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Flow-injection coulometric titrations
0039-9140/92SS.00+ 0.00 PmgamonPrw pk
Talanra, Vol. 39, No. 3, pp. 285-292,1992
Printedin GreatBritain
FLOW-INJECTION
COULOMETRIC
RICIURD H. TAYLOR,JAROMIR Rt3ihCut
TITRATIONS*
and GARY D. thUSTLtNt
Center for Process Analytical Chemistry, Department of Chemistry, RG-IO, University of Washington,
Seattle, WA 98195, U.S.A. (Received 4 March 1991. Reuised 29 Murch 1991. Accepted 12 April 1991) Summary-A flow-injection analysis technique based on stop flow coulometric titrations is described, utilizing a gradient chamber, reagent generation chamber, and detector flow cell integrated into a single unit. The use of stop flow allowed for automated sample dilution up to a factor of 100 times. The system has been used to titrate samples of sodium hydroxide in the range 5 x lo-‘-4M, and nitric acid ranging from 5 x 10-3-15M. Analyses over the entire rangt of concentrations yielded a relative standard deviation of less than 3%. A correlation coe&ient of 0.999 was obtained for all comparisons with manual titrations. Remote spectrophotometric detection was performed with optical fibers. No fiit or membrane is required to separate the generating and counter electrodes within the system, yet the advantages of conventional coulometric titration, which eliminate the problems of reagent and calibration solution handling, storage or degradation, are retained.
Flow-injection analysis (FIA) titrations represent a well known and widely used technique, especially in the field of industrial process monitoring.‘-5 This technique has gained acceptance due to its relative simplicity and good accuracy. Although these titrations are often used in FIA, the area of coulometric titration has gained very little attention. Feher and co-workers coulometrically generated a reagent which was subsequently merged with a carrier stream to perform triangle titrations of phenothiazine compounds6 Ruttinger and Spohn incorporated a coulometric titration cell and a flow through detector into a single component.’ Ilcheva and Dakahev reported a coulometric detection cell for use in an FIA system.* Liang described a method of performing Karl Fischer titrations coulometrically in a close loop system.’ In this paper we describe a novel stopped flow technique which is applicable to a wide variety of chemistries and incorporates a method of automated dilution. A gradient chamber and a detector flow cell are integrated into a single unit, allowing for detection at the site at which dilution and chemical reaction occurs (Fig. 1). In conventional FIA titrations a pair of equivalence points, located on the leading and trailing edge of a dispersed sample zone, is identified lRmsentedat Winter Conference on Flow-Injection Analysis, Scottsdale, AZ, USA January 6-9, 1991. tAuthors for correspondence.
(Fig. 2). The distance between these points (measured in time, At) at a constant flow-rate (Q) has been shown to be a function of the concentration of the sample,’ such that At = (V,,,/Q) In 10 log {Cf/(C$)} +
K/Q> In 10log {K/K,) [l(a)1
where V,,,is the volume of the mixing chamber, Ct is the concentration of the titrant, Ct is the concentration of the injected sample, n is the stoichiometric factor of the reacting components, and S, is the volume of the injected sample (Fig. 1). In a system with a carrier of constant concentration, and a fixed sample and flow volume, the peak width (At) is related to the sample concentration (C,) by the equation At = (k,) log C, + k2
[l(b)1
where k, and k2 are constants. Thus, in conventional FIA titrations the peak width is directly proportional to the logarithm of the sample concentration. The relationship described above is due to the concentration gradient produced by the zone dispersion within a mixing chamber, the volume (I’,,,) of which dominates the volume of the flow system. By injecting a sample, the concentration of which (C,) is much higher than that of the titrant (C,) in the carrier stream, the elements of the dispersal zone are gradually neutralized, until an equivalence point is reached at the leading and the trailing edge of the dispersal 285
286
RICHARD H. TAYLORet al.
(a)
Pump
Flow
cell
valve
(b) Waste
Pump
InJectIon valve
Gradlent chamber/ flow cell unit
Fig. 1. FIA system for titration. In a conventional FIA titration system (1A) detection occurs downstream of the gradient chamber. For the stop flow coulometric titration technique, detection occurs at the gradient chamber (1B) where titrant is produced and chemical reaction takes place. Q = volumetric flow-rate, S, = sample volume, V, = chamber volume.
zone (Fig. 2). This approach, though widely used, has two disadvantages: (1) the distance between the points (At) is a logarithmic function of the sample concentration; and (2) the bulk of the injected sample (shaded area, Fig. 2) remains untitrated. It was Pardue and Fields”*” who first pointed out the second disadvantage, which seriously limits the accuracy and operational range of the flow-injection titration, since it necessitates the use of a diluted (and therefore less stable) titrant when extending to less concentrated samples. It is proposed here to eliminate the above disadvantages by introducing a combination of stopped flow with the coulometric technique.
Time, set
Fig. 2. Conventional FIA titration. The dispersed zone contains two equivalence points (A and B). The distance between them (At) is the measured parameter and is proportional to the logarithm of the sample concentration. The shaded portion of the zone represents the portion of the sample which is not titrated.
