1771
Anal. Chem. 1908, 58, 1771-1777
Conductometric Sensor for Parts per Billion Sulfur Dioxide Determination James S. Symanski’ and Stanley Bruckenstein*
Chemistry Department, University at Buffalo, State University of New York, Buffalo, New York 14214
A conductometric88nsor for the determination of atmospheric sulfur dloxlde levels ls described. I t consists of a hydrophoblc, gas-porous membrane that separates the gas sample from a thln fllm of pure water. Sulfur dloxlde from the gas phase diffuses through the membrane and rapklty equilibrates In the water layer. Conductlvlty electrodes positioned wlthln the thln layer measure Its conductance. The theory relating the square of the equlllbrlum conductance to the partlal pressure of sulfur dloxlde la ghren. The behavlor of the sensor to sulfur dloxlde Is characterized and contrasted to that of carbon dloxlde. Llnear callbratkn curves were obtalned over a range of 20-1000 ppb SOz. Response tlmes were on the order of 90-120 8.
Analyzers based on the conductometric principle have been extensively used for atmospheric sulfur dioxide determination. although the conductometric method is not classified as an ’equivalent” method by the US.EPA, the use of conductometric SO2 analyzers is widespread because of their high sensitivity, fast response, minimal maintenance, and simple operation (1,2). The principle of the operation of these analyzers can be traced to the Thomas autometer (31,in which the conductivity of a dilute solution of sulfuric acidfhydrogen peroxide changed due to the absorption and oxidation of sulfur dioxide by the hydrogen peroxide to form HSO, and H+. Sulfur dioxide was bubbled upward through a column countercurrent to a stream of reagent flowing which then passed through a flow conductivity cell. Approximately 0.5 ppm SO2 could be determined with a response time of about 120 s. Beard (4)described a similar devicewing a column containing glass beads. Forty parts per million of SO2 was detected. Nash (5)built a portable apparatus in which the gas stream impinged directly upon a stationary pool of reagent for 15 min while its conductivity was recorded. The conductivity of the pool increased as sulfur dioxide was absorbed. The reagent pool was replaced for each sulfur dioxide determination. Killick (6) modified Nash’s cell and automated the renewal of the reagent pool prior to each determination. This device was capable of determining 0.2 ppm SO2. Later Nash (7) described an improved conductivity cell capable of determining 2 ppb SO2 within -3 min. Commercial conductometric analyzers utilize the same chemistry and principles described above. The limit of sensitivity of these instruments averages about 50 ppb (8),and they have response times in the range 0.5-6 min (I).All the devices require both air flow (0.25-5.0 L min-’) and absorbing reagent flow (0.7-15 mL min-I) (9). The absorbing solution of hydrogen peroxide/sulfuric acid is stable for a maximum period of about 2 weeks (10). Although these analyzers are nonspecific, they are commonly used where SO2 is assumed to be the principal pollutant present. Present address: Johnson Controls, Milwaukee, WI 53201. 0003-2700/88/0358-1771$01.50/0
In this study, we describe a novel conductometric sensor for sulfur dioxide, using water as the absorbing reagent. It is based on a thin-layer cell having a gas-porous membrane separating a thin f i i of pure water from the gas sample. The porous membrane allows rapid sulfur dioxide transport to the water interface where sulfur dioxide dissolves to produce H+ and HSOf in amounts related to the partial pressure of sulfur dioxide in the gas phase. The conductance is measured by means of electrodes deposited on the membrane’s surface. This arrangement provides the optimal response time and sensitivity. Freshly deionized water is used to flush the cell before each measurement. One of the thin-layer cells we used was applied previously for the determination of atmospheric carbon dioxide (11,121. For this cell, the time of equilibration of the thin-water layer with SO2was on the order of 5 min for parts per billion levels in the gas phase. A revised cell design made it possible to determine 20 ppb SO2 with a response time of 110 s.
