interfering ions and also for solutions containing IO-lM of Cu2+ and A13+. The interference curves for the other two electrodes were similar. Figure 1 shows the order of increasing interference for the strongly interfering ions as Zn2+ < Hg2+ < Fez+ < Sn2+. For Zn2+ and Hg2+ the interference is, no doubt, due to the formation of anionic chloro complexes of these ions, whereas for Sn2+ and Fez+, the effect is almost certainly due to a redox reaction and the subsequent interference from species such as SnC15-1 in the case of tin. The interference curves for the simple anions NO3-, F-, and s04’- are also included in Figure 1 for a constant concentration of the interfering ion of 10-lM. It can be seen that these ions do not interfere strongly; however, very high concentrations of these ions (>lO-lM) should be avoided. The order of increasing interference is S042- < F-
> k cat (since radicals are reduced by radical anions a t rates approaching diffusion control (II), this is a quite reasonable assumption in our system), and applying the steady-state assumption,
ac
(3)
at
(4)
that is, whether the second reduction occurs in solution (in which case the overall process is doubly catalytic) or a t the electrode surface. In more general terms, one can conceive of two classes of catalytic processes which follow-up electron transfer, exemplified as follows:
(12)
= kcatCRCz - k2cyc, = 0
..cy =
kcat cRc
Z/k2CR
(13) (14)
By substitution of this value for C y into Equations 11 and 12, one obtains
Case I 0 -in,e‘
--- R The potential-step experiment is defined by the following set of boundary conditions: 1 = 0, x
>
0: Co =Co*; Cz = Cz*; C,,Cy
= O(17)
Case I1
We were interested in developing a procedure for analyzing such processes, for several reasons: it is very likely that they will be found to be fairly common, particularly in organic systems, which often involve several reduction steps; a procedure for determining k cat, the bimolecular rate constant for electron-transfer between ArH * - and alk-C1 (or in the general case, between R and Z) would provide a means of gaining insight into the nature of solvent and counterion effects as well as the effect of changes in the structure of the aromatic hydrocarbon and the alkyl halide upon the electron-transfer process; knowledge of the rates of infermolecular electron-transfer would permit analysis of intra molecular electron-transfer rates. We also recognized that the electrochemical reduction of some aromatic hydrocarbons, e.g., naphthalene, is electrocatalytic in DMF (see Discussion); hence, we wished to develop a procedure for estimating the importance in this process and for correcting for it if necessary. 96
where C O* = bulk concentration of 0, C Z* = bulk concentration of 2, t = time elapsed from the potential-step, and x = distance from the electrode In order to make the equations tractable, the diffusion coefficients of 0 and R are assumed to be equal, and it is assumed that reactant Z is present a t a concentration much larger than that of 0, so that pseudo first-order kinetics may be assumed for the reaction between R and Z. Solving Equations 15 and 16 simultaneously for the stated boundary conditions by standard methods involving application of Laplace integral transforms, one obtains the following relationship between the current and time a t a planar electrode in the potential-step experiment:
where p = k catCZ, A = area of the electrode, D = diffusion coefficient of 0 (and R), and 5 - =Faraday constant. For large values of fit, Equation 20 reduces to the following expression for the steady-state catalytic current:
ANALYTICAL CHEMISTRY, VOL. 47, NO. 1, J A N U A R Y 1975
F-7 E = 20
B =20
B=10
8=10
a.4 0.4
8.2
B=q
Bs0.2
