LITERATURE CITED (1) R. J. Baczuk and R. J. Dubois. Anal. Chem., 40, 685 (1968). (2) T. M. Hseu and G. A. Rechnitz, Anal. Lett., 1, 629 (1968). (3) 40. - , C- . .I-. Contznn - - - .- - - and -. - H.. Frniser. . .- -. , Anal. - . Chem.. - . - , 2071 - - (1968). (4) M. J. Smith and S. E. Manahan, Anal. Chim. Acta, 48, 315 i1969). (5) R. F. Hirsch and J. D. Portock, Anal. Lett., 2, 295 (1969). (6) N. lshibashi and H. Kohara, AnalLett., 4, 785 (1971). (7) W. Selig and G. L. Crossman, Informal Report UCID-15623, Lawrence Radiation Lab., Livermore, Calif. (8) T.L. Rohm and G. G.Guilbault, Anal. Chem., 46, 590 (1974). (9) C. E. Crouthamel, A. M. Hayes, and D. S.Martin, J. Amer. Chem. Soc., 73, 82 (1951). (10) G. J. Moody and J. ID. R Thomas, "Selective Ion Sensitive Electrodes," Merrow Publishing C.O.,Watfort Herds, England, 1971, p 10. ( 1 1) F. R. Duke, J. Amer Chem. SOC.,69, 3054 (1947). (12) F. R. Duke and V. C. Bulgrin, J. Amer. Chem. SOC.,76, 3803 (1954). (13) G. Dryhurst. "Periodate Oxidation of Diol and Other Functional Groups," Pergamon Press, London, 1966, p 121. ~
I
I
~~~
(14) C. H. Efstathiou, T. P. Hadjiioannou, and E. J. McNelis, unpublished work, Laboratory of Analytical Chemistry, University of Athens, Greece, 1974. (15) P. F. Fleury and J. Lange, J. Pharm. Chim., 17, 107, 196 (1933) (161 PhiliDs Pocketbook. 1971. D 8220. (17) D. j. B. Galliford, R. H. Nuttall, and J. M. Ottaway, Talanfa, 19, 871 (1972). (18) G. J. Buist, C. A. Bunton, and J. H. Miles, J. Chem. SOC.4567 (1957). (19) T. P. Hadjiioannouand C. H. Efstathiou, unpublished work, Laboratory of Analytical Chemistry, University of Athens, Greece, 1974. (20) T. P. Hadjiioannou. M. A. Koupparis, and C. H. Efstathiou, unpublished work, Laboratory of Analytical Chemistry, University of Athens, Greece, 1974.
RECEIVED for review July 29, 1974. Accepted November 7 ,
1974. This research was supported in part by a research grant from the Greek National Institute of Research.
Interactive-Experimentation Employing Ion-Selective Electrodes Jack W. Frazer, Arthur M. Kray, Walter Selig, and Robert Lim Lawrence Livermore Laboratory, University of California, Livermore, CA 94550
An automated titration system has been assembled which consists of ion selective electrodes (ISEs), automatic buret, Interface hardware, minicomputer, cathode-ray tube (CRT) display, light-pen, teletypewriter, and a special function panel. Each of the various parts of the system was designed to perform the task for which it is best suited, with provisions for powerful scientist-computer interactive techniques. The system software changes which are often required for methods development and semiroutine determinations are made in a high-level language FOCAL. Titrations using ISEs as detectcrs and CRT display of the titration curve, Gran plot, second derivative and error function, together with interactive data-reduction techniques, are discussed. Least-square regression fitting was used for extrapolation of the equivalence points.
