Effect of Cell Circuit Resistance in Polarography . with Stationary and Dropping Electrodes M. M. NICHOLSON Humble Oil & Refining Co., Baytown, Tex.
Ohmic drop of several hundredths of a volt, due largely to cell resistance, can change the voltage scanning rate enough to produce a marked effect on the polarographic current at a stationary electrode. By an electromechanical method of instantaneous resistance compensation i t is shown that this effect accounts for most of the variation in the ratio of maximum current to concentration observed in the oxidation of organic sulfides. The compensation system is applicable also to dropping or rotating electrodes.
YHE polarographic current a t a stationary electrode depends upon the rate of change of potential with time (1-6). In previous work in this laboratory ( 4 )a distortion of wave form for the oxidation of organic sulfides a t a cylindrical electrode was observed as the concentration increased, even after subtraction of iR drop in the cell circuit from the apparent applied voltage. Adsorption was suggested as a possible cause of this effect. In the present work an explanation is sought in the variation of dE/dt with the cell current by virtue of the ohmic drop in the cell and current-measuring resistor.
The resistance compensator circuit is shown in Figure 1. Current from a 1.5-volt dry cell is controlled by resistor RI, variable from zero to 5000 ohms, and measured on milliammeter M , which introduced an additional 20 to 80 ohms. R,, a ten-turn 9.52-ohm Helipot with center tap, was mounted on the polarograph recorder in the position provided for a drum-type slidewire, so that the sliding contact is operated by the pen drive mechanism. In this way, a corrective voltage is added in series with the cell, C, which is a t all times equal and opposite to the iR drop in the cell and current-measuring resistor. The effective potential difference between the electrodes is then the linear function of time supplied by the bridge of the polarograph. By means of an adjustable shaft coupling, the center position on Rz is set to correspond to any selected zero current position on the chart. Thus, compensation is achieved for positive and negative cell currents. Setting of the compensator current is determined by = SDR, where S is the sensitivity, current the expression i,, per unit pen deflection, a t which the recording is made, D is the pen deflection per ohm of Rg, and R is the resistance of the cell plus the measuring resistor. The size of the slidewire cable drum attached to the Helipot was such that D = 85.5 mm. per ohm. The influence of resistances larger than those normally found in the cell circuit was determined by addition of resistors in series with the cell. RESULTS AND DISCUSSION
The effect of ohmic drop in 5 mM diethyl sulfide solution, a t relatively high cell current, is shown in Figure 2, where the ab-
TO POLAROGR4PH t
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a Figure 1. Resistance compensator circuit
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This problem of ohmic drop has been discussed by Delahay (3) and Randles ( 5 ) ,and Snowden and Page ( 7 ) incorporated the feature of compensation for the measuring resistor in their oscillographic circuits. An arrangement described here provides instantaneous compensation for both cell and measuring resistor during the recording of a polarogram. This device is applicable also to dropping and rotating electrodes and should be especially useful in organic solutions, where high cell resistances are frequently encountered.