THEORY The conductometric sensor’s response to SO2 is governed by the following equilibria: K,
S02(g) z= S02(aq) + H20
K,
S02(aq)
(1)
+ HS03-(aq)
(2) Raman (131,infrared (141, and ultraviolet (15)spectroscopic studies indicate that aqueous solutions of sulfur dioxide consist almost exclusively of uncombined SOzmolecules. No evidence has been found to support the presence of the H 3 0 3molecule in solution. The rates of both reactions 1 and 2 are fast compared to the time scale of the mass-transfer-controlled equilibration of SO2throughout the thin-water layer in the conductometric sensor. Therefore, the overall equilibrium between gaseous sulfur dioxide and the ions formed in the water layer H+(aq)
KfK,
+
S02(g) + H20 eH+(aq) HS03-(aq) (3) can be used to describe the conductance response. Ka is the “apparent” dissociation constant of S02(aq),and Kp is the Henry’s law constant describing the equilibrium between sulfur dioxide in the gas phase and the unhydrolyzed S02(aq). When the thin-water layer is in equilibrium with gas phase
so29
[H’] = [HS03-] Kp*Ka
= [H+1[HS03-]fH+fHSO,-/PSO,
(4)
(5)
and the specific conductance, k, is given by
k = 10-3(XH+[H+]+ X~so~-[HS03-])
(6)
In eq 5 and 6 the bracketed terms signify equilibrium concentrations, the f terms activity coefficients, and the X terms the equivalent ionic conductances of the specified species. In eq 4-6 we w u m e that (1)the ionic strength is sufficiently small so that the activity coefficients approach unity, (2) the limiting form of the Onsager equation at infinite dilution 0 1988 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
Table I. Thermodynamic Constants for SO2 and Various Gases: Comparison of Sensitivities vs. SO2"
R
B C
so2
COP NH, HSS
1.20 3.39 X lo-' 54.9 0.1
1.29 X lo-' 4.45 X 1.75 X 1.26 X
421
1
395 271 378
8.6 X 2.6 X lo-' 6.6 X
E F
Constants from ref 18-24. applies, and (3) the equilibrium concentrations of SOZ- and HS20B-are negligible. The first "apparent" dissociation constant of S02(aq) is more than 5 orders of magnitude larger than the second (16); thus the concentration of S032-is negligibly small. Although the following slow reaction to form pyrosulfite ion is known to occur 2HS03-(aq) + HS,O,-(aq)
(A,+
CELL SQUARE WAVE GENERATOR
CURRENT To WAVE VOLTAGE + FULL RECTIFIER COMlERTER
L
+ OH-(aq)
(7) Spedding and Brimblecombe (17) have shown that in very dilute sulfur dioxide solutions HS20c is not observed. Substituting eq 4 and 5 into eq 6 yields the expression for the specific conductance in the thin-water layer
k =
Figure 1. Schematic representation of the sensing region of conductometric cell: (A) mixed-bed ion exchanger, (B) Lucite cell body, (C) thin water layer, (D)platinized gold conductivity electrodes, (E) gas-porous Gore-Tex membrane, (F) polypropylene support screen.
+ X,so,-)(KaK,)1~2Ps021/2 (8)
The actual cell conductance, S, is proportional to k ; therefore
S2= ( A / ~ ) 2 ( K & J P s o 2
(9)
where 0 is the cell constant (cm-') and A = 10-3(XH+ + AHSO,-). Equation 9 holds for any gas that dissolves in water to form an acid or base which is weakly dissociated. For example, NH, also obeys eq 9, and Martinchek has verified this expression for the behavior of C 0 2 (11). Therefore, the ratio of the square of the equilibrium conductance for another gaseous species, i, with respect to that of SO2 is given in eq 10.
