iron in the occluded sample solution. A second electrolysis is required to re-deposit any lead which has re-dissolved in the solution film during electrode transfer. Note 5. For >90% anodic deposition yield (>98% when Fe absent), t
t0
te
(111
(I1
Figure 2. Concentration-time profiles for 2 of the possible 8 arrangements of the gradient titration method ( I ) Linearly increasing titrant (reagent) concentration: vessel A, Reagent; vessel B, distilled water-mixed with constant flow of sample. ( 1 1 ) Linearly decreasing titrant (sample) concentration; vessel A, distilled water: vessel B. sample. mixed with a constant flow of reagent. te = time for equivalence point
exp(FB FA- FA) (1) where CA = concentration of solution in cup A, C(B0) = concentration of solution in cup B a t t = 0, CB = concentration of solution in cup B a t time t, V(B0) = volume of solution in cup B a t t = 0, VB = volume of solution in cup B a t t , F A = flow-rate from A to B and F B = flow-rate from B. Inspection of Equation 1 reveals that if F s = W,4,i . e . , if the flow from container B is twice that of the flow into B, Equation 1reduces to B‘
=
cA
+
(cBo
- cA)/v,,
x
(v,
- F4t) (2)
The concentration of B is then a direct linear function of time. Therefore, if flow-rates of F g = FA are maintained, the system produces a gradient titrant with a concentration which is a linear function with respect to time. The basic arrangement for the generation of a gradient titrant can be used in several ways. First, the gradient “titrant” can be either sample or reagent; second, it can be in the form of an increasing or decreasing concentration gradient and, finally, it can traverse some segment of the concentration time profile in either the decreasing or increasing concentration mode and may or may not reach the zero concentration axis. Two examples of the eight possible combinations of linear concentration gradient for reagent/sample interaction are shown in Figure 2. Example I shows the concentration time profiles for a linear increase of reagent concentration (titrant) mixed with a constant flow of sample stream. The second example shows the corresponding profiles for linear dilution of the sample (titrant) mixed with a constant flow of reagent. The choice of the optimum system will depend upon the nature of the sample and the availability of a suitable sensing electrode. As the aim of the present work was to demonstrate the 10
EXPERIMENTAL Apparatus. A Digital Voltmeter (Model 101, Corning, N.Y.) was used for potential measurements. Standard AutoAnalyzer modules (Technicon Inc., Tarrytown, N.Y.) principally the peristaltic pump (Model 11) and Sampler I1 units were used for the gradient generation and also for the analysis manifold. The silver sulfide membrane electrode was constructed as follows: an AgzS pellet 6 X 2 mm was pressed using an infrared pellet press and mounted in the end of a Perspex tube such that 1 mm of disk projected beyond the end of the tube. A 0.5-mm hole was drilled horizontally through the membrane and polished using diamond polishing paste on a piece of string. Inlet and outlet tubes were then sealed with epoxy resin. Alternative flow designs such as flow caps may be used, provided the dead volume is kept to a minimum. Reagents. Stock solutions of sodium sulfide were prepared by dissolving Analytical Reagent grade Na2S.SH20 in oxygen-free water. The concentration of sodium sulfide was determined in alkaline media using the potassium iodate method (11). To improve the stability of the stock sulfide solutions, 1%of ascorbic acid was added and the solutions were stored in polyethene bottles and restandardized every two or three days. Dilute sulfide solutions were then prepared by suitable dilution of the stock solution with oxygen-free water. All other chemicals used were of analytical reagent grade. Mode of Operation. The basic experimental arrangement for gradient titration with increasing concentration gradient of reagent is shown in Figure 3. The reagent in vessel A is pumped into the generator vessel B and the effluent from the latter which is in the form of a linearly increasing concentration gradient is mixed with the continuous sample stream (C). In the present system, the gradient generator consists of a modified AutoAnalyzer Sampler such that alternate sample cups contain the reagent and distilled water. The manifold is designed so that solution from the reagent cup is pumped into the distilled water cup which is continuously mixed with a stream of nitrogen and the gradient reagent abstracted from the latter. The sampler unit is programmed at a suitable rate (10/hr) and the internal relay modified so that the sample tray is advanced two positions at a time. The solutions pass through a conventional AutoAnalyzer mixing coil and then through the measuring electrode. In the system under study, vessel A initially contains mercuric chloride solution and vessel B distilled water with the sulfide sample in C. At the start of the titration, the sulfide sample predominates and the electrode system gives a large negative millivolt reading. As the gradient is developed, the concentration of mercuric ions in the effluent from vessel B approaches that in vessel A and when this exceeds the concentration of the sulfide sample, the resultant excess of mercuric ion causes the electrode system to show a positive potential. The concentration of the mercuric ion is adjusted to give a convenient measured time for the titration. A typical potential-time response for this system is shown in Figure 4; the elapsed time intervals ( t l , t z , f 3 , etc.) are directly proportional to the concentration of the test solutions.
’
(11) P. 0. Bethge, Anal. Chim. Acta. 10, 310 ( 1 9 5 4 ) .