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EXPERIMENTAL
Current-voltage curves were recorded on a Sargent Model XXI polarograph on a 2.00-volt span without damping. Details of procedure for diethyl sulfide are given in a previous paper ( 4 ) . The same platinum wire electrode was used. In addition, a few comparison curves were obtained for reduction of cadmium ion at the dropping mercury electrode in potassium chloride solution. A balancing decade capacitor was used in measurement of cell resistances on a 1000-cycle conductance bridge. 1364
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VOLTS VS. S.C.E. Figure 2. Effect of ohmic drop in 5 mM diethyl sulfide in methanolic 0.1M HCl
R is 670 o h m s I. Uncompensated 11. Compensated 111. i R subtracted IV. d E / d t uncompensated V. d E / d t : compensated
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V O L U M E 2 ? , NO. 9, S E P T E M B E R 1 9 5 5 scissa represents apparent potential as given by the time coordinate of the chart. The measured resistance of the cell was 650 ohms; recordings of curves I and I1 were made with the minimum cell circuit resistance a t suitable current sensitivity. The uncompensated polarogram, when plotted as i/c 0s. E, is similar to that obtained with a 1mM solution and 5100-ohm series resistance. In the absence of an extra series resistor the greatest iR drop in the 1 mM solution is 10 mv., and even in this instance the change by compensation is significant. The maximum compensated current in Figure 2 occurs a t a potential 0.02 volt more anodic than that of the corresponding 1 m X curve. Subtraction of iR along the uncompensated polarogram yields the dotted curve, 111. This type of correction neglects the difference in current a t any corrected potential but apparently permits fairly accurate location of the peak on the potential scale. The pronounced deviation of dE/dt during recording of a large uncompensated current is seen in curve IV, Figure 2. The horizontal dashed line, V, represents the constant voltage scanning rate of the polarograph. Maximum current-concentration ratios with and without resistance compensation are plotted against diethyl sulfide concentration in Figure 3, together with data from a previous investigation using the same electrode. The ordinates are on a large scale. The ratios were computed after subtraction of residual currents. Up to a concentration of 2.5 mM, ohmic drop accounts satisfactorily for the variation of -imo../c with concentration; a t 5 mM, it appears t o account for about 75% of the decrease from the limiting value. A 25% change in compensator current, corresponding to a 10-mv. increment a t the peak, was found to change -i,,, / c in the 5 mM solution by one or two
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(3): (iux,)v = (1 R ~ - . / A E ) ~ ’ *where , (imaX.)” is the peak current a t constant dE/dt, (imor.)u~is the value in the presence of iR drop, and AE is the voltage interval on the ascending branch of the wave. These results reemphasize the importance of cell circuit resistance in the case of stationary electrodes. The automatic compensator appears to retain the essential shape of the polarogram, a critical point in the study of electrode processes by the voltage scanning technique ( 2 ) . It also yields a simpler current-concentration relationship for analytical purposes.
-0.8 -1 .o VOLTS VS. S.C.E. Figure 4. Application of resistance compensator to dropping mercury electrode -0.6
With 0.5 m M CdCli i n 1M KCl containing 0.01% gelatin I. R is 160 o h m s uncompensated 11. R is 30,600 &ms, uncompensated 111. R is 30,600 ohms, compensated 11,111. Drawn through maximum drop currents
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2 4 MILLIMOLES/LITER
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Figure 3.
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Effect of ohmic drop on current-concentration ratio for diethyl sulfide
Application to Other Electrode Types. Although an adequate correction for cell resistance usually can be made arithmetically on polarograms a t dropping or rotating electrodes, an instrumental method is convenient. Figure 4 shows the action of the compensator circuit on a cadmium wave in which a 30,000-ohm series resistor was present. This value was chosen for illustrative purposes, and use of a cell of such high resistance is not recommended.
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0. Uncompensated, this investigation
0 . Compensated, this investigation Q
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Uncompensated, previous investigation ( 4 )
A . Delahay equation (3)
tenths of a unit on the scale of Figure 3. The uncertainty in the alternating current measurement of cell resistance was of the order of 5%. The present compensation method is exact only if the effective cell resistance is a constant, independent of current, and if all of the polarization occurs a t one electrode. The possibility remains that some other complication, such as adsorption on the electrode surface during the passage of current, may contribute to the small slope of the compensated curve of Figure 3, but such an effect is a minor one compared t o that of the estimated ohmic drop. A very satisfactory correction is obtained in this case by use of an approximate equation given by Delahay
ACKNOWLEDGMENT
The writer wishes to thank Carl P. Tyler for aid with the experimental work. LITERATURE CITED (1) Bersins, T., and Delahay, P., J . Am. Chem. SOC.,75, 555 (1953). (2) Delahay, P., Ibid., 75, 1190 (1953). (3) Delahay, P., “New Instrumental iMethods in Electrochemistry,” chap. 6, Interscience, New York, 1954. (4) Xicholson, M. M., J. Am. Chem. Soc., 76, 2539 (1954). (5) Randles, J. E. B., Trans. Faraday SOC.,44, 322, 327 (1948). (6) Sevcik, A., Collection Czechoslov. Chem. Communs., 13, 349 (1948). (7) Snowden, F. C., and Page, H. T., &VAL. CHEY.,22, 969 (1960). RECEIVED for review February 21, 1955.
Accepted May 6, 1955.