Table I presents the data for various gases obtained by substituting the appropriate constants into eq 9. The fourth column of the table compares the analytical sensitivity of the thin-layer cell for these gases vs. SOz. For routine determinations of SOzin the range of 0.1-5 ppm both hydrogen sulfide and carbon dioxide contribute negligibly to the SO2response at their ambient levels. The response of ambient COP(400 ppm) would yield an equivalent response of approximately 3 X lo-* ppm SO2. Ammonia, which is unlikely to be encountered in SO2 determinations, would yield a false SO2 response of 0.03 ppm at a partial pressure of 1 ppm. EXPERIMENTAL SECTION Cell Description. Figure 1is a diagram of the sensing region for both of the thin-layer conductometric cells we used. The sensing region consists of a nonwetting, gas-porous membrane made of Teflon (E) separating the thin water layer (C) from the gas sample. The thickness of the water layer is approximately 0.004-0.005 in. (0.010 cm). The volume of the thin layer is approximately 0.013 mL in the original cell and 0.0008 mL in the modified cell. Gold conductivity electrodes (D) are deposited on the porous membrane's surface. As required, water passes through a mixed-bed ion exchange column (A) and removes all ionic species. This water displaces the previously equilibrated water from the thin layer, preparing the cell for the next SO2 determination. A porous polypropylene screen (F) supports the membrane and minimizes its flexing. Instrumental Methods. Conductance measurements were made with a direct-reading operational amplifier circuit ( I ) . A
Figure 2. sensor.
--
Block diagram of electronic circuit for conductometric
block diagram is shown in Figure 2. The square wave generator imposes a 2-V peak-to-peak square wave across the electrodes in the thin-layer cell. The output of the current-tu-voltageconverter is proportional to the conductance of the thin-layer cell. This output was rectified and filtered by a RC filter (RC = 0.2 s). The filtered output was buffered by a voltage follower whose output was used to drive a DVM or other recording devices. Conductancew. time traces were recorded on a Bristol millivolt strip-chart recorder (The Bristol Co., Waterbury, CT), a Health Model SR-204 strip-chart recorder (Heath Co., Benton Harbor, MI), or a Hewlett-Packard Model 7046-A X,Y,Y' recorder (Hewlett-Packard,Palo Alto,CA). The Bristol strip-chart recorder had a high-impedance buffer amplifier and a resistor divider network to allow input voltages from 1 mV to 10 V full scale. Reagents. Water used in all conductivity experiments type I reagent grade water from a Milli-Q reagent grade water system (Millipore Corp., Bedford, MA). The ion-exchange bed was prepared from analytical grade mixed bed resin, AG-501-X8 (D), 20-50 mesh size (Bio-Rad Laboratories, Richmond, CA). Stock gases of carbon dioxide, sulfur dioxide, and ammonia were suppied as custom mixture grades (Union Carbide, Linde Division) and were as follows: carbon dioxide as 5% and 1.01% C02in nitrogen. Nitrogen used for diluting these stock gases was obtained as boiloff from liquid nitrogen (Union Carbide, Linde Division). Apparatus. Gas mixtures were prepared by proportioning commercial gas mixtures with nitrogen using one or two dualchannel rotameter gas mixer-proportioners, FM4631 (Union Carbide, Linde Division). Mixing accuracy was f 5 % (25). The flow rate out of the fiit mixer-proportioner was 2.0 L min-'. This output was divided between a waste outlet and the next gas proportioner (required to prepare low levels of SO& using a needle valve leak. A needle valve leak was used to divide the gas stream of the fiial composition between waste and a single tube rotameter flowmeter, FM4631 (Union Carbide, Linde Division). This arrangement allowed independent control of mixing ratios and flow rate to the conductometric cell. The flow rate to the cell was adjustable from 0.001 to 2.0 L min-'. All connections between components of the gas train were made with 6-mm-0.d. Pyrex tubing joined by Taper-Tite connectors and fittings made of Teflon (Berghof/America,Inc., Raymond, NH). Two series gas proportioning stages were used to provide the gas streams used in the 0.02-0.2 ppm range. Controlled-temperature experiments were performed in an environmental chamber (Vapor Temp., VP-400, At-1, Blue M Electric Co., Blue Island, IL). Conductometric Cell. The conductometricthin-layer cell was constructed from Lucite. Figure 3 shows an exploded view of the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
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B
E
200
A
1773 I
H
I
&C
f
c
p+ *
D
I
\
i
///
TIHE / (seconds)
Flgure 4. Conductance vs. time for 5 ppm SOz at different values of gas flow rate: (1) 0.2 L min-’, (2) 0.5 L min-’, (3) 1.5 L min-’, (4) 2.0 L min-I.