By stopping the flow at a suitable delay time following sample injection the sample zone will be arrested within the mixing chamber. If the detection and coulometric reagent generation are performed within the mixing chamber, all sample material will be reacted, as in conventional titrimetry. In addition, by selecting an appropriate delay time, a desired trailing section of the dispersal zone can be captured within the chamber, thus allowing automated dilution prior to titration, i.e. a selected portion of the injected sample is titrated. In a coulometric titration,” reagent is produced by the application of a current at an appropriate electrode to an electrolyte. Through control of the current and time a precise amount of reagent is produced at a specified rate. The amount of reagent produced may be calculated with Faraday’s Law of Electrolysis, which states that the quantity of electricity passed through a cell is directly proportional to the quantity of chemical change that occurs at the cell electrode.13 The mathematical expression of this law, when applied to a constant current system, is N = QlnF = it/nF
[WI
where N = moles of substance, Q = total charge passed (coulombs, C), n = number of electrons transferred per molecule (equivalents, eq), i = current (amps), t = time (XX), and F = Faraday’s constant (96,485 C/es). By
Flow-injection coulometric titrations
measuring the time required to reach the titration endpoint and knowing the value of the constant current applied, the amount of reagent generated and reacted to reach the endpoint can then be calculated. Thus the measured parameter, At, the time from the initiation of electrolysis to the titration endpoint, is directly proportional to the sample concentration, as seen by rearrangement of equation [2(a)] to At = NnF/i = C,S,,nF/i = kc,
[2(b)]
where k is a constant. In this study the electrolysis of water was used to generate reagent for acidobasic titrations. The half reactions which occur are, at the anode 2H,0-+02
+ 4H+ + 4e -
and, at the cathode 2H,O+2e-+H,+20HWhen a very large degree of mixing of a segment of a flow system is required, it may be achieved by using a mixing chamber. The chamber allows for the homogeneous dispersion of a flow segment into a much larger portion of the system fluid. This is achieved through the use of an externally driven mechanical stirring mechanism inside the chamber. The gradient chamber has long been implemented in FIA systems.’ Previously, the gradient chamber was used to form a reproducible concentration gradient at the outlet of the chamber. This implies that the portion of the sample remaining in the gradient chamber at a specific time is reproducible. Therefore, instead of placing a detector downstream of the gradient chamber, detection at the chamber itself would
allow for detection of the homogeneous zone of the system and would result in a simplified system where the mixing chamber and detector flow cell are integrated into a single component. The dilution possibilities presented by the concentration gradient are retained through the use of stop flow, which provides the ability to isolate a predetermined portion of the sample within the chamber by stopping the flow at a specific time. An FIA system has been viewed as following the tanks-in-series model,14 introduced by Dankwerts.” The volume of the mixing chamber (V,,,) completely dominates the system volume, and therefore the system behaves as a single mixing tank while the volume of the injected sample (S,) is small. At any time t after the point at which the entire sample has entered the chamber (to), the concentration of a component of the fluid (C) is represented by the equation C = ( l/Ti)eefIc
(3)
where Ti is the mean residence time of a component of fluid in the tank. For a gradient chamber, the mean residence time is dependent upon the volume of the chamber and the volumetric flow-rate, such that Ti=
VmlQ
(4)
Previously in FIA, equation (3) was used to model the concentration of an analyte at the effluent of a gradient chamber.’ In the present case, however, the portion of the sample remaining inside the gradient chamber will be titrated. A representation of the area under the curve of the concentration profile produced (Fig. 3) is therefore needed. The area under this
I Time, set
281
td
1
Time, set
Fig. 3. Detector response to sample concentration within a gradient chamber. Response after all the sample has entered into the chamber conforms to a single tank in the tanks-in-series model. By selecting an appropriate delay time (r,,), a desired trailing section (shaded) of the zone may be arrested within the chamber and analyzed, thus providing a method of automated dilution.
288
RICHARDH. TAYLORet al.
curve can be integrated for any time interval after time = to, as
taining bromothymol blue (BTB) (Merck) as the indicator at a concentration of 0.04% (w/v). For titrations of base, the carrier was made slightly basic with sodium hydroxide and for titrations of acid it was made slightly acidic with nitric which yields the equation acid. This was done to prevent any neutralization of the sample by the carrier. Appropriate C, = e-0, [5(b)] dilution of concentrated nitric acid (J. T. Baker) The dilution which occurs in the system can with demineralized water was used to prepare be described by the inverse mole ratio (X-l), nitric acid samples for titration. Appropriate introduced by Whitman and Christian,16 which dilution of a 5M sodium hydroxide (J. T. Baker) is defined as solution with demineralized water was used for all sodium hydroxide samples. Potassium x-’ = ?lO/& (6) acid phthalate (Allied Chemical) was used as where no is the number of moles injected and ndet a primary standard for manual titrations. For experiments determining the effects of flow-rate is the number of moles detected. By defining n as a product of molar concenand chamber volume the carrier was O.OlM tration and volume, then at a constant sample sodium borate (J. T. Baker) and 0.40% (w/v) volume (S,), X-’ can be redefined as the ratio BTB was injected as sample. of molar concentrations Apparatus
x-’ = COS”/C&,S, = CO/C,,,
(7)
By substituting equation [5(b)] into equation (7), where Co = C, when t = 0 and C,,, = C, when I 2 to, the result is X-1 = Co/C,,, = e-O/?/e-‘K = et/T,
(8)
Thus the portion of a sample remaining in the gradient chamber and the inverse mole ratio can be easily calculated at any time during which the response curve follows the given model. The degree of dilution obtained can be predetermined by calculation and controlled through the use of the stop flow technique. EXPERIMENTAL
Reagents
The carrier for all titrations was an aqueous solution of 0.5M Na,SO, (Mallinckrodt) con-
data
Pump
storage
A single line FIA manifold (Fig. 4) was used in all experiments. The pump was an Alitea C4XV peristaltic pump with a remote controller. A Rheodyne Type 570 1 pneumatic actuator was used with a Rheodyne Type 50 4-way injection valve furnished with a 19-pl sample loop. The PTFE tubing connecting the mixing chambers and the chamber containing the counter electrode had an inner diameter of 1.3 mm, while all other tubing had an internal diameter of 0.82 mm. Stirring in the gradient chamber was performed by means of a TRI-R model MS-7 magnetic stirrer. The gradient chamber was IO-mm inner diameter glass tubing with end caps constructed of PTFE, equipped with a miniature stirring bar (Fig. 5). The net chamber volume could be varied by adjustment of the end cap positions.
and
Inlect Ion valve
electrode
Fig. 4. Stop flow coulometric titration system. Light is transmitted from the light source, across the gradient chamber, and to the detector via optical fibers. The injection valve, pump, and constant current source are controlled by computer.
289
Flow-injection coulometric titrations
The generating and counter electrodes were 1.2-mm diameter platinum wire. The 3.4-cm generating electrode was coiled at the bottom of the mixing chamber (Fig. 5), with a total surface area of 1.3 cm’. The counter electrode was placed in a separate chamber downstream of the mixing chamber. The connecting tubing was 4 cm long. The electrodes were connected to a laboratory built constant current source with four current settings (0.78-3.90 mA, current densities of 0.60-3.0 mA/cm2). Current was continuously measured with a Dynascan 2830 Digital Multimeter connected in line in the constant current source circuit. Current was switched by a relay between the electrodes and a variable resistor which was used as a “dummy cell” in order to have continuous current flow in the current source. The detector was a Bausch & Lomb Spectronic Mini 20 spectrophotometer. The output was directed to an electronic low-pass filter and a linear amplifier and then through the DACA interface board to the computer where the transmittance signal was converted to absorbance. A Volpi Intralux 4000 external light source with a variable intensity control was used. Light was directed from the external light source via a 45 cm long, 5.56~mm diameter optical fiber bundle (Volpi), across the chamber, and collected and directed to the spectrophotometer via a 45-cm long, 3.18mm diameter optical fiber bundle (Twardy) (Fig. 5).
