Although the results shown in Table
I are reported in the number of moles of
standard were exchanged, an average error of 1.6% was obtained.
active hydrogen per mole of compound, it would be also possible to determine the weight per cent of active hydrogen in the sample. Omitting the results for phenylacetylene where it was found that some of the protons of the internal
(1) Harp, R'. R.,Eiffert, R. C., Ax.41,. C H E V . 32, 794 (1960). D., 1bid.j ( 2 ) Paulsen, P. J., Cooke, 1713 (1964). (3) Pople, J. A , , Schneider, IT. G., Bernstem, H. J., "High Resolution Nuclear
LITERATURE CITED
Magnetic Resonance," p. 218, LIcGrawHill, New Tork, 1959. ( 4 ) Siggia, Sidney, "Quantitative Organic Analysis via Funct,ional Groups," p. 41, I$-iley, Sew Tork, 1049. ( 5 ) FYild, F., "Estimat'ion of Organic Compounds," p. 64, Cambridge University Press, Cambridge, 1953. RECEIVED for review February 24, 1964. A4cceptedMay 13, 1964.
Chronopotentiometry and Chronoamperometry with Unshielded Planar Electrodes PETER JAMES LINGANE Division of Chemistry and Chemical Engineering, California Institute o f Technology, Pasadena, Calif.
b It is shown exp'erimentally that the chronopotentiometric and chronoarnperometric constants obtained with unshielded, circular, planar electrodes satisfy the equations
and
Therefore, it is desirable to extrapolate the experimental value to the rl" = 0 or the t 1 i 2 = 0 intercept in careful analytical work.
SINCE
the Sand equation
and the Cottrell equation
are strictly applicable only to conditions of one-dimensional linear diffusion, shielded planar electrodes have been employed in accurate chronopotentiometric ( 2 ) and chronoamperometric ( 7 > (7, I O ) esperiment;i. Bard ( 2 ) has coniliared shieldd and unshielded electrodes and ha. observed that the chronopotentiomrtric constant increases a t long values of the tran:ition time only in the case of unshirlded electrodes. His result; -upgrst that th(3 chronopotentiotnrtric cwnstant obtained with an unsliieltlcd planar disk electrode has the sainr qualitative dependence on the trnniition time as tha,t obtained with a sj)licricnl clcc,trode. 'I'hc puq)c)sc of this paper is to obtain a qunntitntix-e experimental description of the chronopotention.letric and chrono-
amperometric constants obtained with unshielded planar disk electrodes. The chronopotentiometric constants under conditions of one-dimensional cylindrical ( I S ) and spherical (12) diffusion can both be written in the form of the Sand term times a power series in ( D T r 2 ) 1 ' 2 . Similarly the chronoaniperometric constants under conditions of one-dimensional cylindrical (3) and spherical (3) diffusion can be written in the form of the Cottrell term times a power series in ( D t t r 2 ) 1 ' 2 . -4lthough the unshielded disk electrode is a two-dimerisional diffusion problem, we have nonetheless attempted a correction term in the form of a powers series in ( D T r 2 ) l r 2 or (Dt,'r2)liZwhere r is the circular radius of the planar disk electrode which we employed. The D and t dependence were determined explicitly and the r dependence was assumed on the basis of intuitive and dimensional arguments. I t is shown that only the square root term contributes to the correction. Therefore, the nonlinearity of the diffusion field about unshielded, planar, circular electrodes can be corrected for by extrapolating the experimental values of the chronopotentiometric and chronoamperometric constants to the T ~ = ' ~0 or the t 1 ' 2 = 0 intercept. EXPERIMENTAL
The chronopotentiometric setup was usual. The constant' current was obtained by putting large dropping resistors in series with a 270-volt battery bank. A Clare mercury wetted, makebefore-break, d.c. relay was used for switching. -4 Philbrick P2 differential amplifier was used as a follower. The constant currents were determined during the experiment since currents measured prior to the tvqicrinient (when a dummy resistor is sub5tituted for the cell) were about 0.3% greater than those observed during the experiment.