2
time, aec
Figure 1. Current-time curves for case I, for selected values of P
When kcat = 0, Equation 20 reduces to the Cottrell equation ( 9 ) ,and when k 2 = 0, it reduces to the potential-step formulation for the simple catalytic case (scheme I) (2). Equation 20, in fact, differs from the simple catalytic case [Equation 5-38 of Delahay (2)] in that the term 2P replaces the term /3 in the latter equation. Case 11. The appropriate differential equations are:
aZc + ax
= D+
kc,,C,Cz
(24)
Assuming again that, Z is not electroactive and that its concentration is invariant, the faradiac current is given by
The boundary conditions for the potential-step experiment are: 0, x
1
t >; 0, /
>
x
>
0:
co = co*;c ,
- c,
a:
0 , x = 0:
c y
cz
=
c,
= Cz":
c,
=
cy
C,*: = C z * ; C,, c y - 0
= 0;
CR
=.f(t);
cZ
= 0
(26) (27)
=
c,*
(28 ) The current-time behavior for the potential-step experiment may be found in straightforward fashion to be
[
i = FAD~/*c~*
(??l
+
(
1 2 ~(,t)i/2
P'/Zerf
(pt)'l2
b
8
io
Figure 2. Current-time curves for case 11, for selected values of
i = 1.~ ~ ~ Y , S A D " ? C ~ * P ' / ~ (21)
at
4
t i m e , sec
+
) - 22-
('it)l?2]
(29)
fl
The current-time relationships for Equations 20 and 29, for nl = n2 = 1, are presented in Figures 1 and 2, respectively, as families of curves corresponding t o selected values of (3. (Tables of data which can be used to construct such curves and the computer program used to generate the tables are available from the authors.) For analytical convenience, the ordinate is presented as i ca,/SAD1/2C o*, where i cat is the current for the potential-step experiment in the presence of Z. The numerical value of the term AD may be obtained by a potential-step experiment upon 0 in the absence of Z, with subsequent application of the Cottrell equation (9). It will be seen from Figures 1 and 2 that the shape of the i-t curve is markedly different for Cases I and TI a t short times. The currents for Case I1 behavior go through a distinct minimum when fi > 2 sec-I, and the magnitude of this minimum increases as fi increases. This feature may be used as a diagnostic for which of the two mechanisms is operating, although the actual value of the rate constant is best obtained from the steady-state current. (It is not possible to obtain a value for h cat when @ < 0.2 sec-', since for such values of @ the two curees deviate only slightly from Cottrell behavior.) This diagnost,ic feature of the curves at times on the order of one second or less may be applied only in the absence of interferences from charging currents and cell and instrument response times at short times. Another criterion which sometimes can be applied if the latter interferences are present, is that of line slope at long times (> 1 sec) for p between 2 and 100 sec-'. For a given value of p in this range, the current for Case I1 is still rising long after a steady-state has been reached for Case I. For example, for @ = 10 sec-l the function i l S A D 1 / 2 C 0 *reaches a constant value of 4.47 after only 0.2 sec for Case I, while for Case 11, it has values of 4.87, 6.08, and 6.15 for t = 0.2, 5 , and 10 seconds, respectively. (The predicted steady-state value of 6.32 is not reached until much longer times, but convection would probably prevent reaching such times experimentally.)
EXPERIMENTAL Once again, for kcat = 0 , this reduces to the Cottrell equation, and, for n2 = 0 to the simple catalytic case (2). For large values of fit, Equation 29 becomes
i = ~ A D ' / ~ c , * ( z+, ) ~ ~ ) p ~ / ~(30) For n = n = 1, as in our system,
i 25AD'/?Co*P1/2 (31) so that for a given value of kcat, the current will be larger by a factor of d f o r Case I1 than for Case I (cf. Equation 21).