The pump controllers, injection valve actuator, and constant current source were controlled and data were collected with an IBM Data Acquisition and Control Adapter (DACA) in conjunction with an IBM XT computer. General procedure The following steps were performed for each titration: (1) a sample or blank (H,O) was injected into the carrier containing electrolyte and indicator; (2) at a specified delay time the flow was stopped, causing a selected portion of the sample to be arrested in the chamber; (3) at that time a current was applied, electrochemically producing reagent for the titration; (4) a titration endpoint was reached and the current stopped; (5) after sufficient time for the endpoint to have been reached, the flow was resumed to flush out the chamber. This automated sequencing was controlled by an IBM XT computer with the o $ilutlo,
Titration
Wash
I
6A 0 k-
8 0 4.’ f
03.
a
02.
$
I
:,
2
0 I-
25
50
75 100 Time, set
125
150
Wash 68
0
Fig. 5. Integrated flow cell, gradient chamber, and reagent generation chamber. The body of the chamber (A) is 10 mm i.d. glass tubing. The ITFE end caps (C & F) are sealed with 0 rings (B). The chamber is mounted vertically with the inlet cap (C) on the bottom. The star-shaped stirring bar (D) rests atop the coiled generating electrode (E). The outlet cap (F) is domed to prevent any air bubbles which may enter the chamber from becoming trapped. Light is transmitted across the chamber and collected by optical fiber bundles (G) which are held in place by the chamber mounting bracket.
25
50
-z----125
75 Time, see
150
Fig. 6. FIA pro&s of titrations of O.OSOOM sodium hydroxide (6A) and OMOOM nitric acid (6B), at a current of 0.78 mA each, with Sv = 19 pl, Vm = 0.930 ml, and Q = 4.23 ml/min. At the delay time after injection (25 set) at which the desired dilution has been obtained (X-l = 4.78), the flow is stopped and current is applied to begin titration (1). A&r an endpoint (2) is reached and titration is completed, current is turned off and flow is mumed to flush the chamber (3). The titration curve, corresponding to that obtained in conventional titrations, is indicated by the shaded area. The time from start of reagent production to the inflection . . _ point (Al) is the parameter measured from the FIA protile.
290
RICHARDH. TAYLOR et al.
general FIA control software of Clark et al.” This software could also display the first derivative of the FIA profile, which was used to determine the titration curve inflection point, and thus At. The FIA profiles for an acid and a base titration are shown in Fig. 6. The endpoint was detected at a wavelength of 620 nm. RESULTS AND DISCUSSION
The initial set of experiments was performed to determine the parameters of the single mixing tank model for our system and to enable the calculation of the dilution achieved at any specific delay time. Samples of BTB dye (S, = 19 ~1) were injected into a O.OlM borax carrier stream, at different flow-rates (2.83-4.88 ml/ min), with a chamber volume of 0.900 ml, and at a carrier stream flow-rate of 2.9 ml/min with various chamber volumes (0.64-1.10 ml). The area under the absorbance profile at various delay times where f,, > tm, was ratioed with the area at the peak maximum (t,,,,,) to give X-l, 100,
I
I I
80
60 I X
7A 40
20
0
0
20 40 60 Delay time, td , set
80
E
I
0
/
20
40
F/
i
76
/GI
60
80
Delay time, td , set
Fig. 7. The inverse mole ratio obtained as a function of delay time for various values of volumetric flow-rate and chamber volume. In 7A the chamber volume was 0.900 ml with flow-rates of (A) 4.88 ml/min, (B) 4.24 ml/min, (C) 3.95 ml/min and (D) 2.83 ml/min. In 7B the flow-rate was 2.83 ml/min with chamber volumes of(E) 0.635 ml, (F) 0.780 ml, (G) 0.900 ml, (H) 1.10 ml.
Table 1. Comparison of the mean residence times calculated (T,,)
with the mean residence times experimentally determined (T,,,)
Qv
Vm,
ml/min
ml
set
set
4.88 4.24 3.95 2.83 2.83 2.83 2.83 2.83
0.900 0.900 0.900 0.900 1.10 0.900 0.780 0.635
11.1 12.7 13.7 19.1 23.2 19.1 16.5 13.6
11.3 12.5 14.0 19.8 22.8 19.8 16.8 13.4
TI&al 9
TWV’
which was then plotted against delay time for each combination of flow-rate and chamber volume (Fig. 7). The equation of each of the resulting curves was of the form _J-’ = k,@2’d
(9)
The mean residence time, which is l/k, [as seen from equation (811,from each curve (7’i.;,,) was in close agreement with the values calculated from the measured values of the flow-rate and the chamber volume (Ti,_,) (Table 1). The value of k2 is dependent upon the flow-rate and the chamber volume. Each equation also included a constant, k,, which was a factor to correct for the time required for the trailing portion of the injected sample to enter the gradient chamber, where the detection profile deviates from the ideal of the model, which assumes that the entire sample is in the mixing tank at time zero. The value of k, is dependent upon the flow-rate, the chamber volume, the sample volume and all other factors governing the dispersion of the sample zone prior to entering the chamber. It is thus observed that the shape of the X-’ curve does follow the single tank of the tanks-in-series model and, after all of the sample has entered into the chamber, is dependent only upon the chamber volume and the system flow-rate. Thus the amount of dilution obtained at a specific stop time can easily be predicted and controlled by adjustment of either of these two parameters. Once determined for a given set of conditions (I’,,,, (9, S,, etc.), the equation defining X-’ can be used to determine the degree of dilution obtained at a delay time after all the sample has entered into the chamber. The X-’ is used in conjunction with Faraday’s law to calculate the amount of analyte in the injected sample, obviating the need for standards. For all further experiments the flow-rate was 4.23 ml/min and the chamber volume of 0.930
Flow-injection coulometric titrations
Table 2. Experimental data of the coulometric titration of nitric acid (see Fig. 6). For all samples: S, = 19 pl, V,,,= 0.930 ml, Q = 4.23 ml/mm. td = delay time, AI = titration time, i = current, Cont. = concentration, rsd = relative standard deviation
60. i
x
291
Al, set
i,
Cone,
mA
M
5.27
14.97
0.785
0.00760
5.27 5.27 16.79 28.51 40.23 50.00 50.09 62.50 62.50 62.50 62.50 62.50 62.50 62.50
37.78 44.70 37.28 27.11 19.18 14.02 21.83 6.38 8.59 14.45 17.24 19.95 23.37 27.28
2.28 3.84 3.59 3.58 3.85 3.84 3.88 3.85 3.87 3.78 3.80 3.83 3.82 3.83
0.0539 0.110 0.182 0.420 0.851 1.43 2.24 3.44 4.66 8.65 9.16 10.7 12.5 14.6
r, set
’
Delay time, set
Fig. 8. The inverse mole ratio obtained as a function of delay time for the titration of 0.02OOMNaOH. The system flow-rate was 4.23 ml/min and the chamber volume was 0.930 ml.