The i - t curve was displayed on a Sargent-SR recorder; the chart was driven at a rate of 12 inches, min. by a synchronous motor. The transition times mere measured directly from the chart paper by the method of Kuwana (14). The chronoarnperometric experiments employed 2. Kenking T K potentiostat (Wrinkmsnn In*trumenti, Inc., Cantague Road, Westbury, S . IT.), and the current was determined bv measuring the iR drop developed resistor. The Sargent r with a 5-mv. range plug., was used to monitor this current continuously. h jacketed, single-coml of about 125-m1. capaci ployed. The Teflon cap \v openings for the various nitrogen inlets, for the salt bridge, for the reference electrode, and for the working and auxiliary electrodes. The wlt bridge n-as of the cracked glass type. The raxiliary electrode was not placed in a wp-.rate compartment because it was desired to kerp the rest potentials of the auxiliary and working electrodes identical; the ninke-before-break relay, used in the chronopotentiometric circuit to minimize current transients, momentarily shorts these two electrodes together and hence undesired electrochemistry takes place if these two potentials are not identical (I). The cell was stirred with a magnetic stirrer and deaerated with "prepurified" nitrogen. So attempt was made to slioc~kniount the cell. The cell was therniost,atetl at 25.0 = 0.1" C. The electrode emliloycd in this study was a Beckman S o . 39273 platinuni button electrode. The projected area was determined to be 0.2088 0.0004 sq. crn. by measuring mutually p r i m dicular diameters with an optical comparator. -4s received, the electrode surface was dull in color anti dceply scratched; therefore, it way polishrd with 4, 0 emerl- paper and cleaned with aqua regia prior to its initial u i e . The electrode was mounted horizontally in the center of the cell and oriented so that the diffusion was ul)wards. The auxiliary electrode was positioned par-
*
VOL. 3 6 , NO. 9, AUGUST 1 9 6 4
* 1723
RESULTS A N D DISCUSSION
Table I
The experimental values of the chronopotentiometric constant are plotted in Figure 1 as a function of ( D T / r z ) 1 ’ 2 ; representative values of the chronoamperometric constant are plotted in Figure 2 as a function of (Dt/r2)1’2. These plots were constructed by plotting the experimental values us. r 1 ’ 2 or t i l 2 and calculating D from the intercept value. The experimental values were then replotted us. (Drjrz)1’2 or
The Chronopotentiometric Data Were Fitted to the Straight Line i71/Z
(%)’”]
nF.rrl/2Dl/2
-= [1 + A AC 2 Stated Confidence Intervals Correspond to 95% Confidence Level. Platinum Electrode, T = 0.2578 cm.
System K4Fe(CK)e 0 lOOF KC1 FeC13 1.OOF HCl
D X 106 Intercept, amp. sec.lI2 cm./mole
A
9 99
tm., , aec. >62
225.7 f 2 . 3
0.99 f 0.21
6.97
10.49
>74
196.9 f 1 . 2
0.98 f 0.15
5.30
Concn., mF
allel to and about 1 cm. from the working electrode. All potentials are with respect to the saturated calomel electrode (S.C.E.) with exception of the experiments involving perchloric acid where a NaCl-S.C.E. was employed. The potential of this electrode was measured to be -14 mv. us. S.C.E. in 1F sulfuric acid supporting electrolyte. The potassium ferrocyanide was Baker and Adamson K4Fe(CN)8.3H20 and was used directly without assay. The silver nitrate was prepared by weight and the ferric chloride solution was standardized us. potassium dichromate. The quinone was twice sublimed prior to use and solutions were discarded within 30 minutes of their preparation (see text). The hydroquinone and ferrous chloride solutions were prepared by potentiostatic reduction of quinone or ferric chloride in situ a t a large platinum gauze electrode. All solutions were prepared with triply distilled water of specific conductivity less than 1.3 X 10-8 mho/cm. Background currents were measured a t potentiostated electrodes in perchloric and hydrochloric acids and were negligible a t the concentration levels studied.
Q
sq.
cm./sec.
(Dt/r2) l I 2 . It is evident in Figure 2 that the experimental values deviate from the simple (Dt/r2)112straight line a t sufI t is ficiently long times, t > t,,,. thought that this indicates the onset of convective stirring. The deviations have been suppressed by excluding all data pairs-Le., all i, t pairs, for t > t,,,. The values listed in Table I1 under the column heading “t,,,” correspond to the largest value of the time used in calculating the slope and the intercept. I n many of the entries, this value is considerably before the onset of the deviation from the straight line and where this is true it is indicated by the symbol “>.”
