ACKNOWLEDGMENT
follow a signal varying at a maximum linear rate of 104 volts/ sec. Although an unlikely occurrence, a response to a step function requiring a total maximum gain change of 128 would require about 45 psec. The accuracy of the autoranger is about 0.5 Z, when carefully calibrated, 0.2 Z.The system noise is less than 5 mV maximum at the output of A2 at maximum gain.
The authors express their appreciation to M. D. Mercer for technical assistance. RECEIVED for review November 24,1969. Accepted February 27, 1970. Work supported in part by a National Institutes of Health Institutional Grant.
Differentia I Potentiometry with Ion-Selective Electrodes A New Instrumental Approach M. J. D. Brand and G . A. Rechnitz Chemistry Department, State University of New York, Bufalo, N . Y . 14274
A new instrument is described which permits direct differential measurements between two high impedance ion-selective electrodes. In this manner, measurements can be carried out in which glass and other membrane electrodes serve as reference electrodes without liquid junctions. The utility of the instrument and the differential approach is demonstrated for a variety of analytical situations including direct potentiometry, titrations, and null-point potentiometry using glass, crystal, and liquid membrane electrodes.
THEDEVELOPMENTS which have occurred in the last few years in analytical potentiometry are largely a result of the introduction of various types of membrane electrodes which permit the measurement of ionic activities in solution with a high degree of selectivity. . Electrodes based on glass, crystal, liquid, and heterogenous membranes are now available for the determination of a wide range of cations and anions and it may be anticipated that progress in this area will continue ( I ) . Improvements in electrode sensitivities, selectivities, and stabilities have presented a need for more refined techniques in the use of ion-selective electrodes. These electrodes may be used to detect the end point in a titration or they may be calibrated for use as activity (or concentration, at constant ionic strength) probes. In the latter case, membrane electrodes obey an equation of the form of the Nernst equation,
E
=
Eo
+ S In at
(1)
where Eo and S are constants, the latter usually having a value near to the Nernstian RT/nF. Values of S significantly different from the theoretical Nernst value are often indicative of catastrophic failure of the membrane and result in unreliable electrodes. For a given electrode, the constants Eo and S may show small variations with time on a day-to-day basis. This drift is not usually significant during the course of a series of measurements, but frequent calibration is necessary for accurate work. The measurement of the activity (or concentration) of an ion in solution is facilitated by use of a standard addition procedure. In general, for the addition of V , ml of solution of known concentration, C, to Voml of solution of unknown concentration C,, at constant ionic strength,
(1) G. A. Rechnitz, ANAL.CHEM., 41, (12) 109A (1969). 616
0
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
This is a nonlinear equation in 3 unknowns and cannot readily be converted into linear form. Methods for fitting a series of measured values E1 --n for a series of volume increments Vl --n to an equation of the form of (2) are available (2), but are impossibly tedious by hand calculation and beyond the scope of readily available computing calculators. Most of the recommended procedures for standard addition have avoided this problem by assuming that the value for S is known either as the theoretical Nernst value or from a pre-calibration, Thus, the use of a single addition of a known volume of a solution of known concentration to the unknown solution has been proposed (3). A better method uses several standard additions ( 4 ) and linearization of Equation 2 by Gran’s method (5). This has the advantage that a least squares straight line fit can be used to give a more precise value of C, than is obtainable from a single addition. The corresponding technique of known subtration, in which a known increment of a complexing or precipitating reagent is added to the solution, has also been described (6). This method could also be extended to the case of several successive increments with a corresponding improvement in precision. Durst (7) has suggested the procedure of adding known volumes of the solution of unknown concentration to a known volume of solution of known concentration; in this case V, becomes the independent variable in Equation 2. Membrane electrode potentials are most frequently measured with respect to a refercnce electrode which is usually an anion reversible electrode of the second kind, such as a calomel or silver-silver chloride electrode. The reference electrode may, however, equally well be another membrane electrode; the two electrodes may be selective toward different ions or both may be selective toward the same ion. In the former case, if the activity of one ion remains constant, the electrode responding to this ion operates as a fixed potential reference electrode and the cell need include no liquid junction. A fluoride ion-selective electrode has been used in this way in
(2) R. H. Pennington, “Introductory Computer Methods and
Numerical Analysis,” The Macmillan Co., New York, N. Y., 1969, p 380. ( 3 ) Newsletter, Orion Research Inc., Cambridge, Mass., July 1969, p 9. (4) A. Liberti and M. Mascini, ANAL.CHEM., 41,676 (1969). (5) G. Gran, Analyst, 77,661 (1952). (6) Newsletter, Orion Research, Inc., Cambridge, Mass., September 1969, p 25. (7) R. A. Durst, Mikrochim. Acta, 3,611 (1969).
