Flow Electrolysis on Grid Electrodes Sir: Recently, a n interesting article by Blaedel and Boyer has been published on the flow-through gold micromesh electrode ( I ) . The authors described detailed experimental characteristics of such an electrode, which was composed of one to several disks of gold screens of 200-, 1000-, and 2000-mesh. It was discovered that the measured limiting current ( I , ) of the employed model process of the reduction of potassium ferricyanide in phosphate buffer on the micromesh electrode was directly proportional to the number of disks forming the electrode (N), to the concentration of the electroactive material ( c ) , and to the cube root of the volume flow rate ( u ) of the solution through the electrode
The authors indicated suitability of the gold micromesh electrode for conducting analytical determinations in submicromolar concentration range. Flow-through electrodes composed of single and parallel 80-mesh platinum wire grid disks had been studied earlier (2, 3). An electrode composed of several parallel grids resembles a porous electrode. The number of grids forming such an electrode is equivalent to a length of a porous electrode. To such a n electrode has been applied with success, the developed semi-empirical model of the limiting current on flow-through porous electrode (2, 3). The Proportionality 1 formulated by Blaedel and Boyer on the basis of experimental data should follow from the above-mentioned semi-empirical model. The limiting current obtained on a flow-through porous electrode is expressed by the following general equation:
I , = n Fc,uR (2) where rz is the number of electrons transferred per molecule of the electroactive species, F is the Faraday, c, is the initial concentration, u is the volume flow rate, and R is the limiting degree of conversion of the electroactive species on passing the porous electrode ( 4 ) . According to the derived model, the limiting degree of conversion is given by the following equation ( 2 , 3):
R
= 1- exp( -j s a'-"rct-lL)
13)
where s is the specific internal surface, a is the electrode cross-section area, L is the length of the porous electrode, and j and a are constants, a being a fraction of 1. Equation 3 can be expressed in a simpler form, if a dimensionless parameter J is substituted for the expression in parenthesis
.J = j s f l l - ~ k c " -
'L
14)
exp(-J)
(5)
then
R ='1-
For a small value of J , exp(-J) can be approximated by the first member of its power expansion exp(-J) (1) (2) (3) (4)
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1- ./
(6 i
W. J. Blaedel and S. L. Boyer, Ana/. Chem., 45, 258 (1973) R. E. Sioda, Electrochim. Acta, 15, 783 (1970). R . E. Sioda. J. Electroana/. Chem., 34, 411 (1972). R . E. Sioda. Eiectrochim: Acta. 13, 375 (1968).
A N A L Y T I C A L CHEMISTRY, VOL. 46, N O . 7, JUNE 1974
and according t o Equation 5 we obtain:
R=J Hence for small J , according to Equations 2, 4, and 7 ,
I,
nFc,uJ = nFc,jsa'-"uL'L
(8)
and
I , a c,Lu"
(9)
i.e., the limiting current is proportional t o the length of the porous electrode, initial concentration of the electroactive species, and to the flow rate to the power of a. a is a parameter which should be determined experimentally for a given porous electrode. For two porous electrodes investigated by the present author, one composed of rolled together 80-mesh platinum grid, and the other composed of 12 parallel 80-mesh platinum grid disks squeezed together, a has been experimentally found equal to 0.373Le., close to (3, 5 ) . Taking into account the above experimental value of a , Proportionality 9 agrees well with that found by Blaedel and Boyer. The length of the porous electrode L in Proportionality 9 corresponds to the number of grids forming the electrode in Proportionality 1. The small difference in the value of the measured exponent from the cube root dependence of Blaedel and Boyer may be related to different structure of grids and different experimental conditions. Blaedel and Boyer applied screens made of ZOO-, 1000-, and 2000-mesh foil with a regular pattern of square openings, while in the investigation of the present author 80-mesh wire grid has been used. In the cell of Blaedel and Boyer, the gold screens have been separated by washers, while in the investigation of the present author ( 3 ) , grids have been in direct contact. The specific flow rates (volume flow rate divided by electrode cross-section area) applied by Blaedel and Boyer have been generally higher, and the obtained limiting degrees of conversion lower, than in the investigation of the present author. The application of Equation 8 and Proportionality 9 is justified only when J is small, because only then can one neglect the higher members of the power expansion of the exponent. For large J, Equation 8 would generally give too high values of the current. For higher J , the more general equation should be used ( 2 ) :
I , = nFc,u[l - exp(-jsa'-"c"-'L)]
(10)
The error associated with using the approximate Equation 8 instead of the more accurate Equation 10 may be calculated for various values of R: 5.4% error for R = 0.1, 11.6% for R = 0.2, . . . . As can be seen from the calculated values of error, Equation 8 is valid only for small limiting degrees of conversion. Small limiting degrees of conversion are obtained either for high flow rates, small specific internal surface area of the electrode, or small electrode length. Important from the point of view of possible analytical applications of the electrode is the dependence of the limiting current on the flow rate. It would be convenient, if (5) R . E. Sioda, Eiectrochim Acta. 17, 1939 (1972)
the dependence could be described in a form of a simple power equation of the following type:
I,=fcoP
( 11)
where f and m are experimental parameters. However, as Equation 11 is only an approximation to actually more complex dependence given by Equation 10, it is applicable for rather limited ranges of the flow rates, should f and m be constant. Equation 11 transforms into Equation 8 for the case of electrolysis with small limiting degrees of conversion. On the other hand, at high limiting degrees of conversion corresponding to almost complete electrolysis of the flowing substrate, the exponent m becomes close to 1, as was experimentally shown before ( 4 ) . In the interme-
diate range of the limiting degrees of conversion, both the exponent m and constant f change appreciably. The change of the exponent is illustrated by the experimental data obtained for a porous electrode of different heights built of graphite granules (6).