Instrumentation. Electrochemical measurements were made with a Princeton Applied Research Model 170 electrochemical instrument. Current-time curves (Figures 1 and 2) were calculated on an IBM 1130 computer. Materials. Dimethylformamide (Matheson Coleman and Bell analytical grade) was distilled in ~ ' a c u oa t 60 O C from calcium hydride through a %foot glass helix-packed column and was used the day of the distillation. Tetraethylammonium bromide was recrystallized from a mixture of absolute ethanol and absolute ether (1:3) and dried in a vacuum desiccator for a t least fifteen hours prior to use, then stored over calcium sulfate. The methylcellulose gel was made up by saturating a hot solution of 0.1M tetraethylammonium bromide in dimethylformamide with methylcellulose (121.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 1, JANUARY 1975
97
The gel for the anode and reference probe was prepared the day of the experiment. The phenanthrene used was zone refined (ten passes). n- Octyl chloride (reagent grade-Aldrich) was used without further purification. Potential-Step Experiments. The anode compartment of the electrochemical cell was located parallel to and directly above the mercury pool cathode, and was separated from the cathode compartment by a 19-mm coarse frit and 15 mm of gel. The reference electrode was the cadmium chloride-cadmium amalgam reference described by Marple ( I 3 ) ,and was isolated from the cathode compartment by a Luggin capillary filled with gel. Mercury, 1.40 ml, was added to the electrochemical cell via a 5-ml buret. The cell was then filled with 30 ml of a 0.1M solution of tetraethylammonium bromide in dimethylformamide. A t the outset of an experiment, the solution was purged with nitrogen for fifteen minutes, then preelectrolyzed for five minutes at a potential on the diffusion plateau of phenanthrene. The background was taken on the solventelectrolyte system by stepping first to a potential on the foot of the polarographic wave of phenanthrene for three seconds, then to a potential atop the wave. The current-time behavior was then recorded on an x-y recorder for ten seconds. Four background runs were made, and averaged. Between runs, the cathode was stirred by a nitrogen stream for 15 sec. n- Octyl chloride was then injected via syringe, and the solution was stirred by the nitrogen stream for two minutes. Four runs were made with this solution as described above. Ten microliters of a standard phenanthrene solution in dimethylformamide (stored at 0 "C in the dark) was injected into the cell, giving a 2 X lO-4M solution. The potential-step runs were then made as described above. In several runs, a filter with a 100msec time constant was used on the current output. This made the current-time curves easier t o interpret, and did not change the data quantitatively.
2. 2 0
n-CH3(CH2)&H2C1 2
the current values are somewhat larger than one would expect for either case I or case 11. This is due to oscillations in the mercury pool set u p by changes in the surface tension of mercury when the potential is stepped, these oscillations causing a small amount of stirring. It was found that in the absence of octyl chloride phenanthrene adheres to the Cottrell equation at times greater than 1 sec, hence data after this point are considered reliable, but this phenomenon does not permit data taken a t short times to be used to distinguish between cases I and 11. This experimental currenttime curve in the presence of octyl chloride corresponds to a value of /3 of either 19.2 sec-' or 10.2 sec-l, depending upon whether case I or case I1 behavior is operative. The slopes of the computed current-time curves for these values of at times greater than one second are too similar for a distinction to be made upon the base of curve shapes, however; but case I behavior has been clearly established by independent evidence in a closely related system. Sease and Reed found 1-hexene (6) as the sole hydrocarbon product of direct electrochemical reduction of 6-bromo-1-hexene (3a) in DMF, but when electrocatalytic reduction of 698
ANALYTiCAL CHEMISTRY, VOL. 47, NO.
1,
5
~
6
J.!
",
0. 5
0
I O! 6
Zip.3,
10
sec
Potentiostatic current-time curves Lower curve: phenanthrene (2 X 10-4M) in dimethylformamide containing tetraethylammonium bromide (0.1M). Potential stepped from - 1.4 to - 1.75 Figure 3.
vs. the Cd(Hg)/CdCIz reference electrode of Marple (ref. 13). Upper curve: Same as preceding, after addition of octyl chloride (3.4 X 10-2M)
chloro-1-hexene (3b) was effected using electrogenerated naphthalene radical anion, a substantial amount of the hydrocarbon product (23%) consisted of methylcyclopentane (S),along with 6 ( 3 ) . The results were interpreted according to the following scheme:
--- -
RESULTS AND DISCUSSION Although naphthalene radical anion has been used most often for chemical reduction of alkyl halides ( 5 ) ,it turned out to be not well suited for the present application, since there is a finite current for direct electrochemical reduction of octyl chloride at potentials corresponding to the top of the naphthalene polarographic wave. This problem was eliminated by the use of phenanthrene (1) which has a reduction potential ca. 0.04 V positive of that of naphthalene, yet still reduces alkyl halides efficiently ( 3 ) . The current-time curve for a typical potential-step experiment upon a solution of phenanthrene and octyl chloride (2) in DMF is shown in Figure 3. At times less than one second,
1
'
-
e -x-
x
3 a x = Br b,x=CI
.
