Modified linear null-point potentiometry

Modified Linear Null-Point Potentiometry

Richard A. Durst and John K. Taylor Institute for Materials Research, Division of Analytical Chemistry, National Bureau of Standards, Washington, D.C. 20234

A modification of the technique of precision null-point potentiometry has been developed in which a linear titration curve is obtained when the logarithm of the amount of coulometrically generated titrant is plotted against the concentration cell potential. The equivalence point is evaluated graphically and by computer techniques. The analyses of standard 0.1-ml samples containing 0 to 13 pg of silver are discussed in detail. This technique was found to be applicable down to one nanoequivalent (0.1 pg) of silver with an error of less than 5%. Below this value, a positive deviation occurs due to the spontaneous dissolution of the silver indicator electrodes. The interference effects of several cations are also discussed.

A MODIFICATION of a potentiometric technique, originally reported by deBrouckere (1) and more recently improved by Malmstadt et al. ( 2 - 8 , has been employed with success in the microchemical determination of silver. The features of this technique include: sample solution volumes of 0.1 ml analyzed; coulometric generation of the titrant (As+), in situ, for increased accuracy and prevention of dilution effects; instrumentation utilizing operational amplifiers as voltage followers to prevent significant electrochemical reaction at the indicator electrodes ; semilogarithmic plotting of the data whereby the equivalence point can be graphically evaluated by a linear interpolation or extrapolation to zero cell potential; and analysis of the data by computer to obtain the equivalence point from the intercept of a least squares fit to a straight line.

In principle, the null-point titration [In this paper, titration is used in its broadest sense in which known amounts of a reagent (titrant) are added to achieve a definite end point where the amount of titrant is equivalent to (but not neces- sarily reacting with) the sought-for substance (analate).] is a very simple concentration cell technique based on the adjust- ment of the solution concentration in one of the electrochemical half cells to the concentration of the analate half cell as evidenced by zero cell potential at the equivalence point. This potential is measured between two identical indicator electrodes specific for the species being determined.

For the determination of silver, the concentration cell employed is

where CSP is the concentration of the null-point (analate) solution and CVS is the variable (titrant) solution concentration. The emf of this cell is given by Equation 1

where (Ag+)v, and (Ag+)sp are the activities of silver in the variable and null-point solutions, respectively, and E1 is the

(1) L. deBrouckere, Bull. SOC. Chim. Belges, 37, 103 (1928). (2) H. V. Malrnstadt and J. D. Winefordner. Anal. Chim. Acta,

20, 283 (1959). (3) H. V. Malrnstadt and H. L. Pardue. ANAL. CHEM.. 32. 1034 , ,

(1960).

ANAL. CHEM., 32,1039 (1960).

24, 91 (1961).

(4) H. V. Malmstadt, T. P. Hadjiioannou, and H. L. Pardue,

( 5 ) H. V. Malrnstadt and J. D. Winefordner, Anal. Chim. Acta,

liquid junction potential. If a large excess of an inert electrolyte, e.g., 1N H2SO4, is used in both half cells, the liquid junction potential will be negligible since it depends on the difference in concentration between the solutions in the two half cells. Also, the activity coefficients of silver in the null- point and titrant solutions will be practically equal due to the constant high ionic strength maintained in the two half cells. Equation 1 thus simplifies to

2.3RT Cxp E = - log -

F c v s

where the cell emf is dependent only on the ratio of concentrations of silver in the null-point and variable solutions (CNP and CW) when both half cells are at the same temperature. By suitable cell design (described below), the half cell tempera- tures are equal (approximately 25' C), so that at the null- point-Le., where the cell emf is equal to zer0-Ch-p = CVS.

If the titrant solution is added volumetrically, a dilution correction must be applied to the concentration of the variable solution, Le.,

(3)

where Cr is the titrant concentration, V, is the original volume in the titrant half cell, and Vu is the volume of titrant added. In the determination of silver, coulometric generation at constant current, in situ, eliminates the need for a dilution correction factor.