Titration systems employing ISEs as detectors have become very popular judging from the prolific literature on the subject. Anion and cation selective electrodes measure the activity rather than the concentration of the species of interest. The equivalence point for the titrations is usually determined by finding the maximum slope of the potentialvolume titration curve. The method of maximum slope can only be used to evaluate the equivalence point if a well-defined titration break is displayed. In addition, the method is subject to considerable systematic errors ( 1 ) . The electrode potentials art' usually unstable and subject to drifting near the end point because the level of ions being sensed is very low and the establishment of equilibrium conditions may be slow. Also, in low level titrations, the solubility of the precipitate formed or the dissociation of the complex formed may become significant near the end point. These problems may give intrinsic end-point errors (2, 3). Gran ( 4 ) has shown that a linear presentation of the titration offers a number of advantages. The method presented here is similar and involves antilogarithmic conversion of the titration data followed by a straight-line regression analysis of selected sections of the plot to determine the equivalence point. One of the advantages is that information from a large portion of the titration curve can be exploited, not jus1 the small area near the equivalence
point as in conventional titrations. Gran's method has not been widely used because the calculational time required usually offsets the advantages. A volume-corrected graph paper for obtaining linear plots is available from Orion ( 5 ) ; however, the required point-by-point plotting method is very tedious. Contrary to the opinion expressed in Orion Newsletters, ( 5 ) , Eriksson (6) pointed out that greatest precision and accuracy is obtained with the largest number of data points. Furthermore, for dilute solutions, points deviating from the straight line must be rejected or a systematic error will occur. The use of an on-line computer to process and display the data obviously affords a considerable gain in time, accuracy and precision when using Gran's method. Leastsquare curve fitting for a large number of data points is extremely tedious and time-consuming without the aid of a computer. In addition, incorporation of interactive graphics into the computerized system allows the chemist to rapidly apply advanced data reduction techniques. On-line computers have been used for automation of titrations (7-9). T o date. the greatest use of these computers has been for data acquisition, to provide rapid on-line calculations and generate reports. Now, however, there is an increasing trend toward use of the computer for control of instruments and experimental equipment. In this paper, an automated titration system employing ISEs as detectors is described. Because of the non-routine nature of our samples, we chose to design a system to provide easy-to-use hardware and to permit powerful scientistcomputer interactive techniques. The various parts of the integrated automated system will each perform the task for which they are best suited. For example, the computer will perform all the routine operations which can be predefined: i.e., mathematical calculations, optimization, data acquisition, data correlation, control, and report generation. The tasks can also include higher level logic such as that contained in pattern recognition and learning-machine techniques-but note that all these are predefinable algorithms. In short, the computer will perform routine operations and functions that require a series of predefined steps to be performed in a rapid sequence. The scientist is thus free to perform those functions for which he is most suited: observation of unusual events and creative thinking. The ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
869
\
f
Data amp1ifier Osci I loscope Te ktron ix tY Pe
A/ D
t
converter
61 1
Computer
\
/
PDP- 8 / 1
Figure 1. Computer-controlled titration system
system was designed to allow the scientist to investigate the waveform obtained and thus quickly obtain quantitative information for complex solutions and without the aid of calibration curves. Typical titrations are presented to illustrate the capability of the system. Results from some samples are also given to illustrate the interactive characteristics and accuracy obtained.