e *
-
4
5
H'
1-hexene 6
I
7
8
It is known that the 6-hexenyl radical (4) undergoes rapid cyclization to the cyclopentylmethyl radical (7) [ h cyc = lo5 sec-' a t 25 "C] ( 1 4 ) . When 4 is generated a t the electrode surface, it must be reduced very rapidly before cyclization to 7 can occur. On the other hand, when 4 is generated electrocatalytically by the reaction between naphthalene radical anion and 3b, it has a lifetime sufficient to permit partial isomerization to occur. Thus in the latter experiment it must be formed and reduced in solution-ie., according to case I. We assume that the latter mechanism is also operative in our experiments. Before data such as those in Figure 3 could be used to compute k cat for the reaction between phenanthrene radical anion and octyl chloride, it was first necessary to assess the magnitude of an apparent electrocatalytic cycle involving 1 or naphthalene, and the solvent, DMF. Controlledpotential electrolysis of naphthalene in DMF in a divided cell a t a potential corresponding to the top of the polarographic wave resulted in the passage of far more current (ca. 7 $/mole of naphthalene had passed at the point at which the electrolysis was finally interrupted) than necessary for generation of the radical anion. Similar behavior had been observed by Wawzonek and Wearring with naphthalene and phenanthrene (15).They ascribed it to migration of the radical anion to the anode of their divided cell, reoxidation there, and migration of the neutral hydrocarbon back to the cathode. This appears less likely than an
JANUARY 1975
electrocatalytic cycle upon the solvent or a constituent of the solution-e.g., the electrolyte (16)-and cannot be true a t any rate in our case, since the methylcellulose gel used to divide the two compartments effectively completely eliminates diffusion of organic materials between the two compartments. Although an electrocatalytic process must therefore be involved, it turned out that its rate was low enough not to interfere with the process we were interested in. This was shown by the fact that a potential step upon phenanthrene in DMF exhibits Cottrell behavior (for t > 1 sec; vide s u p r a ) . Thus the pseudo first-order rate constant for reaction with the solvent must be less than 0.2 sec-l. If its rate had happened to be larger, the system would still have been tractable, since Equations 20 and 29 (or 21 and 30) may be expanded in straightforward fashion to include any number of parallel electrocatalytic processes, with and without following electron-transfer. Equation 2 1 states that a plot of current us. [Czll/* should be a straight line, passing through the origin, with a slope of 1.414 n 1FAD1/2CO*k cat1/2. Figure 4 represents such a plot for the experimental data. The dotted line, which is a least-squares line through the data at high concentrations of octyl chloride (> 3 X 10-2M), weighted according to the number of experimental points a t each concentration, does indeed pass through the origin. The deviation from linearity a t lower concentrations of octyl chloride is presumably due to the fact that the assumption of pseudo first-order kinetics is unjustified a t low concentrations of octyl chloride-;.e., when the ratio of the alkyl chloride to phenanthrene is less than about 1OO:l. Using the dotted cm3 line, and an experimental value of AD l I 2 of 2.1 x sec1/2 obtained by a potential step upon phenanthrene or anthracene (of similar size and therefore similar diffusion coefficient to phenanthrene), one obtains a value of 490 f 25M- sec-l for k cat, assuming case I behavior; in the less likely event that case I1 is operative, k cat = 260 f 20M-' sec-l. Using an approximate polarographic method, Reed calculated k cat = 450M- sec-l for the reaction between phenanthrene radical anion and n- hexyl chloride ( 1 7 ) , in fair agreement with that measured by us using the more exact potential-step method. Rates of electron-transfer between aromatic radical anions and alkyl halides are highly dependent upon the nature of the cation associated as counterion with the radical anion ( 1 1 ) and the extent of ion-pairing in the system (11, 18).The rate of reaction between sodium naphthalene and n- hexyl chloride is 1080 f 200M- sec-l in dimethoxyethane, in which the sodium and naphthalene radical anion exist as loose ion pairs ( 1 8 ) .It is not easy to relate this rate to that observed by us in DMF, but the two data are not inconsistent, particularly when one appreciates that rates of electron-transfer from phenanthrene radical anion are somewhat lower than from the naphthalene radical anion (3, 18). While the rate constant calculated by us for the phenanthrene radical anion-octyl chloride reaction is undoubtedly fairly close to the true value, there are two sources of error, both associated with the fact that the mathematical model is only approximate for this very complex system. First, it must be recognized that while the current-time curve indicates predominant Case I behavior, there is very likely a small Case I1 component. Second, there is evidence, a t least in the case of reaction between naphthalene radical anion and alkyl chlorides, for a small amount of a side reaction involving combination between ArH- and alk (for nomenclature see Scheme 11),;.e.,
'
-
ArH-
+
alk.