By plotting the logarithm of the amount of titrant added, either coulometrically or volumetrically, vs. the cell emf, a straight line having the theoretical Nernstian slope of 59.2/n mV per tenfold change in concentration should be obtained. Significant deviation from this value indicates improper cell behavior and consequently serves as a check on errors caused by drift of the cell potential during the titration. This check is a notable feature missing in the conventional null-point potentiometric technique.

EXPERIMENTAL The concentration cells and associated instrumentation

(Figure 1) are of primary interest insofar as the solution volumes are concerned. In this study, the 0.1 ml of solution being analyzed is contained in the null-point half cell for which two designs were used. The first consisted of a commercially available Vycor tube (9 cm long x 2 mm i.d,), the lower closed end of which is the Corning No. 7930 porous Vycor glass (6). The other design, shown in Figure 1, is simply a plug of the porous Vycor rod (3 mm long X 3 mm diameter) connected to 3 mm 0.d. glass tubing by a sleeve of Tygon tubing. This analate half cell, which is immersed in the titrant solution, provides a low resistance contact between solutions but prevents mixing. The small sample solution volume in this immersion half cell also permits rapid temperature equilibrium between the solutions.

The solution of variable concentration, initially consisting of 100 ml of the inert electrolyte (1N H2S04), is contained in a 180-ml tall-form beaker. In addition to the null-point half cell with its silver indicator electrode, this titration half cell

(6) R. A. Durst, J. Chem. Educ., 43, 437 (1966).

1374 ANALYTICAL CHEM STRY

ISOLATION

TITRANT SOLUTION [looml)

Figure 1. tic of experimental circuit

Concentration cell (cross sectional view) and schema-

accommodates a matching silver indicator electrode, the high purity silver generator electrode, the auxiliary electrode isolation compartment, and a glass stirrer. Magnetic stirring was found to produce a.c. noise superimposed on the d.c. signal from the cell; hence it could not be used. The isolation compartment contains approximately 10 ml of 1N H2S04 and is separated from the titrant solution by a 6 mm long X 6 mm diameter porous Vycor plug. The constant current source for the silver generation is calibrated to provide digital readout directly in microequivalents.

Inasmuch as the ratio of solution volumes in the titrant and null-point half cells is 1000:1, the number of equivalents of silver generated in the titrant cell must be lo3 times greater than the amount present in the null point cell to achieve the same concentration. For example, if one nanoequivalent of silver in 0.1 ml is to be determined, one microequivalent must be generated in the titrant half cell to reach the null point. This amplification factor allows the determination of amounts of analate too small to be generated reliably. In addition, this volume ratio can be varied to achieve the optimum titrant generation rate.

The matched silver indicator electrodes, which were sealed into glass melting point tubes with paraffin, exhibited asymmetry potentials characteristically less than 0.2 mV when placed in silver solutions of equal concentration and separated by the porous glass junction. The potential of these electrodes showed negligible drift during the titrations except in the case of extremely dilute solutions as discussed below.

The potentiometric circuit, shown schematically in Figure 1, uses solid state operational amplifiers (7) as voltage followers between the silver indicator electrodes and the potential measuring device. A multirange potentiometric recorder is used for this purpose, rather than a more accurate potenti- ometer, to facilitate the direct and continuous observation of the cell potential equilibration and stability with time. The purpose of the voltage followers is to draw as little current as possible from the source while their extremely low impedance output follows the input exactly. In this configuration, the operational amplifiers are noninverting and have a voltage gain of unity. The high input impedance prevents the occurrence of concentration changes in the null point solution and disruption of the equilibrium at the indicator electrodes (polarization) due to significant current flow during recorder off-balance. By measurement of the rate of capacitor dis- charge through the input terminals in the voltage follower configuration, the input impedance was calculated to be

(7) Philbrick Researches Model P65AU general purpose operation amplifiers, Technical Bulletin P65AU/lBl Rev. 1 (May 1, 1966).