EXPERIMENTAL Instrumentation. The system consists of the components shown in Figure 1, described elsewhere (10). Additional features added for the ISE work are as follows: a data amplifier ( 1 1 ) with switch-selectable gain and offset voltage used to adjust the signal t o the proper voltage for the A/D converter input circuitry and a simple control circuit which enables the computer to advance the Mettler digital buret Model DV-101. (The plotter is not mandatory, but is convenient for recording titration curves.) Software. The general purpose system software is written utilizing the FOCAL interpretive language and allows the programmer to use the full power cf the high level language, as well as additional functions for interacting with the display and data acquisition programs. The main functions of the system involve interaction with six data tables (512 data points each) and eight markers which can be positioned with the GRAFiPEN to any position on the screen along with the data tables which are displayed as analog waveforms. Table number “0” is reserved for raw data and the other tables are used for program-derived functions, such as smoothed data, derivatives, Gran functions, regression curves, base-line approximations, etc. The markers are used by the operator t o identify areas of interest such as peaks to integrate, limits to use in performing regression fitting, increments to use in doing recursive analysis on the data and background used for base-line corrections. One simple command [Set U=FD(gNS,T,T,T . . .)] displays one or any combination of tables on the display and activates the mechanism enabling the simultaneous display and manipulation of 870
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
the eight markers. In this command “Set U=” is a high-level instruction which activates the “FD” (Function, Display) program. The FD program then displays in the N O N S T O R E , ‘‘@NS” mode (Le., constantly refreshing the display so that a time-varying picture may be seen). The displayed information consists of the Tables listed “T” (T = 0 through 5) and the eight markers. There are also simple methods for displaying any increment of the x-axis over the full width of the display, plotting a replica of the display on the Calcomp plotter, storing programs and data on the disk, accessing and modifying the contents of the tables, and finding the positions of the 8 markers (10, 12). The software needed to augment the above system for ISE work is: 1) A command to set up the time (in 0.01-second increments) between addition of increments of titrant. A data point is taken and stored in table number “0” immediately prior to each addition of titrant. 2) A command to set the size of the increment of titrant in 0.001 ml per increment units. 3) Commands to start and stop the titrant procedure. The above hardware and software enable the chemist to write high-level language analysis programs to easily specify the parameters of titration, start and stop the titration, view the data, and interactively use the computer to calculate the titration end-point or, in standard addition methods, calculate the sample concentration. The flow of information through the system will now be described in order to present a more nearly complete picture of the operation. The operating system is loaded into the computer and started. The operator then selects and loads a previously developed application program; specifying the electrodeisample relationship, Le., anionication, cationianion; the data reduction method, Le., known addition, known subtraction, etc., depending on the type of titration to be performed. When the application program starts running, a series of TTY messages are sent, prompting the operator to type in replies. If the run is a standardization, the operator types in the milligrams or millimoles of the ion taken, the charge of the ion, the range and gain set on the signal amplifier, the volume of the solution, the time between successive titrant additions and taking of data (T),and the volume of titrant addition (N).The buret is filled for the titration, the electrodes and buret tip are placed into the solution, and the stirrer and cold plate
500 mV
440
380
320
260 h
-0 42
U
L 0
200
7
140
m
.r
c,
E
c,
n -0 W
80
L +-’ U
--
20
F
W
the markers -40
I/
-100 mV
0
I35
-70
1.05
1.40
1.75
2.10
2.45
2.80
3.15
ml titrant Figure 2. CalComp plot of curves for bromide titration with silver ion
Bromide specific ion electrode; 7.017 mg Br taken