the potentiometric determination of nitrate ion (8). In the case of two similar electrodes, no analytically useful information can be obtained from a cell without liquid junction. Potentiometric measurements on concentration cells with similar electrodes and with liquid junctions form the basis of the method known as null-point potentiometry (9-11). In this procedure the unknown solution is placed in one half cell and the activity of the ion to which the system responds is varied in a known way in the other half cell. Durst (12) has described the application of the method to the determination of fluoride. Electrode potential measurements are most conveniently made with a commercially available pH meter, a high input impedance amplifier which provides a direct read-out in millivolts. Such amplifiers invariably provide only one high impedance input, the reference electrode input operates at or near ground potential. This configuration is adequate for measuring the potential ,acrosstwo membrane electrodes forming a cell provided the Impedance of at least one electrode is low. Fluoride electrodes used in reported applications (8, 12) are known to have low impedances (13). However, the use of a single input amplifier to measure the potential of a cell consisting of, for example, two glass membrane electrodes each of which may have a dc impedance of several hundred Mil ( I d ) , is unlikely to be successful. The impedance to ground of the cell vessel wall may be less than or comparable to the impedance of a glass electrode and is in parallel with the electrode connected to the low impedance amplifier input. Khuri (15) has overcome this problem in the measurement of the potential of a sodium glass electrode-potassium glass electrode cell by use of an electrometer with a floating reference input and by careful elimination of ground loops. Friedman (16) has described the use of two vibrating reed electrometer amplifiers to measure the potential of a cell consisting of two glass membrane electrodes; the reference inputs were connected to a common reference electrode (3). A detailed analysis of possible electrical errorj arising in the measurement of the potential of a cell with two high impedance electrodes using a single input amplifier will not be given here. These errors can to a large extent be minimized by using an amplifier with a differential high impedance input. This paper outlines the theory of the differential measurement of the potential of cells consisting of two ion-selective membrane electrodes, describes an amplifier to instrummt such measurements and reports a number of representative applications. THEORY Cells without Liquid Junction. For a cell without liquid
junction consisting of two different types of membrane electrode which respond selectively to the ions A and B, 1 s . E ~j CA, CB 1 1 % ~ the potential of each electrode will be given by
+ S A In U A EB = Ee" + SB In EA = EA"
UB
(3) (4)
(8) S. E. Manahan, 5th Annual Midwest Regional Meeting, ACS,
Kansas City, Mo., October 1969. (9) H. V. Malmstadt and J. D. Winefordner, Anal. Chim. Acta, 20, 283 (1959). (10) R. A. Durst and J. K. Taylor, ANAL. CHEM., 39, 1374 (1967). (11) R. A. Durst, E. L. May, and J. K. Taylor, ibid., 40,977 (1968). (12) R. A. Durst, ibid., p 931. (13) M. J. D. Brand and G. A. Rechnitz, ibid., 42, 478 (1970). (14) Zbid., 41, 1788 (1969). (15) R. N. Khuri, in "Glass Electrodes for Hydrogen and Other Cations," G. Eisenman, Ed., Marcel Dekker, New York, N. Y., 1967, p 478. (16) S. M. Friedman, ibid., p 422.