ml was used. Demineralized water was used as a blank for all titrations. Current values ranged from 0.7 to 4 mA. It should be noted that at high current densities, generating electrode reactions involving gases, as here, may result in increased noise levels if the gas solubility level is exceeded, which would allow bubble formation. Bubble formation was observed at currents of approximately 20 mA. Samples of 0.0200&f sodium hydroxide (S, = 19 ~1) were injected and titrated with various delay times. The resulting X-’ values were plotted versus their respective delay times (Fig. 8). The equation of this plot had the form of equation (9), demonstrating compliance with the given model. The greatest portion of the sample arrested in the chamber was 92%, or an X-i of 1.086, at a delay time of 5.02 sec. The results of a series of titrations performed on the described system were compared with the corresponding manual titrations. For the manual titrations, a sodium hydroxide solution was standardized against potassium acid phthalate and was used as a titrant for all acid samples. For titrating all base samples, a nitric acid solution was standardized with respect to the sodium hydroxide secondary standard solution. Titrant solutions were standardized daily prior to use. Titration of samples ranging in concentration from 5 x 10e4-8 x 10wZM sodium hydroxide was performed with a stop time of 5.25 sec. A linear relationship was obtained from plotting the results against the equivalent manual titration, with an intercept of 1.9 x 10e3, a slope of 0.989 and R2 = 0.999. Additional samples at concentrations up to 4.14M sodium hydroxide were titrated using
rsd, %
1.1 1.2 0.6 0.3 1.9 1.6 0.5 1.3 1.8 2.8 1.9 1.9 2.8 2.9 2.5
various stop times such that the entire analysis time, including flushing the chamber, was 180 sec. The time allotted to flush the chamber was 70 set for all titrations, which was slightly greater than five times the mean residence time for the flow-rate and the chamber volume used. When compared with the manual titration results, the resulting plot was again a straight line with an intercept of 1.5 x 10e2, a slope of 1.033 and with R2 = 0.999. By changing polarity of the constant current source, hydroxide ions were produced in the mixing chamber, allowing titrations of an acid. Samples with concentrations up to 14.7M nitric acid were titrated (Table 2), with no physical modification of the system. The analysis time was increased to 240 set for samples with concentrations greater than 5.OM. The delay time for all samples with concentrations greater than 3.OM was 62.50 sec. When the results were compared with manual titrations, the plot was linear with an intercept of - 5.39 x 10m2,a slope of 0.999 and with R2 = 0.999. Multiple analyses (23) were performed for all samples. The relative standard deviation was less than 1.5% for samples with a delay time of 5.02 set and was less than 3% for samples at a delay time of 62.5 sec. The relative standard deviation tended to increase with an increase in delay time (Table 2). This occurs since any error in stopping the flow had a greater effect on the portion of the sample arrested within the chamber for those samples with the larger delay times, as can be seen in Fig. 8. All comparisons
RICHARDH. TAYLOR et al.
292
between the manual and coulometric titrations produced correlation coefficients of 0.999. CONCLUSIONS
A stop flow coulometric titration technique has been developed and tested. It has been shown to be capable of accurately performing titrations over a wide range of sample concentrations with good precision. The concentration profile produced within the gradient chamber has been shown to follow the tanks-in-series model, allowing for sample dilution of a preselected degree through the use of stop flow. For the first time an actual titration curve is an integral part of an FIA profile (Fig. 6). The stop flow coulometric titration system has several advantages which enhance its appeal for application in process analysis. In industrial processes analyte concentrations are often very high or may vary over a wide dynamic range. The stop flow coulometric titration system can be used to perform a wide range of dilutions without the need for physical reconfiguration. The direct proportionality of the measured parameter (At) to the concentration of the portion of the sample analyzed, instead of the logarithm of the sample concentration, enhances the precision of the analysis. The system is mechanically simple, another advantage for use in the industrial environment. It is a single line system, incorporating only one valve and one pump. The gradient chamber, reagent generation chamber, and the detector flow cell are combined into a single component, and the system contains no frits or membranes which are prone to fouling. The titrant is produced within the system during analysis, thus eliminating the problems of reagent handling, storage and stability. Since unstable reagents can also be produced by electrolysis, a wide range of chemistries can be exploited. Also, calibration solutions are not needed once the system has been characterized, since titrant is produced by electrolysis and the amount of titrant produced for any given current
over a given period of time can be calculated. By varying the intensity of the constant current, reagent can be produced at different rates. The system has been shown to be easily automated and controlled by computer software. The stop flow coulometric titration technique has been demonstrated to be precise and versatile. In the future, a variety of chemistries and detection schemes will be investigated with the aim to exploit them for both laboratory and process control applications. Acknowledgements-The authors thank Camilla Winbc for her technical assistance. We also thank the Electronic and Machine Shops of the Department of Chemistry, University of Washington, for their advice and assistance on materials and construction.
REFERENCES 1. J. Rtieka and E. H. Hansen, Flow Injection Analysis, 2nd Ed., John Wiley & Sons, New York, 1988. 2. C. B. Ranger, Autom. Stream Anal. for Process Control, 1982, 1, 39. 3. K. K. Stewart and A. G. Rosenfeld, J. Autom. Chem., 1981, 3, 30. 4. J. G. Williams, M. Holmes and D. G. Porter, ibid., 1982, 4, 176. 5. R. K. Gilpin and L. A. Pachla, Anal. Chem., 1989, 61, 191R. 6. Z. Feher, I. Kolbe and E. Pungor, Z. Anal. Chem., 1988, 332, 345. 7. H. H. Ruttinger and U. Spohn, Anal. Chim. Acta, 1987, 282, 75. 8. L. I. Ilcheva and A. D. Dakashev, Analyst, 1990, 115, 1247. 9. Y. Y. Liang, Anal. Chem., 1990, 62, 2504. 10. H. L. Pardue and B. Fields, Anal. Chim. Acta, 1981, 124, 39. 11. I&m, ibid., 1981, 124, 65. 12. G. W. C. Milner and G. Phillips, Coulometry in Analytical Chemistry, Pergamon Press, London, 1967. 13. G. D. Christian and J. E. O’Reilly, Insfrumental Analysis, 2nd Ed., Allyn and Bacon, Boston, 1986. 14. 0. Levenspiel, Chemkal Reaction Engineering, 2nd Ed., Wiley, New York, 1972. 15. P. V. Dankwerts, Chem. Eng. Sci., 1953, 2, 1. 16. D. A. Whitman and G. D. Christian, Talanta, 1989,36, 205. 17. G. D. Clark, G. D. Christian, J. R&&a, J. A. van Zee and G. F. Anderson, Anal. Instrumentation, 1989, 1% 1.