turned on. The T T Y space bar is then pressed t o initiate the run. From that point on, the computer automatically performs the following operations until a “stop” button is pushed on the function box: a) Add increment N of titrant; b) Wait for time T; c) Read electrode voltage; d ) Store data; and e) Return to step 1 (add more titrant). During the time the above operations are taking place, the computer also displays the data from the table onto the oscilloscope so the operator can observe the titration as it progresses. This enables him to determine that the proper range and gain have been set, the electrodes are working properly, the noise is not excessive, and completion of the titration, a t which time he presses a button signaling the computer to begin the next phase of analysis. Upon completion of the titration, the data are in memory and the operator can, by choosing the appropriate button(s) on the function box, select any of the data reduction programs. The original data may be smoothed and the results stored in another table t o be used for comparative viewing, or a Gran function and/or sec-
ond derivative of the data may be displayed, along with the original data. Reagents and Electrodes. 1 ) Titration of Bromide w i t h Silver Nitrate. The electrodes used were a Bromide ISE, Orion 94-35 and a double-junction reference, Orion 90-02-00. The solutions were 0.05N silver nitrate, standardized vs. potassium bromide, standard bromide solution, 1 mg/ml, and 5N sodium nitrate. 2) Titration of Low Level Chloride. The electrodes used were a Sulfide ISE, Orion 94-16 and a double-junction reference. The solutions were 0.02N silver nitrate standardized vs. potassium chloride; standard chloride solution, 0.02N; and 1Npotassium nitrate. 3) K n o w n Addition Titration of Fluoride. The electrodes used were a Fluoride ISE, Orion 94-09 and a single-junction reference, Orion 90-01. The solutions were a total ionic strength adjustment buffer containing 1,Z-cyclohexylene diamine tetraacetic acid (TISAB-CDTA) buffer prepared according to Orion ( 1 3 ) , and a standard fluoride solution 0.3 mg/ml. 4) Titration of A l u m i n u m w i t h Fluoride. The electrodes and ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, M A Y 1975
871
180
/
160
14C
-
FLUCRIDE BLANK : 5 m l TISAB CDTA TITRANT : 300.978 ugF/rnl ADDTIO IN : 0.002mP increnents
12c >
RESULTS
m
2
100
01 Y
n
a
W
g
* ”
-4.6 pg -4.6
pg
-4.5
pg
-4.2
pg
-3.4 pq
80
7
Y
60
40
20
0-
-30
io
QO
90
120
150
cc gF Figure 3. Blank determination
standard fluoride were the same as for 3). The solutions were an acetate buffer (164 g sodium acetate and 57 ml glacial acetic acid per liter); and a aluminum standard solution prepared by dissolving pure aluminum in 6 N HC1. 5 ) Titration of Chloride w i t h Mercuric Perchlorate. The electrodes used were Chloride ISE, Orion 94-17 and a double-junction reference. The solutions were 0.1N mercuric perchlorate adjusted to p H 1.2-1.3 with perchloric acid, standardized vs. potassium chloride; and 0.02N potassium chloride. Procedures. The Gran functions
G = k ( V o + U)e+(nE/O.O8616T) where Vo = initial volume; u = volume added; E = electrode potential, mV; k = adjusted so that, ,G , = 4000; n = charge; and T = temperature in K, and second-derivative programs require that the operator mark off the limits of the appropriate areas of interest. A prompting T T Y message requests the operator t o mark them prior to the actual calculations. This is done as follows for a well-behaved titration, with an observable end point (Figure 2). Upon completion of the titration, the operator selects the analysis method to be used. For this example, he would depress the key (on Function Panel) labeled “find Gran function,” place marker D1 on the screen near the approximate end point and depress ‘‘continue.” The computer then plots the Gran function in two sections beginning a t the first and last data points taken, where each are scaled to a value of 4000. The first and last points are always maxima in the Gran plot since the operator has chosen the proper program (anion/cation or catiodanion) which simply changes the sign of the exponent in the Gran equation for the first data point. The sign is automatically reversed when computing the Gran function starting with the last data point on the right. Plotting proceeds from the first data point towards the right and from the last data point towards the left until the marker is encountered. T h e sign of the exponent combined with the sign and magnitude of the ISE potential combine so that the Gran function tends toward zero as the end point is approached. At this point the operator, using his knowledge of sample origin, possible composition, interferences, etc., can select the “best” portions of the Gran plot to provide quantitative analytical values (interactive operation similar to that defined below). Or, he may elect t o run a second derivative analysis on the same data to compare different data reduction techniques. The Gran plot may also be ex872