assuming that each electrode is sufficiently selective that mutual interference effects can be neglected. The differential cell potential is given by EA - E% = EA" - E%"
+ SA In
UA
- SBIn U B
(5)
or AE = AE"
+ S A In
UA
- S B In U B
(6)
If the ionic strength of the solution and the concentration of one ion, A or B, is held constant, Equation 6 reduces to an equation of the form of Equation 1. Cells with Liquid Junction. For a cell with liquid junction consisting of two membrane electrodes of the same type, ZSEi
I C I ' cz 1 ZSEz
the potential of each electrode will be given by
+ SI In ul E2 = Ez" + SZIn uz El = Elo
(7) (8)
The differential cell potential is given by El
- Ez = Elo - Ez" + S1In ul - SZIn u2 + E,
(9)
or, AE
=
AE"
+ S1 In al - SZIn az + E*
(10)
where E, is the liquid junction potential. Assuming the ionic strengths are held constant (but not necessarily equal) in each half cell, E, is a constant. Then ( x ) reduces to AE
=
AE'
+ SIIn
c1
- SZIn cz
(1 1)
for the special case where S1 = SZ= RT/nF, Equation 11 is the equation previously given by Durst (12). When c1 = c2 = c, the differential potential is AE = AE'
+ (SI- Sz)In c
(12)
Thus, in general, it may be predicted that the measured cell potential will be a function of concentration when both half cells contain solutions at the same concentration. It is, therefore, apparent that in the application of null-point potentiometry with ion-selective electrodes the cell-null potential is not necessarily zero and must be determined with the unknown solution in each half cell. INSTRUMENTATION
The requirements for a differential amplifier for the measurement of cell potentials are to some extent identical to those for single ended amplifiers. Thus, each input must have a high impedance to ground, the overall stability of the amplifier must be high as must its accuracy if it is to measure dc signals in the range 0 to +lo00 mV to within 0.1 mV or better. In addition, a differential amplifier must accurately measure the difference between its inputs-that is, it must have good common mode rejection. Ideally, with both inputs at the same , output should be observed, but, in practice potential, E C Mno a small error signal ecy arises. The common mode rejection ratio is defined as CMRR = Ecx/eoM
An accurate measurement of the cell potential can be obtained only if the current through the cell is sufficiently small so that iRcell Eoell/ Rsmp and the error in the potential measurement, iRoe11,is determined by the amplifier bias current. Bates (17) has previously pointed out the importance of bias currents in potentiometric measurements. At the present time, undoubtedly the lowest bias current can be obtained with a vibrating reed electrometer for which ib may be of the order of lo-” A. This high-performance instrument is expensive and relatively large; many commercial pH meters are based on the cheaper and smaller FET amplifier having a bias current of 1 to 10 PA. A better alternative is provided by the recent introduction of small, low cost varactor bridge amplifiers (18) one version of which has a bias current of 0.01 PA. Figure 1 shows the schematic of the differential high impedance input amplifier used in the present study. A detailed account of the mode of operation of this circuit has been given elsewhere (19,ZO) but basically the input stage, amplifiers 1 and 2, consists of two voltage followers, the outputs of which are coupled to provide a floating output with a gain of 2. The output stage, amplifier 3, is a conventional differential-tosingle-ended converter with a gain of 0.5. Amplifiers 1 and 2 were Model 3115 varactor bridge amplifiers and amplifier 3 was a Model 183L differential amplifier (Analog Devices, Cambridge, Mass.). All resistors were metal oxide film, nominally 1% tolerance selected to 0.1% tolerance. The potentiometers used to zero each amplifier were Helitrim Model 56PR and the potentiometer in the negative feedback circuit of amplifier 3 was a Helitrim Model 79PR (Beckman Instruments Inc., Fullerton, Calif.). The instrument was constructed inside a metal cabinet which was grounded to (17) R. G. Bates, “Treatise on Analytical Chemistry,” Vol. I, Part I, I. M. Kolthoff and P. J. Elving, Ed., Interscience, New York, N. Y., 1959, p 388. (18) L. Smith, “Background Information on Varactor Bridge Op Amps,” Tech. Bull., August 1967, Analog Devices, Cambridge, Mass. 02142. (19) “Applications Manual for Operational Amplifiers,” Second Ed., 1968 Philbrick-Nexus Research Inc., Dedham, Mass. 02026, p 82.