Talanra, Vol. 39, No. 3, pp. 285-292,1992
Printedin GreatBritain
FLOW-INJECTION
COULOMETRIC
RICIURD H. TAYLOR,JAROMIR Rt3ihCut
TITRATIONS*
and GARY D. thUSTLtNt
Center for Process Analytical Chemistry, Department of Chemistry, RG-IO, University of Washington,
Seattle, WA 98195, U.S.A. (Received 4 March 1991. Reuised 29 Murch 1991. Accepted 12 April 1991) Summary-A flow-injection analysis technique based on stop flow coulometric titrations is described, utilizing a gradient chamber, reagent generation chamber, and detector flow cell integrated into a single unit. The use of stop flow allowed for automated sample dilution up to a factor of 100 times. The system has been used to titrate samples of sodium hydroxide in the range 5 x lo-‘-4M, and nitric acid ranging from 5 x 10-3-15M. Analyses over the entire rangt of concentrations yielded a relative standard deviation of less than 3%. A correlation coe&ient of 0.999 was obtained for all comparisons with manual titrations. Remote spectrophotometric detection was performed with optical fibers. No fiit or membrane is required to separate the generating and counter electrodes within the system, yet the advantages of conventional coulometric titration, which eliminate the problems of reagent and calibration solution handling, storage or degradation, are retained.
Flow-injection analysis (FIA) titrations represent a well known and widely used technique, especially in the field of industrial process monitoring.‘-5 This technique has gained acceptance due to its relative simplicity and good accuracy. Although these titrations are often used in FIA, the area of coulometric titration has gained very little attention. Feher and co-workers coulometrically generated a reagent which was subsequently merged with a carrier stream to perform triangle titrations of phenothiazine compounds6 Ruttinger and Spohn incorporated a coulometric titration cell and a flow through detector into a single component.’ Ilcheva and Dakahev reported a coulometric detection cell for use in an FIA system.* Liang described a method of performing Karl Fischer titrations coulometrically in a close loop system.’ In this paper we describe a novel stopped flow technique which is applicable to a wide variety of chemistries and incorporates a method of automated dilution. A gradient chamber and a detector flow cell are integrated into a single unit, allowing for detection at the site at which dilution and chemical reaction occurs (Fig. 1). In conventional FIA titrations a pair of equivalence points, located on the leading and trailing edge of a dispersed sample zone, is identified lRmsentedat Winter Conference on Flow-Injection Analysis, Scottsdale, AZ, USA January 6-9, 1991. tAuthors for correspondence.
(Fig. 2). The distance between these points (measured in time, At) at a constant flow-rate (Q) has been shown to be a function of the concentration of the sample,’ such that At = (V,,,/Q) In 10 log {Cf/(C$)} +
K/Q> In 10log {K/K,) [l(a)1
where V,,,is the volume of the mixing chamber, Ct is the concentration of the titrant, Ct is the concentration of the injected sample, n is the stoichiometric factor of the reacting components, and S, is the volume of the injected sample (Fig. 1). In a system with a carrier of constant concentration, and a fixed sample and flow volume, the peak width (At) is related to the sample concentration (C,) by the equation At = (k,) log C, + k2
[l(b)1
where k, and k2 are constants. Thus, in conventional FIA titrations the peak width is directly proportional to the logarithm of the sample concentration. The relationship described above is due to the concentration gradient produced by the zone dispersion within a mixing chamber, the volume (I’,,,) of which dominates the volume of the flow system. By injecting a sample, the concentration of which (C,) is much higher than that of the titrant (C,) in the carrier stream, the elements of the dispersal zone are gradually neutralized, until an equivalence point is reached at the leading and the trailing edge of the dispersal 285
286
RICHARD H. TAYLORet al.
(a)
Pump
Flow
cell
valve
(b) Waste
Pump
InJectIon valve
Gradlent chamber/ flow cell unit
Fig. 1. FIA system for titration. In a conventional FIA titration system (1A) detection occurs downstream of the gradient chamber. For the stop flow coulometric titration technique, detection occurs at the gradient chamber (1B) where titrant is produced and chemical reaction takes place. Q = volumetric flow-rate, S, = sample volume, V, = chamber volume.
zone (Fig. 2). This approach, though widely used, has two disadvantages: (1) the distance between the points (At) is a logarithmic function of the sample concentration; and (2) the bulk of the injected sample (shaded area, Fig. 2) remains untitrated. It was Pardue and Fields”*” who first pointed out the second disadvantage, which seriously limits the accuracy and operational range of the flow-injection titration, since it necessitates the use of a diluted (and therefore less stable) titrant when extending to less concentrated samples. It is proposed here to eliminate the above disadvantages by introducing a combination of stopped flow with the coulometric technique.
Time, set
Fig. 2. Conventional FIA titration. The dispersed zone contains two equivalence points (A and B). The distance between them (At) is the measured parameter and is proportional to the logarithm of the sample concentration. The shaded portion of the zone represents the portion of the sample which is not titrated.