Flgure 3. Exploded view of Lucite thin-layer conductometric cell. Components A-M are described in the text.
cell. Water enters the cell through a port (A) in the cell top (B) and is dispersed by a deflector (C) over the mixed-bed ion exchanger contained within the cell body (D). A vent in the top cell (E) consisting of a porous membrane made of Teflon (E) allows for excape of air bubbles in the incoming water. A polypropylene screen, fastened inside the cell at its bottom, confines the mixed-bed ion exchanger. The cell top (B) is threaded and screws into the cell body (D) and is gasketed with an O-ring (F). The thin layer (H) is a 0.004-0.005-in., 0.5-in.-diameter depression milled into the bottom of the cell body. Water enters the thin layer through the center hole and exits via eight holes drilled along the perimeter of the depression. This water exits the cell through a fitting (K) that is glued to the cell body (D). The two Lucite pieces (L) and (M) comprise the gas inlet. This inlet contains a O.M-in.-diameter,0.10-in.-deep depression that constitutes the volume of gas immediately adjacent to the thin water layer. Gas enters the inlet through a center port in the inlet and exits from four holes drilled around the perimeter of the depression. The inlet is attached to the cell body by three 2-56 screws (0).The sensing membrane (I) and support screen (N) will be described in detail below. The gas-poroussensing membrane used was 0.004-in. Gore-Tex poly(tetrafluoroethy1ene)sheet (W. L. Gore & Associates, E h n , MD). The membrane is 78% porous and has a typical pore size of 0.2 km. Gold conductivity “interlockingfiger” electrodes were painted on one surface of the membrane using a gold resinate solution, 8300 (Engelhard Industries,East Newark, NJ). Alternate fmgers were joined to form each conductanceelectrode. Successive coats of resinate were applied (three to seven applications) and heat cured until the resistance through each f i e r of the electrode was less than 5 Q. After application, the resinate was heat cured with a 20-A heat gun, HG1751 (Master Appliance Corp., Racine, WI),to produce the porous gold electrode (26). The first two coats of resinate were diluted with two parts toluene to ensure complete penetrating (wetting) of the TFE membrane. Gold on the face of the membrane exposed to the gas phase was removed by oxidation in 1M KCl/O.l M KCN at 0.0 vs. SCE until the resistance through the gas-phase side of the membrane to each “finger” was greater than 20 M Q (11). Platinizing the gold electrodes with 0.1 M H,PtC& in 1M HC1 greatly extended the l i e of the conductance electrodes. Platinum was deposited at a constant current of 0.1 mA for a period of 10 min, after which the current was increased to 10 mA. Deposition was halted when the electrodes blackened. The platinizing solution was then replaced with 0.2 M sulfuric acid, and a constant cathodic current of 10 mA was passed through the electrodes, evolving hydrogen gas. Hydrogen evolution was necessary for
0
10
20
30 40 T m / (urmds)
50
60
70
Flgure 5. Conductance vs. time for 1.0% CO at different values of min- 7, (3) 1.5 L min-I.