(20) R. Demrow, “Evolution from Operational Amplifier to Data Amplifier,” Tech. Bull., February 1968, Analog Devices, Cambridge, Mass. 02142. 618
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
screen the entire circuit, The f15-V dc power supply, Model 902 (Analog Devices, Cambridge, Mass.) was external to this screened enclosure. Switches, potentiometers, and input, output, and ground connectors were mounted on the front panel of the cabinet. Setting up the amplifier was performed as follows. Inputs A and B were both connected to ground and the output was monitored on an oscilloscope having a maximum vertical sensitivity of 0.1 mV/cm. The input to amplifier 3 was switched to ground and the balance potentiometer adjusted until zero output was observed. Switching the output to amplifier 1 and then 2 allowed the input stage to be zeroed. The switches were returned to the normal operating position, inputs A and B were shorted together, and a 1-V dc signal was applied between the input and ground. The potentiometer in the negative feedback circuit of amplifier 3 was then adjusted until the output was again zero, thus setting the dc CMRR to 105. The drift observed for the instrument was quite low, and rechecking the amplifier zeros about once a week was adequate. The output of the amplifier has about 1 mV peak-to-peak of high frequency noise but this was not a problem as normally the output was measured with either a digital voltmeter or a pen recorder. The frequency response of the circuit was quite low; Figure 2 shows the small signal response of the gain as a function of frequency, Also shown in Figure 2 is the measured frequency response of the CMRR. Distortion of a l-V sinusoidal signal became apparent above 100 Hz when the overall gain of the amplifier showed a slight increase over its low frequency value of unity. At higher frequencies, above 800 Hz, the gain decreased at 20 db/decade. Figure 3 shows the amplifier response to a step input. The amplifier was apparently slightly underdamped but settled to its final output in 2 to 3 msec. This response time is adequate for most purposes.
>
EXPERIMENTAL
The following ion-selective electrodes were used. The pH glass electrode was a combination pH electrode with semimicro Ag/AgCl internal reference, No. 476050 (Corning Glass Works, Corning, N. Y . ) and the sodium ion glass electrode was a Research Model 914 (Leeds & Northrup, Philadelphia, Pa.). The cupric ion electrode was a mixed
lOOr
8 0-
60 -
40GAIN OB.
20-
L
0 1
I
1
I
l
l
I
I
I
/
I
1
I
I 1
I
10 FREQUENCY
Figure 2. Frequency response of gain (0) and CMRR
sulfide type, Model 94-29 and the calcium electrode was a liquid ion-exchange resin membrane type, Model 92-20 (Orion Research Inc., Cambridge, Mass.). Two silver chloride membrane electrodes were used, a Model 94-17 (Orion Research Inc., Cambridge, Mass.) and a No. 39604 (Beckman Instruments Inc., Fullerton, Calif.). The output of the differential amplifier was measured with a Digital Electrometer Model 101 (Corning Glass Works, Corning, N. Y . ) ,the recorder output of which was connected to a No. 100500 potentiometric recorder (Beckman Instruments Inc., Fullerton, Calif.). This allowed drift in electrode potentials to be readily observed. Solutions for titrations and potentiometry were placed in 100-ml glass beakers which were not thermostated, room temperature being in the range 25 f 1 “C. Magnetic stirring with a rotor coated with Teflon (Du Pont) was used. The input to the differential amplifier was extremely sensitive to interference caused by varying electromagnetic fields inducing currents in the high impedance cells. In most experiments the glass beaker was placed on a thick Teflon block to electrically insulate it from the magnetic stirrer. Under these conditions the only leakage path to ground from the cell was through the amplifier input, an extremely high impedance. Additions of solutions to the cell or inadvertent touching of the beaker sometimes resulted in erroneous potential readings; this may have been caused by the pick up of electrostatic charge by the cell. These problems were entirely eliminated by placing a third electrode in the cell and connecting it to the differential amplifier ground terminal. For the pH electrode, the combined silver-silver chloride reference electrode was used for this purpose but in other cases a small platinum wire was used. This arrangement was preferable to placing the cell directly on a grounded magnetic stirrer. All chemicals were of reagent grade. The ammonia buffer solution was 1M in ammonia and ammonium nitrate and the acetate buffer was 1 M in acetic acid and sodium acetate. Tris-hydroxymethyl-aminomethane(tris) buffers were prepared by adding sufficient tris to 1M hydrochloric acid to give the required pH. At nearly neutral pH values, the ionic strength of the solution is given by the chloride ion concentration. Least squares curve fittings procedures were performed on a computing calculator 9100A (Hewlett-Packard, Palo Alto,
1
I
I
l
l
1
1
1
1
1
1000
100 HZ.
( 0 ) of
differential amplifier
Figure 3. Response of differential amplifier to a step input Oscilloscope calibration: vertical 100 mV/cm, horizontal 1 msec/cm
Calif.) using library programs 70803 (y = mx (z =
a0
+ + azy).