I n all cases, except for the reduction of silver ion, the electrode was also potentiostated 50 mv. less anodic or cathodic in a t least one experiment to demonstrate that the electrode was being potentiostated on the plateau of the current-potential curve. The slopes, intercepts, and confidence intervals were determined by a leastsquares analysis carried out on an IBM 7090 computer. All the data pairs were weighted equally. The stated confidence intervals correspond to the 95y0 confidence level and were calculated from the usual equations (6).
450
F
I
I
2
4
I
1
I
I
6
8
IO
12
t I
I
220
a 200
(D t/r*)’’‘ x I O 0 Figure 2
4
(D‘f/r2)‘*
8
6
x
IO
100
.
Figure 1 “Plot of the Chronopotentiometric Constant” ir’/Z/AC is plotted vs. ( D r / r 2 ) ’ / zfor the reduction of 10.49 mF ferric chloride in 1 .OOF hydrochloric acid and for the oxidation of 9.99 m F potassium ferrocyanide in 0.1 OOF potassium chloride. Each point represents the average of at least three determinations and the straight lines were calculated by a leastsquares analysis
1724
ANALYTICAL CHEMISTRY
2.
“Plot of the Chronoamperometric Constant”
it’l2/AC is plotted vs. ( D t / r 2 ) ’ / ’ for the oxidation of 4 . 7 2 mF potassium ferrocyanide in 0.1 OOF potassium chloride, for the reduction of 4.83 mF silver nitrate in 0.1 F nitric acid, for the reduction of 4.63 mF ferric chloride in 1 .OOF hydrochloric acid, for the reduction of 10.53 mF quinone and for the oxidation of 5 . 2 0 mF hydroquinone, both in 1.03F perchloric acid. The platinum electrode was potentiostated at 0.40,0.00, and 0.15 v. vs. S.C.E. and at 0.00 and 0.75 v. vs. NaCI-S.C.E., respectively. Each point represents the average of at least three determinations and the straight lines were calculated by a least-squares analysis
+ +
+
A = 0.98 i 0.10 The confidence intervals corresponding to the deviations of i ~ ~ ’ ~ / B = 2.12 i 0.11 AC or itl’*/dC from the least-squares 1 line are generally less than i l % . Mamantov and Delahay ( I d ) have Therefore, these deviations are due derived the chronopotentiometric conprincipally to the experimental unstant for one-dimensional spherical certainty associated wii h the individual diffusion. It we expand their result for data pairs. small values of the ratio DT/r,*, we The diffusion coefficients calculated obtain. Since from the intercept values of the chronopotentiometric and chronoamperometic constants agree well 11 ith those determined independently (‘Table 111). This indicates that the slope is not kinetically Table II controlled and suggests, as we would The Chronoamperometric Data Were Fitted to the Straight Line expect, that the intercepts correspond to the simple Sand or Cottrell equations, Equation 1 or Equatioii 2 . Stated Confidence Intervals Correspond to 9570 Confidence The apparent diffusion coefficient of Level. Platinum Electrode, T = 0.2578 em. quinone decreased from 10.6 X Concn., t, Intercept, amp. D X IO6 sq. cm./sec. 30 minutes after the solution System mF see. sec.1/2cm./mole B emp./see. has been prepared to 9.6 X sq. em./ A@OB 4.83 18 222.4 f 5 . 1 2.36 =k 0 . 5 6 16.7 see. 150 minutes after the solution had 0 . IF HXOa been prepared. This suggests that 0 . 0 0 v. quinone is undergoing an acid-catalyzed uinone 10.20 >36 354.0 f 2 . 9 2.36 f 0 . 1 6 10.6 decomposition at a rate of about 2% 10.53” >36 354.2 f 2 . 1 2.25 i 0 . 1 2 10.6 1’.03F HCIO, per hour (4). Therefore, the true 0.00 v diffusion coefficient of quinone in 1F 10.58 >36 326.2 i 1 . 7 1.96 f 0.11 8.97 Hydroquinone perchloric acid is 10.8 X 10+ sq. em./ 1 . 0 3 F HClOi 10.585 >36 327.3 f 2 . 0 1 . 9 7 f 0.13 9.03 see. 49 318.2 f 1 . 8 1.87 f 0.11 8.54 0 . 7 5 v. 5.20 2.60 >36 323.0 i 2 . 2 1.52 i 0.15 8.80 The 16 chronopotentiometric data pairs were normalized to a single line 140.5 i 0.78 2.16 f 0 . 1 4 6.66 10.08 >36 K4Fe(cs)6 >36 142.0 i 0 . 9 7 2.00 i 0.17 6.80 0,lOOF KC1 10.08c by plotting 142.8 f 3 . 6 2.51 i 0.41 6.88 0 . 4 0 v. 4.72 84 >36 139 6 f 1 8 2 02 f 0 32 6 58 1 008 >36 142 8 + 1 4 0 504 1 49 i 0 24 6 88 9 25 42 124 0 i 1 2 2 42 i 0 26 5 19 FeC13 9 25d 42 124 4 i 0 44 2 38 f 0 092 5 22 1.OOF HCl I n a similar fashion, the 199 chrono4 63d 25 126 8 f 0 81 2 04 i 0 20 5 42 0.10 v. amperometric data pairs were norF eC12 9.25 49 140.8 f 1 . 1 2.00 f 0 . 1 6 6.69 malized to a single line by plotting 1.OOF HC1 9.25’ 42 142.2 i 0 . 9 1 1.76 f 0.15 6.82 0.70 v. a 0.05 v. .