-
ArH-alk;
I
6. 0
f
I /
I
,i e// I
lI
I
5. 0 I
I
. a
I I I
I
uo
4 >
I
I
m
I I
4. 0 0. 1
0 . 15
[Octyl chloridej'",
Figure 4. Plot of i/SACD'"
0 2
ll'lz
vs. square root of octyl chloride con-
centration Symbols represent the number of potential-step experiments carried out at each concentration (0 = four experiments; A = eight experiments; = twelve experiments). Average deviation of measurements at each concentration was 3 %
[This is a major reaction in ether solvents with sodium naphthalene ( 5 ) ,but is much less important in DMF ( 3 ) ] which in our case would remove ArH from the catalytic cycle, and probably accounts for the slight decrease in the steady-state current a t long times. These two processes tend to offset each other, since the first will make measured rate constants appear larger than the true value, while the second will make them appear less than the true value, but the extent to which the errors are compensated is uncertain.
ACKNOWLEDGMENT A number of useful discussions and exchanges of information with John Sease and Richard Reed have contributed to the evolution of some of the 'mechanistic proposals presented herein. We acknowledge a helpful interchange of data with Donald A. Juckett, who also supplied a preprint of a manuscript by himself and Shelton Bank.
LITERATURE CITED (1) L. Meites, "Polarographic Techniques." 2nd ed., Wiley-lnterscience. New York, N.Y., 1965, pp 182 ff. (2) P. Delahay, "New Instrumental Methods in Electrochemistry," Interscience, New York, N.Y., 1954, pp 100 ff. (3) J. W. Sease and R. C. Reed, submitted for publication. (4) A. J. Fry, "Synthetic Organic Electrochemistry," Harper and Row, New York, N.Y.. 1972, Chap. 5. (5) J. F. Garst, Accounts Chem. Res., 4, 400 (1971). (6)G. D. Sargent, J. N. Cron, and S. Bank, J. Amer. Chem. SOC., 88, 5363 (1966). (7) S. J. Cristol and R. V. Barbour, J. Amer. Chem. SOC., 90, 2832 (1968). (8) Ref. 4, p 123. (9) R. W. Murray and C. N. Reilley. "Nectroanalytical Principles," Wiley-lnterscience, New York, N.Y.. 1966, p 2132. (10) W. M. Schwarz and L. Shain, J. Phys. Chem., 89, 30 (1965). (11) J. F. Garst and F. E. Barton 11, J. Amer. Chem. SOC., 96, 523 (1964). (12) G. Dryhurst and P. J. Elving, Anal. Chem., 39, 607 (1967). (13) L. W. Marple, Anal. Chem., 39, 844 (1967). (14) D. J. Carlsson and K. H. Ingold, J. Amer. Chem. SOC.,90, 7047 (1966). (15) S.Wawzonek and D. Wearring, J. Amer. Chem. SOC., 81, 2067 (1959).
A N A L Y T I C A L CHEMISTRY, VOL. 47, N O . 1, J A N U A R Y 1975
99
E. E. van Tamelen and D. A. Seeley, J. Amer. Chem. Soc., 91, 5194 (1969). R. C. Reed, Ph.D. thesis, Wesleyan University, 1971. S.Bank and D. A. Juckett, manuscript in press.
Author to whom correspondence should be addressed.
RECEIVEDfor review June 5 , 1974. Accepted September 3,
1974. This work was presented in preliminary form a t the 139th Meeting of The Electrochemical Society in Washington, D.C., May 1971. Financial support was provided by the National Science Foundation. The Wesleyan University Computing Center provided computer time.