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
amined by causing the computer to automatically calculate leastsquares fits for a series of overlapping segments along the curve, moving the segments stepwise by a selected increment along the plot, stopping a t a predetermined termination point. For each segment a least-squares fit to the data points is computed and the fitted line is then extrapolated to the x-axis intercept and the results (in chemical values) are printed out. As an additional aid to the analyst, an error function is computed and output on the CRT. Several error functions were developed and tested; however, a plot of the differences of adjacent intercepts provided the most operator usable information. An example of this technique is show in Figure 3. Shown are the results obtained from the determination of the fluoride blank in a 50-ml sample containing 5 ml of TISAB-CDTA buffer. The interactive interrogation capabilities were not required since the operator could readily detect the curvature in the Gran plot a t lower concentrations and thus select a portion of the plot in the linear section. However, the example illustrates the utility of the interrogation technique. In Figure 3, the operator has set marker 1 through 4 as shown. When the key “linear least-squares” on the function panel is depressed, the computer calculates a fit for all data points lying in the segment bounded by markers 1 and 3, extrapolates the fitted line to the intersection and calculates the corresponding quantity of fluoride determined (in pg). Upon completion of the above, the segment determined by the distance between markers 1 and 3, is moved towards marker 4 a distance equal to that between markers 1 and 2, after which the above process is repeated. This procedure is continued until the segment is advanced to the boundary delineated by marker 4. As the intercepts are determined, they are in turn subtracted from the previously determined value and the difference plotted (Curve A, Figure 3). The results shown in Figure.3 are the fluoride values obtained from successive segments, proceeding from the segment bounded by the markers 1 and 3 moving towards the origin in step size as defined by markers 1 and 2. As will be illustrated later, when discussing the results shown in Figure 6, the error function(s) provides the operator with detailed features of the curve being interrogated. To enhance specific features, the operator can vary the segment length and step distance. From the foregoing discussion, it should be apparent that the “error function” being employed is effectively a means for testing linearit y of the Gran plot. A minimum in the error function plot therefore indicates the region of maximum linearity of the Gran function. In turn, because the Gran function is based upon the assump-
400
Titration curve
Residual errors
300
section yielding residual error
1
200
0.1
0.2
0.3 AgN03 Volume of 0.049
- m.!
0.4
0.5
Figure 4. Titration of 35.5 pug chloride with silver ion in 0.1M KN03 ___
Table I. Bromide Titration with Silver N i t r a t e Standardization Silver nitrate concn, .$la
Re1 std dev, %
0.05011 i 0.00012 0.04992 i 0.00010
0.24 0.20
Bromide recovery determinations Taken, mg
Found, mg
Error,
@@
Re1 std dev, g o b
7.0121 -0.07 7.0172 4.24 5.0123 5.0002 a Standard deviation of 6 or 7 determinations. dard deviation of 6 or 7 determinations. -
0.16 0.46 Relative stan-
tion that electrode response follows the Nernst equation, the error function minimum can be associated with the most ideal or Nernstian part of the titration curve.
R E S U L T S AND DISCUSSION The titration of bromide with silver nitrate shows the precision and accuracy obtainable with the system. T o the sample was added 2 ml of 5M sodium nitrate as an ionic strength adjustor followed by dilution to 50 ml with water. The titration curve and Gran plots are shown in Figure 2. T h e results (Table I) show the method to be quite accurate, with errors equivalent to the one sigma value of t h e silver nitrate standardization. Because of the well defined titration break, this titration may also be carried out with a commercial automatic titrator. However, in commercial automatic titrators, the total volume of titrant delivered from a syringe buret is usually synchronized to a recorder drive mechanism. This synchronization is subject to mechanical errors, There is also a time-lag due to mixing and the reaction time which will re-