-40

-60

-701 I I 1 1 1 1 1 1 1 I 1 I m , . , , I 1 I t !

.01 ,0Z .G5 .I .Z .5 I 2 5 ,3 23 5C IC0 2rX 5 X

peq nq+ GE~EWA:ED/IOC ml

Figure 2. Semilogarithmic plot of titration data

approximately 108 0 or about three orders of magnitude greater than the input impedance of the recorder at off- balance. Because of the interaction of indicator and generator electrode pairs, emf measurements could not be made during the coulometric generation of titrant. The double- pole double-throw switch is therefore in the grounded (non- measuring) position leaving the indicator electrodes open- circuited to further prevent any current flow.

All chemicals were reagent grade and used without further purification. Sulfuric acid was chosen as the inert electrolyte because of its very low chloride content (0.00001 C1-). The standard silver solutions were prepared by coulometric generation in the 1N H2S04 solution using the same instrumentation employed in the actual titration. Distilled water was used throughout, and all titrations were made at room temperature (25 i- 1 O C) in the presence of air.

The indicator electrode in the null-point solution is connected to the positive input of the recorder (through the voltage follower) so that, prior to the coulometric generation of silver in the variable concentration half cell, the cell potential is indeterminate and off-scale in the positive direction. As titrant is generated, the variable solution concentration, CVS in Equation 2, increases, causing the positive cell potential to decrease. The emf measurements are started when the cell potential falls below 50 mV and at arbitrary generation intervals thereafter, depending upon the particular concentration range and reliability of the linear fit desired. The titrant generation is carried past the null point into the negative potential region and as far beyond as required. It is not necessary to obtain a titration value at the equivalence point itself. The data are then plotted on semilogarithmic graph paper to obtain a linear plot of the logarithm of the amount of silver generated with respect to the cell potential. The equivalence point is then graphically evaluated by a linear interpolation or extrapolation to zero potential, as shown for a series of titrations in Figure 2. In this way, the null- point determination is based on a series of data points on both sides of the equivalence point, instead of only on a single measurement as in the conventional technique, thereby increasing the reliability of the null-point value.

Data analysis may be easily accomplished by computer techniques to obtain the equivalence point from the intercept of a least squares fit of the data to a straight line. The computer readout also provides the slope of the best straight line through the titration data points for comparison with the theoretical Nernstian slope. The computer data analysis is su- perior to the graphical evaluation of the equivalence point for the same set of titration values insofar as the fit of the line to the data i s concerned. However, both methods usually

VOL 39, NO. 12, OCTOBER 1967 1375

Table I. Summary of Null-Point Potentiometric Determinations of Silver

Titn. Pg nanoequiv. nanoequiv. detns 73 Pg

Ag+ taken- Ag+ found,b No. of Error

1 12.94 120.0 119.5 i 2 .6 7 -0.4 -0.05 2 1.29 12.0 12.3 i. 0 . 6 8 2.5 0.03 3 0.129 1,20 1.24 i. 0.04 7 3.3 0.004 4 0.0129 0.120 0.207 f 0.024 6 72.5 0.0094 5 0.0065 0.060 0.173 5 0.033 7 188 0.0122 6 0 . 0 0.0 0.151 i 0.026 7 0.0163

Q Sample volume = 0.1 ml. Average of graphical and computer evaluations of the data (with the 95 73 confidence limits).

-slope*

59.1 i. 0 .2 58.6 i. 0.8 58.7 i 1.0 58 .8 i. 0 .2 58.3 zk 1 .1 57.6 i 1.0

give equally reliable results for the average of several determinations. For this reason, the data given in Table I are the combined results of computer and graphical evaluations.

