Diffusion Coefficients of Ferri- and Ferrocyanide Ions in Aqueous Media, Using Twin-Electrode Thin-Layer Electrochemistry
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S. J. Konopka and Bruce McDuffie Department of Chemistry, State University of New York at Binghamton, Binghamton, N. Y. 13901
The diffusion coefficients, D0 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 D0 and DR at 25° C in LOOM KCI were 0.726 (±0.011) X IQ-5 and 0.667(±0.014) X 10-5 cmVsec, respectively, covering a concentration range from 0.61 to 6.36mM 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.
Various methods 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 (12,14,15), 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 10-20% (13, 77). Macero and Rulfs (13) have attributed these differences largely to uncertainties in the effective electrode area and to the necessity for using a suitable reference ion. Thin-layer steady-state methods are characterized by mathematical 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. Chem. 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) . A. Laitinen and I. M. Kolthoff, ibid., 61, 3344 (1939). (9) . A. Laitinen and I. M. Kolthoff, /. 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, Z. Elektrochem., 57, 342 (1953). (12) P. J. Lingane, Anal. Chem., 36, 1723 (1964). (13) D. J. Macero and C. L. Rulfs, J. Amer. Chem. 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.
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, iss, followed by coulometric analysis of the thin layer. The iss between closely spaced twin working electrodes is given by the equation: ~nFAC~
l
2DqDr _Dq + Dr_
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, / is the thickness of solution between the two working electrodes, and D0 and DI{ are the diffusion coefficients of the oxidized and reduced species, respectively (19, 22). D values are calculated according to the following equations
(19): Do
Dr
iss(c)l2
(2)
IqT iss{a)l2
(3)
where /33(C) and iSS(a) 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 /33 has been reached, and Qa is the charge required to oxidize all of the reduced species in the thin layer at the iss condition. The values of iSS(c) and iSS(a) 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/z'3S(c), 1 /iss(a), Qc and Qa are each plotted against the /-setting of the micrometer, giving the respective slopes, Si/i33 2q, thicker settings corresponding roughly to / > 3>q and / > 4q. Thus nonparallelism could have caused the slopes of the 1 ¡iss vs. /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) =
=
=
Q
=
tlFAlC +
Qads
+ Qd.l.
where Qaae and Qa.i. represent the contributions caused by reaction of adsorbed species and by change in double layer capacitance, respectively. A plot of Q vs. I gives an intercept at /-zero equal to Qais + Qd.i., 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
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constant potential and has immediately adjacent to it in the solution nearly the same concentration of electroactive species (as 100% O 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-l plot, the number of coulombs at /-zero (obtained from /S5 or R data) can be expected to give Qaas directly without any Qua. term: the intercept from the Qa-l data should give the amount of species R previously adsorbed at the cathode, and the Qc-l intercept should give the amount of species O previously adsorbed at the anode, assuming that the time required for desorption of these species is short compared 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 10-9 and 2.6 X 10-9, 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 Helium Content of Gas Mixtures David E. Emerson and Richard L. Kaplan1 Division of Helium, Bureau
of Mines,
V. S. Department
of the Interior, Amarillo,
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 is then used to determine the
helium pressure. Twenty or more analyses with a standard deviation of ±0.04% can be made in an 8-hour day.
Activated
at liquid nitrogen temperature coconut charcoal is used to adsorb all gases except helium and neon, and the neon concentration is usually negligible. This ad-
(77 °K)
sorptive property of activated charcoal was discovered by Dewar (1) 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 (J) 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
(1) J. Dewar, Nature (London), 12, 217-218 (1875). (2) Hamilton P. Cady and David F. McFarland, J. Amer. Chem. Soc., 29, 1523-1536(1907). (3) C. C. Anderson, U. S. Bur. Mines, Inform. Cir., 6796 (1934). (4) E. M. Frost, Jr., U. S. Bur. Mines Rep. Invest., 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).
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proper payment. Approximately 2000 samples per for the Helium Conservation Program must be analyzed. year Because the previous method (5) was time consuming and required frequent calibrations, the present apparatus was assure
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% he-
lium. 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-pérsquare-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 Vie-inch capillary tubing to obtain the pressure range required (7). Charcoal trap, 8, contains The in3 grams of 50-60 mesh activated coconut charcoal. let line to the charcoal is as short as possible (6 inches) to minimize the volume of Na 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