suit in a systematic error between the actual volume of titrant delivered and that shown by the recorder (14). T o show other capabilities of this approach, low level chloride was also determined with silver nitrate. The sample contained 35.5 pg of chloride per 50 ml of solution, or 5 X 10-5M chloride, which is near the detection limit of the chloride ISE as determined by the solubility of the silver chloride sensing element (1.4 X 10r5M at 25 "C). Therefore, an ideal sigmoidal titration curve could not be obtained and the equivalence point could not readily be determined. The sample was titrated with a large enough excess of silver ion so the solubility product for silver chloride was exceeded. The linear portion of the Gran plot for excess silver ion was used to extrapolate t o the end point on the horizontal axis. The result of the titration utilizing 0.1N potassium nitrate to maintain constant ionic strength is shown in Figure 4. The recovery was 38.6 pg of chloride or 108.7% which is considered good in view of the fact t h a t we operated near the detection limit of the electrode. Using this technique, trace chloride was determined in an explosive formulation and an organic compound. These samples were burned in a Parr oxygen bomb. Table I1 gives the results obtained. The solubility of silver halides can be lowered by operating in a non-aqueous medium. The experiment was therefore repeated in 80 (v/v) acetic acid. The potential break in this medium is considerably larger than in an aqueous medium, and recovery was 36.4 pg of chloride or 102.7%, an improvement over titration in an aqueous medium. Further improvements may be possible with a titrant of lower normality and by substituting a 1-ml buret for the 10-ml buret used. The procedure is equally applicable to known addition titrations. An example is the determination of fluoride in a ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
873
8C
6C
4c
> E
2c
-.-I 0
c
: c 'g
U a
2
c
E w
-2c
- 40
-6c
-100 -138
1
/
- 80
-92
-46
0
92
46 Fluoride added
- pg
138
184
230
Figure 5. CalComp plot of curves for known addition titration of fluoride
Fluoride Ion-specific Electrode. 100.0 pg F- Taken.
Table 11. Low Level Chloride Samples Sample
RX -04 -E F RX-04-EF RX-04-EF
Benzotrifuroxane Benzotrifuroxane Benzot rifur oxane
Table 111. Known Addition Titration of Fluoride Samples
Sample s i z e , mg
C1 found, ppm
601.3 606.4 607.8 503.9 502.7 500.9
86 83 89 360 353 321
Sample
Bomb W a s h 1 Bomb W a s h 2
mq F- ml of sample found
0.676 0.660 0.670 0.652 0.642 0.63 8
~~
TISAB-CDTA buffered solution ( 1 5 ) .The known addition titration curve and Gran plot for 100.0 kg of fluoride ion are shown in Figure 5 . For such ideal samples, the method is extremely sensitive and accurate. Unlike the normal double known addition technique, ( 1 6 ) ,the computerized system uses all the available information, thus improving the signal-to-noise ratio. The known addition method is most applicable when interfering ions are present. An example of this is in bomb washes from a calorimeter experiment. The heats of detonation were determined for fluorine containing compounds. The determination of the fluoride content of the bomb washes was necessary for the thermodynamic calculations. Because of attack of the bomb by hydrofluoric acid, these bomb washes contained various cations. Therefore, a lanthanum or thorium titration cannot be used without a prior 874
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
separation step. In the known addition titration, the cations are preferentially complexed by the addition of TISAB-CDTA, thus releasing the fluoride to be measured by the specific ion electrode. Table I11 gives results obtained by a knownaddition titration of calorimeter bomb washes. The results obtained from the titration of aluminum with fluoride illustrate most fully the capabilities of the interactive system. A fluoride electrode is used to follow the titration which is continued far beyond the equivalence point (Figure 6 a ) . Fluoride forms a sparingly ionized complex with aluminum. We found the stoichiometry to be 2.7F:Al. This is in agreement with the value obtained by Orion Research using Gran plot paper ( 1 7 ) .The stoichiometry found by Jaselskis and Bandemer (18) was lower using conventional titration methods.
/2
1601
Table IV. Determination of Aluminum via Interactive Ion-Selection Electrode System CURSORS
*I, "'3
/' 120-
100mV
80-
IrIlR4TION
.
CURVE
60'
ml. of 0.3005mq F l m l
/
I80
2OI0 '
o
o
.r
w
,
1.4
.
,
.
,
2.1 2.8 3.5 4.2 4.9 m l . o f 0 . 3 0 0 5 m ~F l m l .
,
,
5.6
6.3
.