Roman E. Sioda Institute of Physical Chemistry Polish Academy of Sciences Warszawa, ul. Kasprzaka 44, Poland Received for review August 22, 1973. Accepted December 6, 1973. (6) R E
Sioda, Electrochm Acta
13, 1559 (1968)
I AIDS FOR ANALYTICAL CHEMISTS Dissolution of Silicate Minerals and Glass for Trace Analyses Pieter Knoop Analytical Department of the Glass Development Centre, Production Division Glass, N. V. Philips' Gloeilampenfabrieken, Eindhoven, The Netherlands
In trace analyses, the problem with materials which are difficult to dissolve-e.g., glass, sand, and mineral silicates-is the impurity of the reagents to be used. Sometimes the amount of an element added together with the reagents is larger than the quantity originally present. To avoid these difficulties, we made solutions of pure sand and glass with the aid of Eppendorf micro-test tubes (Cat. No. 3810).
EXPERIMENTAL For t h e determination of trace elements, 50 mg of sample was weighed into the test tube. With the aid of a n Eppendorf pipet, 500 ~1 of' Merck supra-pure HF 40% was added and t h e lid firmly closed. After mixing, the test tube was placed in a Teflon-lined bomb ( I , 2 ) . These bombs, the dimensions of which are given in Figure 1, are easily made in a normal factory workshop. Ten test tubes ( e . g . , 8 samples and 2 blanks) are conveniently placed in a bomb of the size stated in Figure 1. About 10 t o 15 ml of the same hydrofluoric acid as is used in the test tubes is poured over these tubes t o balance the pressure build-up during t h e heating period. The Teflon lid of the bomb is replaced a n d t h e bomb is closed handtight. T h e whole is placed in a laboratory furnace for 1 hour a t a temperature of 130 "C (max. 150 "C). After cooling to room temperature, the bomb is opened. T h e test tubes are inspected for complete dissolution and rinsed with distilled water. Samples were directly injected by means of pl Eppendorf pipets into a flameless atomization device, in our case t h e Perkin-Elmer HGA 70. To protect the windows of t h e atomic absorption spectrophotometer Perkin-Elmer 403, a n exhaust system was installed on either side of the atomization device.
RESULTS AND DISCUSSION In this way we could determine in sand, 0.1 ppm Al, 0.1 ppm Cu, and 0.2 ppm Fe, with blanks of about of the ( 1 ) 6. Bernas,Ana/.Chem.. 40, 1682 (1968). (2) F. J. Langrnyhr and P. E. Paus, Anal. Chim. Acta, 43,397 (1968)
Figure 1. Physical dimensions of Teflon-iined bomb
above-mentioned values and a relative precision of 10%. In pure glasses we also determined Ni and Co in an order of 0.1 ppm. The micro-test tubes, together with the two types of tips for the Eppendorf ~1 pipets were left for at least 24 hours in a mixture of equal parts HC1 ( 1 M ) and acetone. Test tubes were handled with laboratory tongs made of a material not to be determined and rinsed with plenty of double-distilled water. The adhering water was removed by vigorous shaking. Then the tubes were put in a rack and left in a dust-poor environment for YZ hr to evaporate the last traces of water. If iron had to be determined. the A N A L Y T I C A L C H E M I S T R Y , VOL. 46, N O . 7, J U N E 1974
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