RESULTS

Using these modifications of the null-point technique, standard 0.1 ml samples containing 0 to 13 pg of silver in IN H2SOI were analyzed. Titrations illustrating the use of the semilogarithmic data plot are shown in Figure 2. The equivalence point values and slopes of these titrations are given in Table I. Each titration curve starts at the top (positive potential), crosses the null-point, and is continued into the region of negative potential beyond the equivalence point. Titration curves 1, 2, and 3 show an almost ideal response-Le., they are linear over the entire titration with slopes of approximately 59 mV/pAg unit. The most dilute of these solutions, titration 3, contains 0.129 pg of silver and can be determined with an error of only 0.004 pg,

The remaining titrations at lower concentrations exhibit considerable deviation from linearity prior to the null-point and give consistently high results. This nonlinearity and the positive error are believed due to the significant dissolution of the silver indicator electrodes in extremely dilute silver solutions. This effect will be discussed in more detail below. The slopes of the titration curves 4 and 5 are still quite close to the theoretical value indicating good electrochemical behavior, but the lO-?pg errors caused by electrode dissolution are large.

The summary of results in Table I gives the amount of silver present in the standard samples in micrograms and nanoequivalents, and the amount of silver experimentally found, expressed as an average of the graphical and computer analyses of the data, with the 95% confidence limits of the mean for the number of determinations indicated. The errors reported illustrate the range of applicability in terms of the accuracy of this method. I t is obvious that below about 0.1 pg of silver (10 p M ) , there is a rapid decrease in accuracy. I t is calculated that 10-9 equivalent of silver can be determined with a positive error of only 5 z, and at 6 X equivalent (or 0.065 pg) the error is just under 10% (approximately 0.006 pug). Finally, for amounts below equivalent of silver the error exceeds loo%, and the reproducibility of the method rapidly deteriorates. The slopes reported in the last column of the table indicate good Nernstian response in all concentration ranges within the precision of the measurements. In the least squares computer calculations of the intercept (equivalence point) and the slope for titrations 4, 5 , and 6, the data points a t concentrations less than 0.3 peq Ag+/100 ml were not used because of the large deviation from linearity in this region.

As mentioned briefly above, the proposed explanation for the positive deviation occurring in very dilute solutions (below 10 p M ) is the dissolution of the silver indicator electrodes. Assuming this to be the case and further assuming similar dissolution rates initially in two cells, one would expect the silver concentration in the null-point cell to increase more rapidly due to its thousandfold smaller volume. The resulting higher concentration in the null-point cell would thus explain the positive deviation occurring in dilute solutions. In more concentrated solutions, the presence of significant amounts of silver would suppress the rate of dissolution to a negligible value. Two studies may be cited in support of this hypothesis, The first, concerned with the stability of silver electrodes in perchloric acid solutions (8), indicates a definite corrosion of silver, the rate of which decreases with time as the silver concentration of the solution increases. Since these studies were made in solutions containing dissolved oxygen, two thermodynamically spontaneous reactions are involved :

2 Ago + '/z 0 2 = AgO

followed by

Ag2O + 2 H+ = 2 Ag+ + HzO

for a net reaction :

2 Ago + 2 H+ + '/z 0 2 = 2 Ag+ + HzO

or, stated simply, the dissolution of silver in aerated acid solution. The hrst reaction is extremely slow and is rate determining (9) . However, in small volumes of extremely dilute silver solutions, this dissolution process is certainly not negligible. The formation of the oxide may not be a necessary reaction step since the affinity of silver for oxygen is well known and even high purity silver contains a significant amount of the oxide, In addition, silver may also go into solution as a result of galvanic corrosion a t local anodic and cathodic areas on the silver surface.

The second study was performed in conjunction with the present null-point determinations and is a variation of the blank titration. In Table I and Figure 2 (titration 6), the results obtained for the blanks indicate the presence of 0.15 nanoequivalent (0.16 pg) of silver in these solutions. How- ever, in an attempt to demonstrate the dissolution of silver as the cause of the positive errors observed, the titration itself was not performed. Instead, after the concentration cell

(8) D. N. Craig. C. A. Law, and W. J. Hamer, J . Res. Natl. Bur.