gas flow rate: (1) 0.2 L min-‘, (2) 0.5 L
removal of chloride adsorbed during platinum deposition. During both platinum deposition and hydrogen evolution, nitrogen gas was passed over the side of the membrane facing the gas phase to prevent the uptake of oxygen. The sensing membrane (I) (Figure 3) was affixed to the body of the cell by using a pressure-sensitivesilicone transfer adhesive (Densil, Dennison ManufacturingCo., Framingham,MA). Contact wires (J)were affixed to pads painted on the outside edge of the membrane made of Teflon with a conductive silver-impregnated epoxy resin (Eccobond Solder 57C, Emerson and Cumming, Inc., Canton, MA). The 100 mesh polypropylene support screen (N) used to support the sensing membrane was 0.007 in. thick and had 34% open area (Tetko, Inc., Elmsford, NY). Water Flow System. Feed water was stored in a 500-mL polyethylene bottle at a level below the thin-layer cell. A simple pulse pump was constructed from a 2-in. length of gum rubber tubing between two one-way check valves (Clippard Valve Corp., Cleveland,OH) arranged 80 as to permit only unidirectional water flow when the tubing was squeezed. When the tubing was squeezed between the thumb and forefinger,approximately0.460 mL of water passed through the thin-layer cell. The wastewater reservoir was a 500-mL polyethylene bottle positioned above the cell and pulse pump in order to maintain a constant water pressure on the Teflon sensing membrane and check valves. The components of the water flow system wre joined with ‘Is-in. tubing and miniature fittings all made of Teflon (BerghofIAmerica,Inc., Raymond, NH). RESULTS AND DISCUSSION Transient Response of Circular Membrane Cell. Dependence on Gas Flow Rate. Conductance vs. time transients for 5 ppm SO2 are shown in Figure 4 for different values of
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986 250
Table 11. Response Time vs. Gas Flow Rate and PartTal Pressure for Sulfur Dioxide response time (s) at the following gas flow rates 0.5 L min-' 1.5 L min-'
200
Pso,/ppm
v1
.i150 u1
iD
-
0.2
L
1
300
5 10 55
210 165 50
270 145 120 40
120 120 110 40
0
\
100
Table 111. Response Time vs. Gas Flow Rate and Partial Pressure for Carbon Dioxide
$
1 50
PCO,l% 0.05 0.5
response time (8) a t the following gas flow rates 0.2 L min-' 0.5 L min-' 26 27
24 25
0
0
60
120 TIME
180
240
/ (seconds)
Figure 6. Conductance vs. time for 5 ppm SO2 at different values of gas flow rate over 4 min: (1) 0.2 L min-', (2) 0.5 L min-I, (3) 1.5 L min-I .
gas flow rate to the thin-layer cell shown in Figure 4. The cell's response to sulfur dioxide shows a marked dependence on gas flow rate. These responses are contrasted to those for 1.0% carbon dioxide that are given in Figure 5. The shape of the transient conductance responses at a constant partial pressure of COz was found to be independent of flow rate of sample gas. The slight decrease in conductance with flow rate is caused by evaporative cooling. In the case of carbon dioxide, the rate equilibration of the water layer is controlled by diffusion of COz in the thin water layer and not by transport to, or through, the membrane. This diffusion model has been treated by Crank (27),and the time, T, required to reach 98% of the equilibrium uptake of C 0 2after a water pulse is
T = 1.50LW2/D,
(11)
where L, is the thickness of the thin water layer and D, is the diffusion coefficient of the dissolved species in water. Using values of L, = 0.004-0.005 in. and D, = 10" cmz/s yields an approximate value of T equal to 15-24 s. This time agrees satisfactorily with the transient conductance data for carbon dioxide. However sulfur dioxide requires several minutes to reach conductance equilibrium. This difference between the behavior of carbon dioxide and sulfur dioxide is readily explained. The total solubility, S,, of the sulfur dioxide species in the aqueous phase is equal to the sum of the dissociated and undissociated forms, HS03- and SOz(aq)
St =
[Sodaq
+ WS03-1aq
(12)
Substituting for the equilibrium concentrations from eq 2 and 3 into eq 12 yields
s, = K,.PSO, + [KaKp~p,0,1"2
(13)
where the first term of the right-hand side arises from the undissociated form and the second from the dissociated form. An analogous relationship may also be written for carbon dioxide equilibration. Inserting the numerical values for the equilibrium constants shows that S,is orders of magnitude larger for sulfur dioxide than for carbon dioxide. For example a gaseous phase containing 5 ppm of sulfur dioxide is in equilibrium with a 2.84 X M solution of total sulfur dioxide species, while a 1.0% gaseous phase containing carbon