By stopping the flow at a suitable delay time following sample injection the sample zone will be arrested within the mixing chamber. If the detection and coulometric reagent generation are performed within the mixing chamber, all sample material will be reacted, as in conventional titrimetry. In addition, by selecting an appropriate delay time, a desired trailing section of the dispersal zone can be captured within the chamber, thus allowing automated dilution prior to titration, i.e. a selected portion of the injected sample is titrated. In a coulometric titration,” reagent is produced by the application of a current at an appropriate electrode to an electrolyte. Through control of the current and time a precise amount of reagent is produced at a specified rate. The amount of reagent produced may be calculated with Faraday’s Law of Electrolysis, which states that the quantity of electricity passed through a cell is directly proportional to the quantity of chemical change that occurs at the cell electrode.13 The mathematical expression of this law, when applied to a constant current system, is N = QlnF = it/nF
[WI
where N = moles of substance, Q = total charge passed (coulombs, C), n = number of electrons transferred per molecule (equivalents, eq), i = current (amps), t = time (XX), and F = Faraday’s constant (96,485 C/es). By
Flow-injection coulometric titrations
measuring the time required to reach the titration endpoint and knowing the value of the constant current applied, the amount of reagent generated and reacted to reach the endpoint can then be calculated. Thus the measured parameter, At, the time from the initiation of electrolysis to the titration endpoint, is directly proportional to the sample concentration, as seen by rearrangement of equation [2(a)] to At = NnF/i = C,S,,nF/i = kc,
[2(b)]
where k is a constant. In this study the electrolysis of water was used to generate reagent for acidobasic titrations. The half reactions which occur are, at the anode 2H,0-+02
+ 4H+ + 4e -
and, at the cathode 2H,O+2e-+H,+20HWhen a very large degree of mixing of a segment of a flow system is required, it may be achieved by using a mixing chamber. The chamber allows for the homogeneous dispersion of a flow segment into a much larger portion of the system fluid. This is achieved through the use of an externally driven mechanical stirring mechanism inside the chamber. The gradient chamber has long been implemented in FIA systems.’ Previously, the gradient chamber was used to form a reproducible concentration gradient at the outlet of the chamber. This implies that the portion of the sample remaining in the gradient chamber at a specific time is reproducible. Therefore, instead of placing a detector downstream of the gradient chamber, detection at the chamber itself would
allow for detection of the homogeneous zone of the system and would result in a simplified system where the mixing chamber and detector flow cell are integrated into a single component. The dilution possibilities presented by the concentration gradient are retained through the use of stop flow, which provides the ability to isolate a predetermined portion of the sample within the chamber by stopping the flow at a specific time. An FIA system has been viewed as following the tanks-in-series model,14 introduced by Dankwerts.” The volume of the mixing chamber (V,,,) completely dominates the system volume, and therefore the system behaves as a single mixing tank while the volume of the injected sample (S,) is small. At any time t after the point at which the entire sample has entered the chamber (to), the concentration of a component of the fluid (C) is represented by the equation C = ( l/Ti)eefIc
(3)
where Ti is the mean residence time of a component of fluid in the tank. For a gradient chamber, the mean residence time is dependent upon the volume of the chamber and the volumetric flow-rate, such that Ti=
VmlQ
(4)
Previously in FIA, equation (3) was used to model the concentration of an analyte at the effluent of a gradient chamber.’ In the present case, however, the portion of the sample remaining inside the gradient chamber will be titrated. A representation of the area under the curve of the concentration profile produced (Fig. 3) is therefore needed. The area under this
I Time, set
281
td
1
Time, set
Fig. 3. Detector response to sample concentration within a gradient chamber. Response after all the sample has entered into the chamber conforms to a single tank in the tanks-in-series model. By selecting an appropriate delay time (r,,), a desired trailing section (shaded) of the zone may be arrested within the chamber and analyzed, thus providing a method of automated dilution.
288
RICHARDH. TAYLORet al.
curve can be integrated for any time interval after time = to, as
taining bromothymol blue (BTB) (Merck) as the indicator at a concentration of 0.04% (w/v). For titrations of base, the carrier was made slightly basic with sodium hydroxide and for titrations of acid it was made slightly acidic with nitric which yields the equation acid. This was done to prevent any neutralization of the sample by the carrier. Appropriate C, = e-0, [5(b)] dilution of concentrated nitric acid (J. T. Baker) The dilution which occurs in the system can with demineralized water was used to prepare be described by the inverse mole ratio (X-l), nitric acid samples for titration. Appropriate introduced by Whitman and Christian,16 which dilution of a 5M sodium hydroxide (J. T. Baker) is defined as solution with demineralized water was used for all sodium hydroxide samples. Potassium x-’ = ?lO/& (6) acid phthalate (Allied Chemical) was used as where no is the number of moles injected and ndet a primary standard for manual titrations. For experiments determining the effects of flow-rate is the number of moles detected. By defining n as a product of molar concenand chamber volume the carrier was O.OlM tration and volume, then at a constant sample sodium borate (J. T. Baker) and 0.40% (w/v) volume (S,), X-’ can be redefined as the ratio BTB was injected as sample. of molar concentrations Apparatus
x-’ = COS”/C&,S, = CO/C,,,
(7)
By substituting equation [5(b)] into equation (7), where Co = C, when t = 0 and C,,, = C, when I 2 to, the result is X-1 = Co/C,,, = e-O/?/e-‘K = et/T,
(8)
Thus the portion of a sample remaining in the gradient chamber and the inverse mole ratio can be easily calculated at any time during which the response curve follows the given model. The degree of dilution obtained can be predetermined by calculation and controlled through the use of the stop flow technique. EXPERIMENTAL
Reagents
The carrier for all titrations was an aqueous solution of 0.5M Na,SO, (Mallinckrodt) con-
data
Pump
storage
A single line FIA manifold (Fig. 4) was used in all experiments. The pump was an Alitea C4XV peristaltic pump with a remote controller. A Rheodyne Type 570 1 pneumatic actuator was used with a Rheodyne Type 50 4-way injection valve furnished with a 19-pl sample loop. The PTFE tubing connecting the mixing chambers and the chamber containing the counter electrode had an inner diameter of 1.3 mm, while all other tubing had an internal diameter of 0.82 mm. Stirring in the gradient chamber was performed by means of a TRI-R model MS-7 magnetic stirrer. The gradient chamber was IO-mm inner diameter glass tubing with end caps constructed of PTFE, equipped with a miniature stirring bar (Fig. 5). The net chamber volume could be varied by adjustment of the end cap positions.
and
Inlect Ion valve
electrode
Fig. 4. Stop flow coulometric titration system. Light is transmitted from the light source, across the gradient chamber, and to the detector via optical fibers. The injection valve, pump, and constant current source are controlled by computer.
289
Flow-injection coulometric titrations
The generating and counter electrodes were 1.2-mm diameter platinum wire. The 3.4-cm generating electrode was coiled at the bottom of the mixing chamber (Fig. 5), with a total surface area of 1.3 cm’. The counter electrode was placed in a separate chamber downstream of the mixing chamber. The connecting tubing was 4 cm long. The electrodes were connected to a laboratory built constant current source with four current settings (0.78-3.90 mA, current densities of 0.60-3.0 mA/cm2). Current was continuously measured with a Dynascan 2830 Digital Multimeter connected in line in the constant current source circuit. Current was switched by a relay between the electrodes and a variable resistor which was used as a “dummy cell” in order to have continuous current flow in the current source. The detector was a Bausch & Lomb Spectronic Mini 20 spectrophotometer. The output was directed to an electronic low-pass filter and a linear amplifier and then through the DACA interface board to the computer where the transmittance signal was converted to absorbance. A Volpi Intralux 4000 external light source with a variable intensity control was used. Light was directed from the external light source via a 45 cm long, 5.56~mm diameter optical fiber bundle (Volpi), across the chamber, and collected and directed to the spectrophotometer via a 45-cm long, 3.18mm diameter optical fiber bundle (Twardy) (Fig. 5).