b c
The experimental intercepts did equal the expected value of 1.00; the slopes were determined to be
Table 111.
(15) (7)
Polarographic: (6) (16)
1 20. 0.35. 0.15. 0.65.
Comparison of Diffusion Coefficients Calculated from Intercept Value of Chronopotentiornetric and Chronoamperometric Constants with Selected Literature Values
Technique Unshielded Electrodes Chronopotentiometric Chronoamperometrica Shielded Electrodes Chronopotentiometric (9) Chronoamperometric i(8) (10)
I
K4Fe(C S ) S 0 , l0OF KC1 6.97 6 . 7 0 f 0.185
(In units of FeC13 1 .OOF HC1 5.30 5 . 2 9 f 0.15
sq. cm./sec.) FeCL 1.OOF HC1 6 . 7 5 i 0.07
AgE,’Os
Quinone
0 . I F HSOa 1 03F HClOh
16.7
10.8c
Hydroquinone 1 , 0 3 F HClO4 8 . 8 9 i 0.26
4.69 7.18 6.87 i 0.08 6.50
13.gd 15.5 d
17.4d 1 5 ,4d
IO. 2 d . c 9.5’
8 , 7d.e
a Values and confidence intervals are based on a single extrapolation of all data pairs for each system and are not simple averages of the data in Table 11. 5 Three data pairs, t . ; 36 see., were neglected in computing this value. c See text. 0 . 1‘11 KSOB. * Reralculated on the basis of the experimentally modified Ilkovic equation ( 1 2 ) . f 1 .O A l l KNOZ. ~~
VOL. 36, NO. 9, AUGUST 1964
1725
1
~-
1 - x
[I
...
- 1+z+z2+
(+ +) ($)+ . .I (4)
+ $ ($)”+
-
X
,
The corresponding chronoamperometric equation is (3):
The coefficients of the first-order terms are
d’ =
Bl
r1i22 =
= =li2
=
0 89 1 77
These are essentially identical to the corresponding experimental coefficients for the unshielded planar electrode. Therefore, it is numerically valid but philosophically misleading, to ‘Yransform” the chronopotentiometric and chronoamperometric constants for spherical electrodes into the correspond-
ing constants for unshielded disk electrodes by substituting the radius of the circular disk for the radius of the sphere. This is not to say the unshielded electrode has an “effective spherical radius” equal to its circular radius. What is true is that the constants obtained with an unshielded electrode have, to first order, the same functional dependence on the radius of the circular electrode as the constants obtained with a spherical electrode have on the radius of the spherical electrode. When using unshielded electrodes, the chronoamperometric technique is superior to the chronopotentiometric technique for analytical purposes and for the determination of n-values and diffusion coefficients. Chronoamperometry avoids the uncertainty associated with the measurement of the chronopotentiometric transition time and requires only a fraction as much time to obtain sufficient data to perform the extrapolation to t 1 ’ 2 = 0.