dioxide is in equilibrium with 3.51 X M total dissolved carbon dioxide species. Thus much more gaseous sulfur dioxide than carbon dioxide must enter the thin water layer to reach equilibrium, and the approach to equilibrium becomes limited by transport through the gas phase. In the gas phase, diffusion and natural convection are able to supply enough carbon dioxide to the thin layer of water without a significant partial pressure decrease of carbon dioxide occurring at the membrane/gas-phase interface. This situation arises because the value of the equilibrium constant for eq 3 is relatively small, so only a fraction of the maximum possible gas-phase flux to the membrane is required during the conductance transient. However, exactly the opposite situation exists in the case of sulfur dioxide because the equilibrium shown by eq 3 lies almost completely to the right during the transient period. Thus, the partial pressure of sulfur dioxide at the membrane/gas interface is much lower than in the bulk of the gas. This situation produces a flux of sulfur dioxide that approaches the maximum possible flux for the existing gas boundary layer thickness. Increasing the gas velocity decreases the boundary layer thickness and increases the flux of sulfur dioxide. This is seen in Figure 4, where the difference in the conductance-time curves becomes smaller at higher gas velocities. At higher gas flow rates, the flux becomes limited by transport through the stagnent gas in the tortuous, inteconnected pores in the membrane. Under these conditions the gas-phase convective-diffusion layer thickness is small compared to the effective membrane pore length. Dependence on Gas Partial Pressure. The transient sulfur dioxide conductmetric response in the range of PSO,= 1-55 ppm was a function of the partial pressure of gas. Equilibration times were longer a t the lower sulfur dioxide concentrations. Data from these experiments are listed in Table 11. Similar experiments were performed for carbon dioxide. These data appear in Table 111. There is virtually no effect on the response time for the carbon dioxide concentrations investigated, while there is a pronounced effect in the case of sulfur dioxide. At a gas flow rate of 0.5 L mi&, 1 ppm sulfur dioxide requires approximately 2.5 min to equilibrate in the water layer. At the same flow rate, 55 ppm sulfur dioxide requires only 40 s for equilibration. This phenomena was also observed by Terraglio and Manganelli (28) who absorbed sulfur dioxide into 20-mL volumes of distilled water. They reported that the rate of solution of sulfur dioxide into water, over a range of atmospheric concentrations of 0.31-3.3 ppm, was a function of the partial pressure of the gas, with saturation being reached more
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
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4
6
8
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10
Figure 7. Calibration curve for SO2 in the range of 1.0-10 ppm: conductance recorded at (1) 300 s, (2) 60 s, and (3)30 s followlng a water pulse.
0.0
0.2
0.4
0.6
0.8
1.0
P c02
rapidly at higher concentrations. The effect of equilibration time on concentration is the result of the large value of the “apparent” dissociation of S02(aq)(K, = 1.3 X eq 2. When the thin water layer is in equilibrium with 5 ppm sulfur dioxide, about 98% of the dissolved species is in the form of HS03-. The second term on the right-hand side of eq 13, arising from the dissociation reaction that produces HSO,-, is significantly larger than the first due to undissociated sulfur dioxide. Equation 13 predicts that the total solubility of sulfur dioxide is proportional to P s O f / 2at low partial pressures and proportional to the Pso2 at high partial pressures. Since the conductance transient (a) is directly related to the instantaneous concentration distribution with the thin water layer, (b) and the rate of supply of sulfur dioxide to the thin layer is mass-transport limited on the gas-phase side, (c) then the shapes of the conductance transients will reflect this transport limitation in the gas phase at gaseous levels of sulfur dioxide for which the dissociation of dissolved sulfur dioxide is substantial. The response time for carbon dioxide at ambient levels and higher (70.033%)does not depend on its partial pressure. The rate of conductance equilibration is