(9) D. N. Craig, J. I. Hoffman, C . A. Law, and W. J. Hamer, Std., 64A, 127 (1960).

J . Res. Narl. Bur. Std., 64A, 381 (1960).

1376 ANALYTICAL CHEMISTRY

r

! TlME(min)

I

Figure 3. Variation of cell potential due to silver dissolution

was set up containing only the sulfuric acid electrolyte, the potential was measured as a function of time, In all cases, a curve of the general type shown in Figure 3 was obtained, Since there is a finite time between the point when the indicator electrodes are inserted and the start of the potential measurements (usually about 5 to 10 seconds), the initial potential rise showed considerable variation, 'although the actual curves showed remarkable overall similarity. In all cases, there was first a large potential rise into the positive region indicating a more rapid increase in silver ion concentration in the null-point half cell. Usually between 10 to 20 minutes later, a leveling-off occurred with the potential still in the positive region. At longer times, the potential slowly drifted in a negative direction, although as shown in Figure 3 it was still positive after 21/2 hours.

This elementary study using the titration equipment clearly exhibits the behavior expected for the dissolution of silver in greatly differing volumes of solution. Initially, the silver ion concentration in both half cells is zero, and the rates of silver dissolution are approximately the same except for dif- ferences in the electrode areas. Since the volume of the null- point cell is lo3 times less than the titration cell volume, the silver ion concentration increases more rapidly in the null- point cell thereby giving rise to the large positive potential change at the start. It is important to keep in mind the dis- tinction between the rate of dissolution and the rate of concentration change. It is the latter that affects the cell potential. Since at no time is the rate of dissolution greater in the null-point half cell, it is merely a consequence of the small volume that this half cell initially increases in concentration more rapidly. However, the rate of dissolution decreases more rapidly in the null-point half cell because of the greater concentration increase and, after about 10 minutes, the rate of concentration change in both half cells is approximately equal, briefly resulting in no net change in cell potential. The null- point half cell still has the higher silver ion concentration as evidenced by the continued positive cell potential. Beyond this point, the silver ion concentration increased more rapidly in the titration half cell, because of the suppression of the dissolution rate in the null-point half cell by the higher concentration. The difference in the rate of concentration change is small so that the potential drifts very slowly in the negative direction. Theoretically, at infinite time the overall cell potential would reach zero volts (assuming no asymmetry potential), and the two half cells would contain equal silver ion concentrations.

Qualitatively, the positive errors and the nonlinearity in the titration curves at very low concentrations may be interpreted

.I . 2 .5 1 2 5 IO 20 50 100 200 500 1000 5001 [ I N T E R F E R E N C E ION] /[Ag']

Figure 4. Cation interference curves at [&+I = 10-4M

as a consequence of the dissolution of silver (oxide) in the sulfuric acid solutions. Another less important source of error at these concentrations may be the offset current of the P65AU voltage follower amplifiers which was measured to be approximately 1.5 nanoamperes. For a measurement time of 5 minutes (maximum), this current is equivalent to approximately 6 picoequivalents of silver. This amounts to an error of about 10% at the lowest concentration of silver studied (6.5 pgjO.1 ml) and therefore could account for only a small fraction of the observed error. Since the offset current is relatively constant, the significance of this error decreases as the amount of silver increases, Le., at higher concentrations. To further reduce this error, an operational amplifier of the P25A type (high input impedance, low offset current, < 150 PA) could be used.