ANALYTICAL C H E M I S T R Y , VOL. 46, NO. 1, J A N U A R Y 1974
w
s1
52
53
W
w
Table I. Elapsed-Time Intervals in the Gradient Titration of Sulfide Samples of Various Concentrations Concentration of sulfide ( X 104M)
Time elapsed. seca
1.o 2.0 3.0
2a 57 a7 117 148 178
4.0 5.0
6.0
Concentration of sulfide
(x 105~)
Time elapsed,
secb
2.0 4.0
6.0 8.0
10.0 12.0
a Gradient developed with a 0.0005M HgC12 solution. veloped with a 0.0001M HgCI? solution.
28 58 89 118 149 179
+ 5
Gradient de-
10 TIME lminutesi
15
20
Figure 4. Potential-time response for gradient titration of sulfide ion with H g ( l l )
RESULTS AND DISCUSSION The manifold for the gradient titration of sulfide is shown in Figure 5. The gradient generator vessel B initially contains 10 ml of distilled water and vessel A, the Hg(I1) titrant. The lengths of transmission tubings were so arranged that the flows from B and C coincided a t the mixing point. Sample and gradient flows were presented for 4 minutes followed by a 2-minute water wash. The next sample is then presented together with a fresh gradient titrant. Results Obtained with Known Sulfide Samples. The silver sulfide membrane gave a Nernstian response to both sulfide ions and mercuric ions down to a concentration level of ca. 10-6M. The sodium sulfide test solutions contained a constant background of 0.2M NaOH to provide a fixed high pH and also to ensure that the total sulfide was present in the form of sulfide ions. The mercuric nitrate titrant contained a constant background of 0.2M " 0 3 to suppress hydrolysis. Using 0.0005M HgClz solution to generate the gradient with 10 ml of water initially present in the gradient cup, B, 6 different concentrations of sulfide solutions were titrated by the gradient technique. The elapsed-time intervals ( t l , t z , t3, etc.) were proportional to the concentration of the sulfide samples. The results are summarized in Table I. The same sulfide samples were then diluted 5-fold and titrated with a gradient generated by a 0.0001M HgC12 solution in cup A. The results were comparable to those corresponding to the more concentrated samples. The precision of the method was evaluated by repeated titrations of sulfide samples of the same concentration (0.0004M),with a gradient made with a 0.0005M HgC12 solution in cup A. The mean of the elapsed time intervals for 10 determinations was 118 seconds, maximum deviation from the mean = 2 seconds, standard deviation = 1.37, and coefficient of variation 1.16%. Advantages of Gradient Titration. The initial study has shown that the gradient titration technique is experimentally feasible when an appropriate ion-selective electrode with a rapid response is available as the end-point sensor. Most glass and solid state electrodes have response times of the orders of milliseconds (12, 13), hence, even in dilute solutions, are ideally suited as sensors for gradient titration. With liquid membrane and related systems, however, response times are markedly dependent on the activity of the primary ion and on the nature and extent of any interfering species ( 1 4 ) . Measured values of t 9 5 (response time to reach 95% of steady state) varying from (12) G. Johansson and K. Norberg. J . Eiectroanai Chem., 18, 239 (1968). (13) K. Toth. I. Gavaller, and E. Pungor, Anal. Chim. Acfa, 57, 131 (1971). (14) 5 . Fleet, T. H. Ryan, and M. J. D. Brand, Anal. Chem., 46,12 (1974).
W = wash solution; S1, 2.0 X 10-4M S 2 - ; S2, 4.0 X 10-4M S 2 - S3, 6.0 x 1 0 - 4 s*~ Flow rate irnl/minl
n 2.0 v
I
+Waste
5. Manifold design for gradient titration of sulfide ion with
one or two seconds up to several minutes have been observed. Hence the applicability of this type of electrode as a monitor for gradient titration will be dependent on the nature of the system. One other important advantage of the technique is that no sophisticated potential measuring device is required; simple, inexpensive operational amplifier modules can be used for the potential readout (15). The procedure as described is not fully automatic, however, with part of the sample (and reagent titrant) handling step being done manually. Full automation, however, is possible by incorporating a modified Technicon Sampler into the system. This modified sampler consists of a sample plate-drive which advances two cup positions for each cycle. One cup contains the sample while the other cup is for the generation of the gradient titrant. This latter cup is provided with two probes; one for delivering reagent (or diluent) while the other is for abstracting a gradient titrant. Agitation required for mixing in the gradient cup is provided by a small electromechanical stirrer or a stream of nitrogen. When these improvements in mechanical design are incorporated, it is apparent that the gradient titration technique will become very useful for continuous automated analysis. Work is a t present in progress on the application of the method as a routine monitor for the presence of heavy metals in natural waters and industrial effluent (16). Received for review December 27, 1972. Accepted July 23, 1973. (15) M . J. D. Brand and 5 . Fleet, Chem. Brit.. 5, 557 (1969). (16) B. Fleet, S.das Gupta, and A . Y . W . Ho, J. Envrron. So..in press
ANALYTICAL
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