present work, it appears that the thinnest layer used for data collection was at 1 2 2q, thicker settings corresponding roughly to 1 2 3q and 12 4q. Thus nonparallelism could have caused the slopes of the l/issus. [lines to be high, and the D values low, by a maximum of 3 %, only slightly larger than the standard deviation of the experimental results. For increased accuracy, the degree of nonparallelism or tilt could be reduced by a more careful polishing and assembling technique. Coulometry with Elimination of Charging Current. For thin-layer potential-step coulometry in a cell with only one working electrode, Faraday's law takes the form (24)
z
z,
Q
+
nFAlC f Q a d s Qd.1. where Qads a n d Q d . z . represent the contributions caused by reaction of adsorbed species and by change in double layer capacitance, respectively. A plot of Q us. I gives an intercept at I-zero equal to Qads + neither of which is usually known. [The slope, SQ,equal to nFAC, provides the basis for determining C.] By contrast, in the coulometric method used here for D value determinations, there should be no significant contribution from charging current. The electrode used for coulometry after initiation of the steady-state current remains at =
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
e
1745
constant potential and has immediately adjacent to it in the solution nearly the same concentration of electroactive species (as 100% 0 or 100% R) before and after coulometry. Thus one would expect no appreciable change in the double layer capacitance of this working electrode. From a Q-1 plot, the number of coulombs at E-nero (obtained from issor R data) can be expected to give Qads directly without any & . l . term: the intercept from the Qa-l data should give the amount of species R previously adsorbed at the cathode, and the Qc-1 intercept should give the amount of species 0 previously adsorbed at the anode, assuming that the time required for desorption of these species is short cornpared to the duration of the individual Q-t curves. At the higher concentrations used in the present studies, the amounts of adsorption of
electroactive species at the anode and at the cathode appear to be 2.0 X low9 and 2.6 X respectively. These results would indicate several monolayers of electroactive material. Obviously further studies of this aspect of the system are needed.
RECEIVED for review June 1, 1970. Accepted September 17, 1970. Presented in part at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 5, 1970. The authors acknowledge financial support of the National Science Foundation under Grant NSF-G9925 and the Research Foundation, State University of New York, under Grants 40-223A, FRF-40-035, and 40-223B.
Method and Apparatus for Determining as Mixtures David E. Emerson and Richard L. Kaplanl Dicision of Helium, Bureau of Mines, U.S. Department
of the Interior, Amarillo, Texas 79106
A method and apparatus are described for determining the helium content of gaseous mixtures. The work was done so that the Bureau of Mines could more accurately and economically analyze helium-containing natural gases, crude helium purchased from private industries, and helium in gases used in research. Activated coconut charcoal is utilized at liquid nitrogen temperature to adsorb components other than helium in the mixture. A transducer i s then used to determine the helium pressure. Twenty or more analyses with a standard deviation of 3~0.04% can be made in an 8-hour day.
ACTIVATED COCONUT CHARCOAL at liquid nitrogen temperature (77 OK) is used to adsorb all gases except helium and neon, and the neon concentration is usually negligible. This adsorptive property of activated charcoal was discovered by Dewar ( I ) in 1875. Cady and McFarland ( 2 ) utilized activated coconut charcoal at liquid air temperatures to determine the helium content of natural gas. The Bureau of Mines adopted this method with minor modifications as reported by Anderson (3). Frost in 1946 ( 4 ) also utilized activated charcoal to analyze concentrations of helium below 10 %. Frost, Kirkland, and Emerson ( 5 ) described an apparatus and procedure for determining the helium content of gases containing 10% or more helium. However, these methods require corrections for volumes, pressures, and temperatures, and the apparatus must be calibrated with weighed primary standard mixtures (6) to obtain accurate results. The Bureau of Mines purchases crude helium from private industry and must accurately determine the helium content to Present address, Health and Safety, Bureau of Mines, U.S. Department of the Interior, Denver, Colo. 80225 (1) J. Dewar, Nature (London),12,217-218 (1875). (2) Hamilton P. Cady and David F. McFarland, J . Amer. Chern. SOC.,29,1523-1536 (1907). (3) C. e.Anderson, U.S. Bur. Mines, Inform. Cir., 6796 (1934). (4) E. M. Frost, Jr., U.S. Bur. Mines Rep. Znaesf., 3899 (1946). ( 5 ) E. M. Frost, C. G. Kirkland, and D. E. Emerson, ibid., 6545
(1964). (6) J. E. Miller, A. J. Carroll, and D. E. Emerson, ibid., 6674 (1965). 1746
assure proper payment. Approximately 2000 samples per year for the Helium Conservation Program must be analyzed. Because the previous method (5) was time consuming and required frequent calibrations, the present apparatus was developed. This paper describes the new apparatus and procedure for determining the helium content of gaseous mixtures. This method simplifies the calculations by eliminating the necessity of correcting volume, temperature, and pressure. The pressure of helium in the unknown sample is compared with the pressure of high-purity helium at the same conditions. This results in a primary standard method of determining the helium content of samples that contain from 0.1 to 100% helium. APPARATUS
The gas flow and the essential elements of the analyzer are shown schematically in Figure 1. Vacuum valve A is a pneumatic on-off valve. Sample inject valve B is an 8-port pneumatic valve and is shown in the sample flush and sample inject positions in Figure 1. Valves C-F are 3-port pneumatic valves, and the air-control valves G-K are 3-port solenoid valves. Metering valves L-N control the gas flow to flowmeters 4 and 7. The pressure is measured by a 0-1 pound-persquare-inch-differential transducer, 1, with its electrical span set to give 0 to 1.5 volts for the pressure of helium in the sample. The voltage is then converted by a voltage-to-frequency converter and counter. The resulting reading for a 100% helium sample is approximately 150,000 counts on the digital readout, 3, for about 0.2 psid. Flowmeters 4 and 7 are differential pressure gauges that have been calibrated by using a predetermined length of 1/16-inchcapillary tubing to obtain the pressure range required (7). Charcoal trap, 8, contains 3 grams of 50-60 mesh activated coconut charcoal. The inlet line to the charcoal is as short as possible (6 inches) to minimize the volume of Nz pusher gas that must be extracted by cryogenic pumping and diffusion. Volume tank, 10 (500 ~~~
(7) G. W. Munns, Jr., and V. J. Frilette, J . Gas Chromatogr., 3,
145-146 (1965).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970