Although interferences were not studied in detail, several selected cations were used which give some indication of the cationic tolerance levels in the silver determination. Anions such as the halides and cyanide will of course interfere as will any species which acts to reduce the concentration of free silver ion in solution. These effects are rather straight- forward, but cation interferences are more difficult to predict because of the nature of the interference. Instead of a purely chemical interference, such as anion complexation or precipitation of silver, the cationic interference may occur as a mixed potential of varying degrees of significance. Since the high purity silver electrode is normally specific for silver ions, only those cationic species which can spontaneously reduce to the metallic state on the silver electrode (more noble than silver) or exist in two stable oxidation states in solution should produce an electrochemical interference. For the case of a more noble metal, the existence of the metallic form on the silver electrode establishes a metaljmetal ion couple which produces a mixed potential with the silverjsilver ion couple. When two stable oxidation states of a cation exist, the silver electrode then acts as an inert electrode for the redox system while still responding to the silver ion activity. The cations of any metal more active than silver should not seriously interfere since the metallic form cannot be spontaneously produced by reduction thus preventing the establishment of a potential-determining half-reaction-Le., the metal/metal ion couple.

The cation interference study was performed by adding

VOL. 39, NO. 12, OCTOBER 1967 1377

successively increasing amounts of the interfering ion to a constant concentration of silver and observing the effect on the cell potential. The concentration cell used in the null- point titrations (minus the silver generation electrode and the isolation compartment) was utilized for this study by placing identical solutions containing 10-4M Ag+ and 1M H2S04 in the null-point and titration half cells. After a stable potential (0.00 =t 0.05 mV) was established for this concentration cell, weighed solid samples of the metal nitrate or sulfate salts we;e added to the titration half cell and allowed to dissolve. The cell potential was recorded and plotted as a function of the ratio of the interference ion and silver ion concentrations. As evident from Figure 4, Hg+z and Fe+3 interfere strongly while Ni+2, Cd+2, and C U + ~ have very little effect on the potential. In the case of mercury, which is the most noble of the elements studied, reduction to the metallic state was evidenced by an amalgamation of the silver electrode surface. Since the standard potentials for the reduction of Hg+2 and Ag+ to the metallic state are 0.854 and 0.799 volts (IO), respectively, and assuming the formal potentials in 1M H2SO4 maintain a similar relationship, mercury is the more noble metal and spontaneously forms a amalgam with silver as observed. This provides the half- reaction couple necessary to establish a potential responding to mercuric ion activity. In Figure 4, the slope of the curve for the potential us. [Hgf2]/[Ag+] shows this response assuming a constant silver ion concentration. However, this negative potential shift could also be accounted for by the increase in the silver ion concentration produced when the mercuric ion is reduced at the silver electrode.

The ferric ion may show the second type of interference in which the silver acts as an inert electrode for the ferric/ferrous redox couple. In this case, the standard potential for the reduction of ferric ion to ferrous ion is 0.771 volt (10) which, although slightly less than the reduction potential for silver, indicates a significant equilibrium concentration of ferrous ion. However, as in the case of mercury, this reaction produces an equivalent amount of silver ion which, in the titration cell, could also account for the negative shift in potential. The air oxidation of the ferrous ion formed introduces a third factor which makes any description of the potential change, either qualitative or quantitative, impossible with the limited information available. Suffice it to say that, whatever the cause, the determination of silver is strongly interfered with by mercuric and ferric ions.

The remaining three ions show little, if any, interference below a concentration ratio of 1 O O : l . Figure 5, an enlarge- ment of that portion of Figure 4 concerning these three ions, clearly shows the effect of higher concentrations of these ions on the cell potential.

Copper, the next most noble metal studied, does not show significant potential deviation until its concentration is almost 10-ZM or [Cu+*]/[Ag+] = 1 O O : l . Above this concentration, the cell potential shifts to more negative values up to 0.2M Cu+* where the potential shift reverses toward positive values. The negative shift may be interpreted as being the start of a copper/copper ion mixed potential on the silver electrode or an increase in the silver ion concentration produced during the reduction of Cuf2. However, at these levels the ionic strength of the titration cell solution is significantly different from the null-point solution so that activity coefficient

-2

(10) W. M. Latimer, “Oxidation States of the Elements and Their Potentials in Aqueous Solution,” 2nd ed., Prentice-Hall, Engle- wood Cliffs, N. J. , 1952.