+ b) and 70814
a1x
RESULTS AND DISCUSSION Direct Potentiometry in the Differential Mode. To test the performance of the differential amplifier with a very high impedance cell, measurements were made on a cell consisting of two glass membrane electrodes, a pH electrode and a sodium ion electrode. Cell potentials were measured for solutions containing sodium chloride over the concentration range to 10-1M and a fixed concentration of tris buffer solution (final buffer ionic strength 0.1). Under these conditions the pH electrode served as a reference electrode and Figure 4 shows calibration curves obtained at four pH values. Polarity of the measured potential depends upon which of the amplifier inputs is used for the reference electrode; in this example the polarity is the inverse of the conventional potential. Over the concentration range 10-4 to 10-’M, the elecANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
619
-5
I
I
I
-4
-3
-2
LOG
-I
CONCENTRATION
Figure 4. Potential of pH glass electrode-sodium glass electrode cell as a function of sodium ion concentration Limiting pH as sodium ion concentration tends toward zero; I, 6.85; II,7.55; III, 8.05; IV, 8.37 _____
Table I. Calibration of Sodium IonSelective Electrode against pH Glass Reference Electrode PH E", mV S, mV/decade r@ I 6.85 -226.8 -58.15 -0.99993 I1 7.55 -254.7 -57.95 -0.99996 I11 8.05 -281.8 -54.90 -0.99940 IV 8.37 -303.5 -58.40 -1.ooooo a Correlation coefficient of linear least squares fit used to calculate E o and S.
trode potential was a linear function of log concentration and a least squares fit was used to calculate E and S,shown in Table I together with the linear correlation coefficient, r. The ionic strengths of the solutions used for the preparation of each calibration curve were not constant but tended toward a constant value as the sodium ion concentration became small with respect to the buffer solution concentration. The sodium and hydrogen ion activities varied with ionic strength but over a wide concentration range the variation was negligibly small as shown in Figure 4. The pH of each solution was measured with a calibrated pH glass electrode, and the activity of sodium ion calculated from published activity coefficients (21). A least squares method was used to calculate the dependence of the cell potential on log sodium ion activity and on log hydrogen ion activity. Over the sodium ion concentration range to 10-'M and the pH range 6.5 to 8.5, the equation obtained was
E
=
+
135.3 - 56.17 log U N ~ + 51.76 log U H +
This equation is of the form of Equation 6, the theoretical equation for the response of a two-membrane electrode cell (21) J. Kielland, J . Amer. Chem. SOC.,59, 1675 (1937). 620
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
without liquid junction. The rather low value for the slope of the hydrogen ion activity response probably resulted from errors in the pH measurements. Over a narrow pH range, even small errors can exert a considerable effect, and the pH electrode was only calibrated at a single point. Obviously use of a pH electrode as a fixed potential reference electrode requires that the hydrogen ion activity remain constant and this condition is most easily satisfied by use of a buffer solution of high ionic strength. The results obtained demonstrated satisfactorily that stable potential measurements could be obtained with the differential amplifier on a very high impedance cell. Differential Potentiometric Titrations. In addition to using a membrane electrode as a reference in direct potentiometry, several potentiometric titrations were performed with glass membrane reference electrodes and ion-selective indicator electrodes. Figure 5 shows the potentiometric titration curves for the titration of calcium ion with EDTA. As the calcium ion-EDTA complex is best formed at high pH values, the solution was strongly buffered with an ammonia buffer and a pH glass electrode formed a convenient reference. A calcium ion-selective liquid membrane electrode was used as the indicator electrode. The shape of the titration curve was entirely adequate for analytical purposes and the system had the advantage that the cell was free from difficulties often encountered with reference electrode junctions. During the course of the titration, the buffered calcium solution was diluted by addition of titrant and a change in ionic strength and hydrogen ion activity occurred. The potential of the pH glass electrode was not, therefore, absolutely constant throughout the titration. Satisfactory titration curves were also obtained for the titration of cupric ion in an acid acetate buffer with EDTA solution. Figure 6 shows the titration curve obtained with a solid state membrane cupric ion indicator electrode and a pH glass reference electrode. Again, in this titration the reference
-180
-1
Figure 5. Titration of 10 ml of 10-2M Ca2+ solution is ammonia buffer with 1W2M EDTA. Calcium ion-selective indicator electrode, pH glass reference electrode