LITERATURE CITED
(1) Anson, F. C., ANAL.CHEM.3 6 , 520 (1964). ( 2 ) Bard, .4.J., Ibid., 3 3 , 11 (1961). (3) Delahay, Paul, “Sew Instrumental Methods in Electrochemistrv.” ChaD. 3 , Interscience, Xew York, i954. (4) Fieser, L. F., Fieser, &I., “Advanced Organic Chemistry,’’ p. 846, Reinhold, S e w York, 1961. (5) Kolthoff, I. M.,Orlemann, E. F., J . Am. Chem. Soc. 6 3 , 664 (1941). (6) Laitinen, H. A,, “Chemical Analysis,” Chap. 26, RlcGraw-Hill, New York, IF)^
ACKNOWLEDGMENT
(7)-Laitinen, H. A , Trans. Electrochem. SOC.82, 289 (1942). (8) Laitinen, H. .4.,Kolthoff, I. M.,J . Am. Chem. SOC61, 3344 (1939). (9) Lingane, J. J., J . Electroanal. Chem. 2, 46 (1961). (10) Xlacero, D. J., Rulfs, C. L., J . Am. C‘hem. Soc., 81, 2942 (1959). (11) Ibzd., 81, 2944 (1959). (12) llarnantov, Gleb, Delahay, Paul, Ibid.. 76. 5323 119543. (13) Peters, D. G , Lingane, J. J., J . Electroanal. Chem. 2 , 1 (1961). (14) Russell, C. D., Peterson, J. M., Ibid., 5 , 467 (1963). (15) Stackelberg, von, hf., Pilgram, M., Toome, V , , Z . Electrochem. 57, 342 (1953).
I t is a plreasure to thank Fred C. Anson and Robert A. Osteryoung for helpful discussions and Martin S. Itzkowitz for assistance in the leastsquares programming.
RECEIVED for review March 12, 1964. .4ccepted April 17, 1964. This investigation was supported in part by a Public Health Service fellowship, GPM-16, 81 1, Division of General Medical Sciences, held by the author
Characterization of Selected Heavy-Metal Salts as Adsorbents for Gas Chromatography ALAN G. ALTENAU’ and L. B. ROGERS Department o:f Chemistry, Purdue University, lafayette, Ind.
b Adsorbents were produced by careful elimination of water from crystals of CuSO4.5H20, 3CdS04.8Hz0, and MgC12.6H20; pyridine from Cu(Py)4(NOB).! and Cu(Py),SO4; and ammonia from C U ( N H ~ ) ~ ( N O &These . adsorbents had small specific surface areas that necessitated very small samples. A column of Cu(Py)2(N03)2 gave very good separations of numerous aliphatic and aromatic hydrocarbons, alcohols, esters, ethers, and ketones with minimal tailing of peaks. It was particularly effective for separating 2- and 3aliphatic ketones. At the other extreme, C u S 0 4 . H z 0showed strong adsorption for aromatics and oxygencontaining compounds. Separations appeared to b e greatly influenced by interaction between the metal ion of the adsorbent and the 7r-electrons or nonbonded electrons of the adsorbate. Heats of adsorption and effects on the efficiency of particle size, column temperature, and flow rate of the carrier gas were determined.
1726
ANALYTICAL CHEMISTRY
F
Y E A ~ Z S adsorbents have been used as column packings in gas chromatography. The most common adsorbents have been activated carbon, activated alumina, and silica gel (22-25). These adsorbents have relatively large specific surface areas with no definite pore size (4). They have been used quite successfully for the separation of small molecularweight substances such as CH,, C2H6,He, Oz. S p ICO, CO,, etc., but have not found much application in gas chromatography for the separation of larger compounds because strong adsorption and unsymmetrical peaks are usually obtained. However, renewed interest in gas solid chromatography has recently occurred from both the theoretical and practical aspects (18, 34). hnother type of high-capacity adsorbent is the molecular sieve. I t separates molecules on the basis of molecular size and polarity (4). Most other inorganic substances, particularly salts, are never thought of OR VANY
as adsorbents although the surface area of many salts and oxides has been determined by adsorption of nitrogen and adsorption isotherms have been obtained using a few gases and relatively volatile liquids. These compounds have not heen used as adsorbents because of their relatively small specific surface areas. However, if sufficiently small samples of volatile substances are injected into chromatographic columns packed with a salt, selective retention (10, f 1, 33) and symmetrical peaks will often be observed. As a result, a large number of potentially useful adsorbents are available. Most of the adsorbents used in the present study were produred by driving off water from a hydrate or an amine from a transition-metal complex. As shown below, separations of a larger number of organic sitbstances have been accomplished easily with 1 Present address. C S ,4rniv S a t i c k Lahoratories, Xatick, Mass