The pump controllers, injection valve actuator, and constant current source were controlled and data were collected with an IBM Data Acquisition and Control Adapter (DACA) in conjunction with an IBM XT computer. General procedure The following steps were performed for each titration: (1) a sample or blank (H,O) was injected into the carrier containing electrolyte and indicator; (2) at a specified delay time the flow was stopped, causing a selected portion of the sample to be arrested in the chamber; (3) at that time a current was applied, electrochemically producing reagent for the titration; (4) a titration endpoint was reached and the current stopped; (5) after sufficient time for the endpoint to have been reached, the flow was resumed to flush out the chamber. This automated sequencing was controlled by an IBM XT computer with the o $ilutlo,
Titration
Wash
I
6A 0 k-
8 0 4.’ f
03.
a
02.
$
I
:,
2
0 I-
25
50
75 100 Time, set
125
150
Wash 68
0
Fig. 5. Integrated flow cell, gradient chamber, and reagent generation chamber. The body of the chamber (A) is 10 mm i.d. glass tubing. The ITFE end caps (C & F) are sealed with 0 rings (B). The chamber is mounted vertically with the inlet cap (C) on the bottom. The star-shaped stirring bar (D) rests atop the coiled generating electrode (E). The outlet cap (F) is domed to prevent any air bubbles which may enter the chamber from becoming trapped. Light is transmitted across the chamber and collected by optical fiber bundles (G) which are held in place by the chamber mounting bracket.
25
50
-z----125
75 Time, see
150
Fig. 6. FIA pro&s of titrations of O.OSOOM sodium hydroxide (6A) and OMOOM nitric acid (6B), at a current of 0.78 mA each, with Sv = 19 pl, Vm = 0.930 ml, and Q = 4.23 ml/min. At the delay time after injection (25 set) at which the desired dilution has been obtained (X-l = 4.78), the flow is stopped and current is applied to begin titration (1). A&r an endpoint (2) is reached and titration is completed, current is turned off and flow is mumed to flush the chamber (3). The titration curve, corresponding to that obtained in conventional titrations, is indicated by the shaded area. The time from start of reagent production to the inflection . . _ point (Al) is the parameter measured from the FIA protile.
290
RICHARDH. TAYLOR et al.
general FIA control software of Clark et al.” This software could also display the first derivative of the FIA profile, which was used to determine the titration curve inflection point, and thus At. The FIA profiles for an acid and a base titration are shown in Fig. 6. The endpoint was detected at a wavelength of 620 nm. RESULTS AND DISCUSSION
The initial set of experiments was performed to determine the parameters of the single mixing tank model for our system and to enable the calculation of the dilution achieved at any specific delay time. Samples of BTB dye (S, = 19 ~1) were injected into a O.OlM borax carrier stream, at different flow-rates (2.83-4.88 ml/ min), with a chamber volume of 0.900 ml, and at a carrier stream flow-rate of 2.9 ml/min with various chamber volumes (0.64-1.10 ml). The area under the absorbance profile at various delay times where f,, > tm, was ratioed with the area at the peak maximum (t,,,,,) to give X-l, 100,
I
I I
80
60 I X
7A 40
20
0
0
20 40 60 Delay time, td , set
80
E
I
0
/
20
40
F/
i
76
/GI
60
80
Delay time, td , set
Fig. 7. The inverse mole ratio obtained as a function of delay time for various values of volumetric flow-rate and chamber volume. In 7A the chamber volume was 0.900 ml with flow-rates of (A) 4.88 ml/min, (B) 4.24 ml/min, (C) 3.95 ml/min and (D) 2.83 ml/min. In 7B the flow-rate was 2.83 ml/min with chamber volumes of(E) 0.635 ml, (F) 0.780 ml, (G) 0.900 ml, (H) 1.10 ml.
Table 1. Comparison of the mean residence times calculated (T,,)
with the mean residence times experimentally determined (T,,,)
Qv
Vm,
ml/min
ml
set
set
4.88 4.24 3.95 2.83 2.83 2.83 2.83 2.83
0.900 0.900 0.900 0.900 1.10 0.900 0.780 0.635
11.1 12.7 13.7 19.1 23.2 19.1 16.5 13.6
11.3 12.5 14.0 19.8 22.8 19.8 16.8 13.4
TI&al 9
TWV’
which was then plotted against delay time for each combination of flow-rate and chamber volume (Fig. 7). The equation of each of the resulting curves was of the form _J-’ = k,@2’d
(9)
The mean residence time, which is l/k, [as seen from equation (811,from each curve (7’i.;,,) was in close agreement with the values calculated from the measured values of the flow-rate and the chamber volume (Ti,_,) (Table 1). The value of k2 is dependent upon the flow-rate and the chamber volume. Each equation also included a constant, k,, which was a factor to correct for the time required for the trailing portion of the injected sample to enter the gradient chamber, where the detection profile deviates from the ideal of the model, which assumes that the entire sample is in the mixing tank at time zero. The value of k, is dependent upon the flow-rate, the chamber volume, the sample volume and all other factors governing the dispersion of the sample zone prior to entering the chamber. It is thus observed that the shape of the X-’ curve does follow the single tank of the tanks-in-series model and, after all of the sample has entered into the chamber, is dependent only upon the chamber volume and the system flow-rate. Thus the amount of dilution obtained at a specific stop time can easily be predicted and controlled by adjustment of either of these two parameters. Once determined for a given set of conditions (I’,,,, (9, S,, etc.), the equation defining X-’ can be used to determine the degree of dilution obtained at a delay time after all the sample has entered into the chamber. The X-’ is used in conjunction with Faraday’s law to calculate the amount of analyte in the injected sample, obviating the need for standards. For all further experiments the flow-rate was 4.23 ml/min and the chamber volume of 0.930
Flow-injection coulometric titrations
Table 2. Experimental data of the coulometric titration of nitric acid (see Fig. 6). For all samples: S, = 19 pl, V,,,= 0.930 ml, Q = 4.23 ml/mm. td = delay time, AI = titration time, i = current, Cont. = concentration, rsd = relative standard deviation
60. i
x
291
Al, set
i,
Cone,
mA
M
5.27
14.97
0.785
0.00760
5.27 5.27 16.79 28.51 40.23 50.00 50.09 62.50 62.50 62.50 62.50 62.50 62.50 62.50
37.78 44.70 37.28 27.11 19.18 14.02 21.83 6.38 8.59 14.45 17.24 19.95 23.37 27.28
2.28 3.84 3.59 3.58 3.85 3.84 3.88 3.85 3.87 3.78 3.80 3.83 3.82 3.83
0.0539 0.110 0.182 0.420 0.851 1.43 2.24 3.44 4.66 8.65 9.16 10.7 12.5 14.6
r, set
’
Delay time, set
Fig. 8. The inverse mole ratio obtained as a function of delay time for the titration of 0.02OOMNaOH. The system flow-rate was 4.23 ml/min and the chamber volume was 0.930 ml.