Comparison of High Precision Coulometric and West-Gaeke Methods with the Gravimetric Method for Preparation of Standard Sulfur Dioxide Gas Blends Using Permeation Tubes Anders Cedergren, Anders Wikby, and Kurt Bergner Department of Analytical Chemistry, University of UmeB, S-90 7 87 UmeB, Sweden
A high precision coulometric method has been developed to determine the permeation rate of sulfur dioxide from FEP permeation tubes. The relative standard deviation of the method was about 0.04% for titrations performed during a couple of hours. The relative standard deviation of titrations performed on different occasions over a period of one month was 0.1-0.2% which corresponds to a temperature control better than f0.02 OC during the whole period. The coulometric method has been compared with a modified West-Gaeke method according to Scaringelll ef a/. and with a gravimetric method. Some anomalities observed in the West-Gaeke method were explained from the kinetic behavior of the involved reactions. The relative standard deviation of the modified West-Gaeke method was found to be 3 % and this procedure was shown to constitute a significant improvement of the original West-Gaeke method. A comparison between the mean values obtained by the modified West-Gaeke and the coulometric methods and the mean value obtained gravimetrically gave ratios of 97.2 and 99.9 %, respectively. Because of its accuracy, the coulometric method made it possible to detect significant dlfferences in permeation rates for environmental gases such as nitrogen, oxygen, and air.
Several methods for the determination of sulfur dioxide in ambient air have been proposed. The analyses have been carried out by means of, for instance, spectrophotometry (1-4), gas chromatography (5-8), conductometry (9-12), coulometry (13-15), polarography (16), titrimetry (17, 18) and flame photometry (19).Among these methods, the colorimetric procedure developed by West and Gaeke (20) is considered to be the most selective, one of the most sensitive and suitable for field conditions (21 ). It includes a stable fixation of sulfur dioxide as dichlorosulfitomercurate ion by reaction with tetrachloromercurate ion. Nevertheless, there have been difficulties in obtaining reliable results with this method mainly because of variations in the quality of the pararosaniline dye ( I , 4,22). A general problem when comparing the various methods is the lack of reliable primary standards. The introduction of permeation tubes for various gases as proposed by O'Keeffe and Ortman (23) represents a significant step forward in this respect. Sulfur dioxide is condensed within a sealed tube and, provided that a steady state prevails, the gas permeates the tube in accordance with the permeation equation 100
where F is the rate of flow per unit length of the cylinder, D is the diffusion constant, S the solubility coefficient, and 1 and p 2 the partial pressures outside and inside, respectively. b and a are outer and inner radii, respectively. The permeation rate P is affected by the temperature, T , according to
p
P = Po exp (-E/RT)
(2 1
where E, the activation energy, is about 11 kcal as estimated from data given by Scaringelli ( 1 3 ) .A constant permeation rate in the steady state therefore requires a rigorous control of the temperature. The main advantage with this technique is that the weight loss of the tube per unit time corresponds to the rate of permeation of sulfur dioxide, i.e., the standardization procedure can be performed gravimetrically. To increase the versatility, however, several investigators have reported alternative methods for calibration of the tubes. Among these investigations, those of Saltzman et al. ( 2 4 ) and Scaringelli et al. ( I ) should be mentioned. Saltzman developed a simple and rapid microgasometric technique for calibration of sulfur dioxide permeation tubes. With careful work, the deviation from the average (at 95% confidence) was found to be fl% for measurement periods of 1-2 hours, and the average agreed within 1-2% with the gravimetric mean value. Scaringelli successfully modified the West-Gaeke procedure ( 1 ) and later (13), when this method was compared with the gravimetric method, he reported agreement in permeation rate for thick-walled tubes of 97.5 f 6.5% (at 95% confidence). The permeation rate was also determined with a coulometric procedure and he obtained 96.6 f 9.0%. Reports on calibration of permeation tubes for sulfur dioxide thus suggest an accuracy of about f1% in the most favorable cases. Within these limits, i t has been stated that minor variations in environmental conditions, i.e., relative humidity, gas composition, or pressure, do not cause significant changes in permeation rate. Earlier work ( 1 4 ) at our institute, with a coulometric determination of sulfur dioxide as a digestion product of sulfur in hydrocarbons showed that sulfur dioxide could be determined quantitatively and with high reproducibility. This suggests the possibility of developing a high precision method for standardization of permeation tubes. A high precision method would be of great value, partly because the permeation tubes are regarded as primary standards
ANALYTICAL CHEMISTRY, VOL. 47, NO. 1, J A N U A R Y 1975