I 1 I l l l l l l 1 I 1 1 1 1 1 1 1 I I1’h-d -I I*

effects and/or liquid junction potentials could be operative. The positive shift in potential at higher concentrations is most likely due to the decrease in silver ion concentration by precipitation with chloride, an impurity (0.0027J in the copper sulfate used. Volume changes accompanying the addition of large amounts of salt to the titration half cell and causing a decrease in the silver ion concentration would also account for a positive potential shift, but corrections for dilution have been applied to reduce this factor for these three salts.

Cadmium shows the smallest influence on the concentration cell potential as would be expected for such an active metal. A deviation in potential is not observed until the concentration ratio of cadmium to silver is greater than 1000:l-Le. >0.1M Cd+2. Even at a ratio of 5000:1, the error in the silver determination amounts to less than 4%. This value is based on the fact that the error introduced by a displacement of the potential (bias) is 473mV as calculated from the 59mV/pAg slope of the titration curve.

Nickel, which causes the greatest positive deviation in potential, is considerably more active than silver and thus does not form the half-reaction couple necessary to produce a mixed potential. The positive deviation is again attributed to the chloride impurity rather than to interference by the metal ion itself. Indeed, the points at which the positive deviation occurs for all three ions correspond to the calculated value where the solubility product of silver chloride is ex- ceeded.

DISCUSSION

From the preceding considerations, two principal dis- advantages may be cited for the null-point technique. One is concerned with the errors in cell potential caused by the presence of interferences, e.g., redox couples and species more noble than the ion being determined. The other is the need to know the nature and amounts of electrolytes in the unknown solution in order to eliminate or reduce ionic strength and interference effects.

On the positive side, this technique offers several important advantages in addition to its intrinsic simplicity. It in- corporates the advantages usually associated with null-type comparison methods. By performing the titration in a cell other than the one containing the unknown, the sample solution is uncontaminated by the titrant solution and preserved

1378 ANALYTICAL CHEMISTRY

for additional study, while the actual titration in the second cell is conveniently carried out in any desired volume of solution. This separation of titration and sample cells also permits the use of micro volumes of the sample solution since the sample need only serve as a reference solution. As pre- viously stated, the volume ratio between the sample and titration solutions acts as an amplification factor and permits the titration of amounts of material too small to be determined by an ordinary potentiometric titration. In addition, the

use of the new highly selective specific ion electrodes should permit the extension of this technique to many more elements with much higher interference tolerance levels. Work is presently in progress to use fluoride-specific electrodes in this way and to reduce the sample volume required to 0.01 ml.

RECEIVED for review June 8, 1967. Accepted July 27, 1967. Presented in part, Division of Analytical Chemistry, 153rd Meeting, ACS, Miami Beach, Fla., April 1967.

Control led - Po tent i a I Differentia I DC Polarography Comparative Polarography

W. D. Shults and D. J. Fisher Oak Ridge Notional Laboratory, Oak Ridge, Tenn.

W. B. Schaap Department of Chemistry, Indiana University, Bloomington, Ind.

37830

Comparative polarography is a differential polarographic technique that involves the measurement of the small difference between two diffusion currents, one due to the electroactive species of interest in the unknown solution and one due to the same electroactive species (present in accurately known concentration) in a similar reference solution. This comparative technique provides analytical results with accuracy and precision of 0.1% when cathode ray differential polarographic instrumentation is used in conjunction with two polarographic cells having syn- chronized dropping-mercury electrodes. The present paper gives the results of our study of the comparative technique with our controlled-potential differential dc polarograph that does not require the use of syn- chronized dropping-mercury electrodes. We have evaluated the dual-cell comparative technique and we have developed and evaluated a single-cell comparative technique. Using either of these dc comparative techniques, we obtain analytical results with accuracy and precision of 0.1% under optimum experimental conditions.