-200
2
0
4
6
8
12
IO
16
14
ML. OF TITRANT
2 ML.
I
I
I
I
I
I
I
I
I
I
I
I
I
ML. OF T I T R A N T
Figure 6. Titrations of 10 ml of -10-2MCu2f
solution in acetate buffer with 10-2MEDTA
Cupric ion-selective indicator electrode and pH glass (0)and sodium ion glass ( 0 )reference electrodes
electrode potential showed a small change on addition of the titrant due to dilution. This effect was eliminated in titrations using a sodium ion glass electrode as reference. The 10-2M EDTA titrant was adjusted to 0.1Min sodium by addition of sodium chloride, and the cupric ion solution was also made 0.1Min sodium ion by addition of acetic acid-sodium acetate buffer. The cupric ion concentration in the solution before titration was negligibly small in comparison to the sodium ion concentration so the total ionic strength remained constant during the titration. Figure 6 shows the titration curve obtained when the sodium ion activity in the solution remained
constant. In this case, the solution was not buffered with respect to sodium ion and unless titrant and solution had approximately the same sodium ion concentration, severe distortion of the titration curve was obtained. Null-Point Potentiometry with the Differential Amplifier. As an illustration of the use of the differential amplifier in null point potentiometry, measurements were made on a concentration cell consisting of two chloride ion-selective membrane electrodes. These electrodes showed small differences in standard potential, AEO, and in slope, AS (SI- S,). Measurements of cell potential as a function of chloride ion ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
621
Table 11. Measured Values of AEo and AS for Chloride-Chloride Electrode Cell Without liquid junction With liquid junction AS. AS. AEO, mV mV/decade AE', mV mV/decade 18.65 2.21 28.42 7.21 3.64 15.38 0.52 19.30 2.75 23.34 3.85 20.67 2.91 18.61 2.25 18.06 Table 111. Results of Determination of l F 3 M Cl- in 0.1M Potassium Nitrate by Null-Point Potentiometry Nullpoint potential, S, C, mV E', mV mV/decade ra M x 103 56.49 0.9998 1.003 1 6.7 176.1 0.9995 1.004 187.0 57.73 2 13.9 0.986 58.30 0.9999 3 13.1 188.4 4 9.9 180.5 56.77 0.9999 1.012 57.45 0.9998 0.983 5 14.8 187.6 a Correlation coefficient of least squares fit used to calculate E and S.
concentration were made at a constant ionic strength of 0.1 (adjusted with potassium nitrate) on cells without liquid junction. Measurements were also made on cells with liquid junction (0.1M potassium nitrate bridge) with equal chloride ion concentration in each half cell. Values of AE' and AS for the cell without liquid junction and AEO and AS for the cell with liquid junction were calculated from Equations 6 and 12, respectively, by a least squares method. Table I1 shows a number of calculated values taken over a period of several days; apparently these parameters were by no means constant. The determination of the chloride concentration of a standard 10-aM sodium chloride solution adjusted to an ionic strength of 0.1 with potassium nitrate was used to evaluate the method. After measurement of the cell null potential, the solution in one half-cell was replaced with a known volume of standard 2
622
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
x 10-4M sodium chloride solution (ionic strength 0.1) to which standard additions of 0.1M sodium chloride solution were made. A least squares fit to an equation of the form of Equation 2 allowed Eo and S to be calculated, and, hence, the concentration corresponding to the cell null potential, Table I11 shows the results of a series of replicate determinations. The accuracy of the method was limited by the accuracy of the determination of the null-point potential (&O.l mV); errors in the potential measured after each standard addition were less critical. At the present time, it is sometimes possible to achieve potential measurement accuracy slightly greater than &O.l mV but probably ion-selective electrode potential measurements at the *lo pV level are not meaningful. The purpose of this paper has been to show that differential potential measurements on cells consisting of two ion-selective membrane electrodes can be useful in all the conventional methods of analytical potentiometry. The use of a membrane electrode as reference for direct potentiometry and potentiometric titration is particularly advantageous as problems associated with normal reference electrodes such as electrolyte leakage and unstable liquid junction potentials are el'.rinited. Further, such measurements can be made reliably under worst case conditions by use of a high-input impedance differential amplifier. It may be argued (20) that measurement of the small potentials typically found in electrochemical cells is always best achieved by a differential amplifier. There is no reason why all types of potentiometric measurements (including those using conventional reference electrodes) should not be made differentially. Apparently many other applications of two membrane electrode cells without liquid junction are possible. ACKNOWLEDGMENT
We thank Corning Glass Works for the loan of the Digital Electrometer. RECEIVED for review January 2, 1970. Accepted March 4, 1970. The support of NSF Grant GP-11727 is gratefully acknowledged.