not limited by carbon dioxide transport from the gas phase (see Figure 5), and minor variations from proportionality between the total amount of dissolved carbon dioxide and its partial presure do not effect the shape of the conductance transient. Effect on Calibration Curves. Figures 7 and 8 are calibration plots for sulfur dioxide in the range of 1.0-10 ppm and carbon dioxide in the range of 0.05-l.O%, respectively. The conductance for sulfur dioxide was recorded 30 s, 60 s, and 5 min after the water pulse. Carbon dioxide data was recorded 60 s following the water pulse. The gas flow rate in both experiments was 0.5 L min-’. The slope of the sulfur dioxide calibration curve at 5 min is (0.953 f 0.007 45) X S2/ppm with an intercept of -0.0579 f 0.0444 S2.For carbon dioxide, the slope of the curve is (106 f 1.46) X S2/% with an intercept of 0.882 f 0.760 S2. The ratio of (S2/ p)soZ/(s2/p)~o2, 9.0 X lo5, is approximately 25% lower than that predicted by eq 10. Figure 7 also presents the calibration data for sulfur dioxide at times of 30 s and 60 s following the water pulse. At short times, before concentration equilibrium is attained, the square of the conductance is not proportional to the partial pressure of sulfur dioxide. This result is a consequence of this nonequilibrium situation. The fraction of dissolved sulfur dioxide
Figure 8. Calibration curve for C02 in the range of 0.05-1.0%: conductance recorded 60 s following water pulse. that is dissociated varies with distance and time until a uniform concentrationg radient is established at equilibrium. Therefore, the thin-layer conductometric cell described, which functions well in the case of carbon dioxide (14),has limitations if the rapid determination of low levels of sulfur dioxide is a requirement. Equilibration times on the order of 5 min are required for analysis in the range of 1-5 ppm, and sub-parts-per-million determinations take significantly longer. Transient Response of Narrow-Channel Cell. Rationale. The time of response to sulfur dioxide is governed by the rate of mass transfer to the porous membrane’s surface. The geometry of the circular membrane cell described above permits mass transport through the gas phase only in a direction normal to the membrane’s surface. However, changing the geometry to permit transport to the membrane’s surface over a wider range of angles would increase the flux of sulfur dioxide to the surface of the membrane. One geometry that leads to a marked increase in mass transport is that of a “narrow-channel membrane cell”, which is a modified linein-a-plane geometry. Figure 9 compares the circular membrane and narrow-channel cell geometries. The narrow-channel cell shown in Figure 9 was fabricated by milling a narrow channel in a Lucite block, providing a liquid inlet and outlet at the ends of the channel, and attaching a gas-porous membrane over the milled-outstrip. Interlocking finger electrodes were formed on the solution side of the membrane, just as was done for the circular membrane cell. All other features of the strip cell correspond to those shown in Figure 3 for the circular membrane cell. The thickness of the thin water layer is the same in both cells, while the volume of water required by the narrowchannel cell is approximately 0.8 FL, of that required by the other cell. Narrow-Channel Cell Behavior. Figures 10 and 11are the conductance vs. time traces obtained by using the narrowchannel cell for sub-parts-per-million levels of sulfur dioxide. The gas flow rate of gas to the cell was 0.5 L min-’. The conductance traces for the range of PSO,= 0.02-0.2 ppm and 0.1-1.0 ppm were obtained. The sulfur dioxide level equivalent of the N2 blank at 120 s is -0.3 ppb sulfur.dioxide. The times required to reach 95%
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
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0.20
ppm
3
1
4
W
SIDE VIEW
I
WATER
I
I
WATER
I
I
2 2 \
e
R 1
I
GAS
I
GAS
FWr 9. Schematic comparison of circular membrane conductometric cell and narrow-channel membrane conductometric cell: (A) thin water layer, (B) Gore-Tex membrane, and (C) gas inlet. Circular membrane ceH (left) has a ' I 2 in. diameter, 0.0044. depression comprising the thin layer. The narrow-channelmembrane cell (rigM) has a channel milled in the bottom between two holes drilled perpendicular to the bottom. One hole serves for water entry and the second for water exit. The dimensions of the channel are 0.030 in. wide X 0.4 in. long X 0.004 In. deep.