THE PREVIOUS two parts in this series (1, 2) have dealt with, first, the design and performance of the controlled-potential differential dc polarograph and, second, the application of that instrument to (and the theory of) AE-differential polarography. The present paper deals with another differential dc polarographic technique, namely, comparative polarography. Comparative polarography is the technique in which the small difference between the polarographic diffusion currents at two dropping-mercury electrodes is measured, one electrode being in contact with a solution that contains an unknown concentration of the electroactive species of interest and the second electrode being in contact with a similar solution that contains an accurately known concentration of the electroactive species of interest. The unknown concentration can be determined with better precision and accuracy by this comparative technique than by conventional polarographic techniques.

Comparative polarography is a relatively recent innovation although the differential technique itself has been known (3,

(1) W. D. Shults, D. J. Fisher, H. C. Jones, M. T. Kelley, and W. B. Schaap, Z . Anal. Chem., 224, 1 (1967).

(2) W. D. Shults and W. B. Schaap, Ibid., p. 22. (3) E. A. Kanevskii,J. Appl. Chem. (U.S.S.R.), 17, 514 (1944).

47401

4 ) and studied (5-12) for many years. Vogel and Valenta (10-12) described a differential oscillographic polarograph which they used for comparative (as well as other differential) measurements, but the instrument lacked long-term stability and both the instrument and the comparative technique at- tracted little attention. Davis and Seaborn (13) developed a stable differential cathode-ray polarograph which, when used in conjunction with a device for the electromechanical syn- chronization of two DME’s, performs excellently in the comparative mode (14-18). Their instrument is available commercially (Model A1660 ; Southern Analytical Ltd., Frimley Road, Camberley, Surrey, England).

There has been no previous report of an investigation in which differential direct-current polarographic techniques and/or mercury electrodes with uncontrolled drop times were utilized in comparative polarography; that is the subject of the present paper. Results obtained by the dual-cell dc

(4) G. Semerano and L. Riccoboni, Gazz. Chim. I t d , 72, 297

( 5 ) L. Airey and A. A. Smales, Analyst, 75,287 (1950). (6) M. T. Kelley and D. J. Fisher, ANAL. CHEM., 30, 929 (1958). (7) K. J. Martin and I. Shain, ANAL. CHEM., 30, 1808 (1958). (8) 0. Nesvadba, Collection Czech. Chem. Commun., 15, 751

(1942).

(1950). 373 (1951).

Proc. Intern. Polarog. Congr. Prague, 1st Congr., 111,

(9) S. Stankoviansky, Chem. Zoesti, 2, 133 (1948). Ibid., 3, 266

(10) P. Valenta and J. Vogel, Collection Czech. Chem. Commun.,

(1 1) J. Vogel, Dissertation, Karlsuniversitat, Prag, 1952. (12) J. Vogel and P. Valenta, Chem. Listy, 49, 361 (1955). (13) H. M. Davis and J. E. Seaborn, “Advances in Polarography,”

I , I. S. Longmuir, Ed., Pergamon Press, Oxford, 1960, pp. 239- 50.

(1949).

21, 502 (1956).

U. K. At. Energy Authority Rept. R/3472, September 1960. (14) H. M. Davis, Chern.-1ng.-Tech., 37, 715 (1965). (15) H. M. Davis and R. C. Rooney, J. Polarog. SOC., 8 (2), 25

(1962). (16) H. M. Davis and H. I. Shalgosky, “Advances in Polarog-

raphy,” ZI, I. S. Longmuir, Ed., Pergamon Press, Oxford, 1960, pp. 618-27. U . K. At. Energy Authority Rept. R/3473, Septem- ber 1960.

(17) H. I. Shalgosky, R. C. Smart, and J. Watling, U.K. At. Energy Authority Report AERE-R 4270, June 1964.

(18) H. I. Shalgosky and J. Watling, Anal. Chem. Acta, 26, 66 (1962). U.K. At. Energy Authority Rept. R/3590, February 1961.

VOL. 39, NO. 12, OCTOBER 1967 1379

Modified linear null-point potentiometry

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