ml was used. Demineralized water was used as a blank for all titrations. Current values ranged from 0.7 to 4 mA. It should be noted that at high current densities, generating electrode reactions involving gases, as here, may result in increased noise levels if the gas solubility level is exceeded, which would allow bubble formation. Bubble formation was observed at currents of approximately 20 mA. Samples of 0.0200&f sodium hydroxide (S, = 19 ~1) were injected and titrated with various delay times. The resulting X-’ values were plotted versus their respective delay times (Fig. 8). The equation of this plot had the form of equation (9), demonstrating compliance with the given model. The greatest portion of the sample arrested in the chamber was 92%, or an X-i of 1.086, at a delay time of 5.02 sec. The results of a series of titrations performed on the described system were compared with the corresponding manual titrations. For the manual titrations, a sodium hydroxide solution was standardized against potassium acid phthalate and was used as a titrant for all acid samples. For titrating all base samples, a nitric acid solution was standardized with respect to the sodium hydroxide secondary standard solution. Titrant solutions were standardized daily prior to use. Titration of samples ranging in concentration from 5 x 10e4-8 x 10wZM sodium hydroxide was performed with a stop time of 5.25 sec. A linear relationship was obtained from plotting the results against the equivalent manual titration, with an intercept of 1.9 x 10e3, a slope of 0.989 and R2 = 0.999. Additional samples at concentrations up to 4.14M sodium hydroxide were titrated using
rsd, %
1.1 1.2 0.6 0.3 1.9 1.6 0.5 1.3 1.8 2.8 1.9 1.9 2.8 2.9 2.5
various stop times such that the entire analysis time, including flushing the chamber, was 180 sec. The time allotted to flush the chamber was 70 set for all titrations, which was slightly greater than five times the mean residence time for the flow-rate and the chamber volume used. When compared with the manual titration results, the resulting plot was again a straight line with an intercept of 1.5 x 10e2, a slope of 1.033 and with R2 = 0.999. By changing polarity of the constant current source, hydroxide ions were produced in the mixing chamber, allowing titrations of an acid. Samples with concentrations up to 14.7M nitric acid were titrated (Table 2), with no physical modification of the system. The analysis time was increased to 240 set for samples with concentrations greater than 5.OM. The delay time for all samples with concentrations greater than 3.OM was 62.50 sec. When the results were compared with manual titrations, the plot was linear with an intercept of - 5.39 x 10m2,a slope of 0.999 and with R2 = 0.999. Multiple analyses (23) were performed for all samples. The relative standard deviation was less than 1.5% for samples with a delay time of 5.02 set and was less than 3% for samples at a delay time of 62.5 sec. The relative standard deviation tended to increase with an increase in delay time (Table 2). This occurs since any error in stopping the flow had a greater effect on the portion of the sample arrested within the chamber for those samples with the larger delay times, as can be seen in Fig. 8. All comparisons
RICHARDH. TAYLOR et al.
292
between the manual and coulometric titrations produced correlation coefficients of 0.999. CONCLUSIONS
A stop flow coulometric titration technique has been developed and tested. It has been shown to be capable of accurately performing titrations over a wide range of sample concentrations with good precision. The concentration profile produced within the gradient chamber has been shown to follow the tanks-in-series model, allowing for sample dilution of a preselected degree through the use of stop flow. For the first time an actual titration curve is an integral part of an FIA profile (Fig. 6). The stop flow coulometric titration system has several advantages which enhance its appeal for application in process analysis. In industrial processes analyte concentrations are often very high or may vary over a wide dynamic range. The stop flow coulometric titration system can be used to perform a wide range of dilutions without the need for physical reconfiguration. The direct proportionality of the measured parameter (At) to the concentration of the portion of the sample analyzed, instead of the logarithm of the sample concentration, enhances the precision of the analysis. The system is mechanically simple, another advantage for use in the industrial environment. It is a single line system, incorporating only one valve and one pump. The gradient chamber, reagent generation chamber, and the detector flow cell are combined into a single component, and the system contains no frits or membranes which are prone to fouling. The titrant is produced within the system during analysis, thus eliminating the problems of reagent handling, storage and stability. Since unstable reagents can also be produced by electrolysis, a wide range of chemistries can be exploited. Also, calibration solutions are not needed once the system has been characterized, since titrant is produced by electrolysis and the amount of titrant produced for any given current
over a given period of time can be calculated. By varying the intensity of the constant current, reagent can be produced at different rates. The system has been shown to be easily automated and controlled by computer software. The stop flow coulometric titration technique has been demonstrated to be precise and versatile. In the future, a variety of chemistries and detection schemes will be investigated with the aim to exploit them for both laboratory and process control applications. Acknowledgements-The authors thank Camilla Winbc for her technical assistance. We also thank the Electronic and Machine Shops of the Department of Chemistry, University of Washington, for their advice and assistance on materials and construction.
REFERENCES 1. J. Rtieka and E. H. Hansen, Flow Injection Analysis, 2nd Ed., John Wiley & Sons, New York, 1988. 2. C. B. Ranger, Autom. Stream Anal. for Process Control, 1982, 1, 39. 3. K. K. Stewart and A. G. Rosenfeld, J. Autom. Chem., 1981, 3, 30. 4. J. G. Williams, M. Holmes and D. G. Porter, ibid., 1982, 4, 176. 5. R. K. Gilpin and L. A. Pachla, Anal. Chem., 1989, 61, 191R. 6. Z. Feher, I. Kolbe and E. Pungor, Z. Anal. Chem., 1988, 332, 345. 7. H. H. Ruttinger and U. Spohn, Anal. Chim. Acta, 1987, 282, 75. 8. L. I. Ilcheva and A. D. Dakashev, Analyst, 1990, 115, 1247. 9. Y. Y. Liang, Anal. Chem., 1990, 62, 2504. 10. H. L. Pardue and B. Fields, Anal. Chim. Acta, 1981, 124, 39. 11. I&m, ibid., 1981, 124, 65. 12. G. W. C. Milner and G. Phillips, Coulometry in Analytical Chemistry, Pergamon Press, London, 1967. 13. G. D. Christian and J. E. O’Reilly, Insfrumental Analysis, 2nd Ed., Allyn and Bacon, Boston, 1986. 14. 0. Levenspiel, Chemkal Reaction Engineering, 2nd Ed., Wiley, New York, 1972. 15. P. V. Dankwerts, Chem. Eng. Sci., 1953, 2, 1. 16. D. A. Whitman and G. D. Christian, Talanta, 1989,36, 205. 17. G. D. Clark, G. D. Christian, J. R&&a, J. A. van Zee and G. F. Anderson, Anal. Instrumentation, 1989, 1% 1.