0
30
60
90
120 150
180 210
TIHE / seconds
Figure 10. Conductance vs. time for strip channel thin-layer cell: range of Psop = 0.1-1.0 ppm.
II
0 0
30
60
90
120 150
180
210
TIME / seeonds
Figure 11. Conductance vs. time for strip channel thin-layer cell: range of P,? = 0.02-0.2 ppm.
of the equilibrium conductance for various values of Pso, are as follows: (1) 1.0 ppm, 58-60 s, (2) 0.1 ppm, 98-100 s, and (3) 0.2 ppm, 110 s. These response times are a marked improvement over those listed in Table I1 for the circular membrane cell at much higher concentrations of sulfur dioxide. Linear calibration curves were obtained a t both 60 s and 120 s for PSO,in the range of 0.1-1.0 ppm. The leastsquares slopes and intercepts were as follows: 60-s data, slope = (5.65 f 0.098) X lo-" S2/ppm and intercept = (-0.0716 f 0.555) X lo-" S2;120-s data, slope = (6.39 f 0.14) x lo-" S2/ppm and intercept = (0.109 f 0.078) X S2.The value of the calibration slope at 60 s was 88% of that at 120 s. The narrow-channel cell's conductance transient response for carbon dioxide (Pco, = 5.0%) was nearly the same as for the circular membrane cell. This result is the predicted one when there is no mass transport limitation in the gas phase and the thickness of the water layer is the same in both cell geometries. For the sulfur dioxide studies in the range of 0.02-0.2 ppm, the calibration line was also linear using the conductancedata obtained at 120 s. The slope of this calibration line differed from the one a t the higher concentration range by only 670, which is within the experimental error introduced by using the tandem gas proportioning system required to prepare these low concentrations of sulfur dioxide. Unlike the results at higher sulfur dioxide concentrations, nonlinear calibration curves were obtained et 60 s. The transient response vs. gas flow rate for the strip thinlayer cell is shown in Figure 12 for Pso, = 0.2 ppm. A nominal flow rate of 0.5 L min-' is sufficient to achieve equilibration of the thin layer in 100 s. This is a marked improvement,both in response speed and required gas flow rate, over the behavior determined at the circular membrane cell. As is seen in Table 11, a concentration of 55 ppm of sulfur dioxide is required for this kind of performance at the circular membrane cell.
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
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values. All points are within 6% of the predicted response. CONCLUSIONS
A simple, accurate, and convenient sensor for the determination of atmospheric SOz can be constructed from a
3 Lo
B
conductance cell having one gas-porous wall confining a thin layer of water. By use of appropriate cell geometries and gas flow rates, good accuracy and a rapid response time were obtained for Pso, levels in the range 20-5000 ppb. Registry No. SOz, 7446-09-5.
E,
.rl
m
8
iijl
LITERATURE CITED
03 P 8
0
180
120
60
0
TIME / (seconds)
Figure 12. Conductance vs. time for 0.2 ppm SO, at different values of gas fiow rate for strip channel thin-layer cell: (1) 0.2 L mtn-’, (2) 0.5 L mln-’, (3) 1.5 L min-’.
4 l.l0
iP
0.90
0.70
1 0
1 10
20
TEMPERATURE
30 /
40
( OC )
Figure 13. Effect of temperature on conductance. Data are normallzed to 25 OC for 60 ppm sulfur dioxide. SolM line Is theoretical conductance: circles are experimental conductances.
Temperature Dependence of Sulfur Dioxide Response. Equation 9 predicts the cell conductance in terms of wellknown transport and thermodynamic quantities. Their temperature dependences are also well-known (19,20)and were used to calculate the conductance as a function of temperature. The results of this calculation are given in Figure 13. The line represents the predicted conductance, normalized with respect to the value at 25 “C,and the circles the experimental
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RECEIVED for review July 26,1985. Resubmitted December 4,1985. Accepted December 27,1985. This work was supported by the Air Force Office of Scientific Research under AFOSR Grant 83-0004.