7.0
200'
Taken
Found
100 100 100 100 300 3 00 3 00 500 500
101.9 99.5 101.4 100.6 301.3 299.2 298.7 505.9 493.9
Deviation,
c_
+1.9 -0.5 +1.4 +0.6 i0.4
-0.3 -0.4 L1.2 -1.2
the segment length per step (Figure 66). Note the random characteristics of the error function in the region of 4.9 to 7.0 ml of titrant where the activity is undergoing changes resulting in voltage changes of the same order as the system noise. T h a t is, one can identify the part of the Gran plot where the end point has been well exceeded, even though the plot has curvature in this region. Note, in some instances, there is even a reversal in error sign. The area having a random error function contains no useful information and can be eliminated in the subsequent interrogations. The region containing the equivalence point, 0 to 4.9 ml, is interrogated again. Since we are now searching for a point of minimum change in activity equivalence point, markers are set to provide a step size equal to -90% of the segment length. Note the well defined minimum in the resulting error function. I t is now only necessary to reset the markers as shown in Figure 6c which results in the printing out of the analytical results in appropriate units. Unlike conventional procedures (14), this method does not require calibration curves. Interferences and drift in the ISE are compensated for without recalibration. Table IV shows typical results obtained without the use of calibration curves.
180-
LITERATURE CITED
160-
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1 1) (12) O
0
M
.7
1.4
'
1
Z.'.l ml. 01
2.8
3:5
4.2
4.9
5.6
6.3
7.0
0.3005rnq F l m l .
Figure 6. Three hundred p g AI run as a n unknown titration with 0,3005mg F-/ml solution using a fluoride electrode
The Gran plot as shown in Figure 6 has a sharp to slight curvature representative of a non-ideal solution. However, the end point can readily be determined by interactive interrogation of the Gran plot as described under Procedures. The Gran plot is first interrogated by short segments moved stepwise a distance equal to approximately one-half
(13) (14) (15) (16) (17) (18)
L. Meites and J. A. Goldman. Anal. Chim. Acta, 29, 472 (1963). P. W. Carr, Anal. Chem., 43, 425 (1971). P. W. Carr, Anal. Chem., 44, 452, (1972). G. Gran, Analyst(London), 77, 661, (1952). Newsletter, Orion Reseach Inc., Cambridge, MA., 2, 11 and 12 (1970). T. Eriksson, Anal. Chim. Acta, 58, 437 (1972). T. Anfalt and D. Jagner, Anal. Chim. Acta, 57, 177 (1971). U. Keller, J. Padel, H. Gamsjager, and P. Schindler, Chimia, 27, 90 (1973). S. Gobom and J. Kovacs, Chem. Scripta, 2, 103 (1972). J. W. Frazer, L. R. Carlson, A. M. Kray, and M. R. Bertogiio, Anal. Chem., 43, 1479 (1971). Data Amplifier, Lawrence Livermore Laboratory Internal Drawing, LEA70617445-SO. S. P. Perone. J. W. Frazer, and A. M. Kray, Anal. Chem., 43, 1479 (1971). Orion Application Bulletin on TISAB-CDTA. A5. D. Jagner, Anal. Chim. Acta, 50, 15 (1970). Analytical Methods Guide, Orion Research Inc., Cambridge, MA. (1973). NeWS/8tt8r, Orion Research Inc., Cambridge, Mass., 2, 7 and 8 (1970). Newsletter, Orion Research Inc., Cambridge, Mass., 3, 1 and 2 (1971). 8. Jaselaskis and M. K. Bandemer, Anal. Chem., 41, 855 (1969).
RECEIVEDfor review August 12, 1974. Accepted January 13, 1975. This paper was presented a t the 143rd Meeting of the Electrochemical Society, Chicago, Illinois, May 14, 1973, T h e algorithms can be obtained upon request from the senior author. This work was performed under the auspices of the United States Atomic Energy Commission.
ANALYTICAL CHEMISTRY, VOL. 47. NO. 6, MAY 1975
875
