Anal. Chem. 1986, 58, 1766-1770
1766
5.9% in the range 100-1OOo rg/g, and 4.6% for concentrations above 1000 kg/g. Registry No. K, 7440-09-7;Ca, 7440-70-2;Ti, 7440-32-6;V, 7440-62-2; Cr, 7440-47-3; Mn, 7439-96-5; Fe, 7439-89-6; Ni, 7440-02-0; Cu, 7440-50-8; Zn, 7440-66-6; Pb, 7439-92-1; Br, 7726-95-6;Rb, 7440-17-7;Sr, 7440-24-6.
lr
8 096
LITERATURE CITED
w
sample load imgcm'i
F w e 3. Enhancement correctkm factor as a functlon of sample load for elements Mg, Ai, K, and V in geological standard.
spurious characteristic X-rays induced in the irradiation chamber walls. The standard deviation per measurement for the overall procedure amounts, on the average, to 13.8% for concentrations below 10 pg/g, 8.6% in the range 10-100 kg/g,
(1) Van Dyck, P.; Van Grleken, R. E. Anal. Chem. 1880, 52, 1958. (2) Sherman, J. Specfrochlm. Acta 1955, 7 , 283. (3) Shiraiwa, T.; Fujino, N. Jpn. J . Appl. Phys. 1866, 5 , 886. (4) Sparks, C. A&. X-Ray Anal. 1975, 79, 19. (5) Abramowitz, M.; Segun, J. Handbook of Mathematical Functlons; Dover, New York, 1968 Vol. 5. (6) Van Espen, P.; Adarns, F. Anal. Chem. 1976, 4 8 , 1823. (7) Van Espen, P.; Van't dack, L.; Adams, F.; Van Grieken, R. E. Anal. Chem. 1979, 51, 961. (8) Smits, J. Ph.D. Thesis, U.I.A., Antwerpen, 1979. (9) Ring, E. J.; Hanssen, R. G. The Preparation of Three So& Afrlcan Coals for Use as Reference Materials, Mintek Report NO. M189; Council for Mineral Technology: Randburg, South Africa, 1984.
RECEIVED for review December 23, 1985. Accepted March 3, 1986. This work was partially supported by the Belgian Ministry of Science Policy under Contracts 80-85110 and 84-89/69. L. Van't dack carried out the coal analyses.
Continuous Conductometric Sensor for Carbon Dioxide Stanley Bruckenstein* and James S. Symanski'
Chemistry Department, University at Buffalo, State University of New York, Buffalo, New York 14214
A contlnuour conductometric sensor is described for the determination of carbon dloxMe in the atmosphere and innonaddic and nonbask gases. Gaseous carbon dloxide dlffusesthrough a h y gabporouomembrane into a Wn layer of pure water. The back wall of the thln water layer is a porous screen that separates the water layer from a mlxed-bed Ion exchanger column. The Ion exchanger continuously removee knlc speclea franthe water layer hdu&lgthe products from the dlssoclation of COJaq). ConductlvHy electrodes porltloned In the thin water layer measure Hs conductance. The dlffuslon of carbon dioxide through the membrane into the thln water layer and the removal of lonlc specks through the screen by the mixed-bed ion exchanger estabkh a steadydate concentration gradlent of CO,. This gradient Is proportionalto the partial pressure of COPIn the gas phase, and cell conductance is proportional to Pm21'2. This devlce was evaluated for use in the determination of carbon dloxkie levels up to -1% and conformed to the theoretical predlctions.
The application of conductometry to the determination of gaseous carbon dioxide was first demonstrated by Cain and Maxwell (I). Their method along with other early methods relied on measuring the decrease in conductance of hydroxide solutions as the gas sample containing carbon dioxide was bubbled through the absorbing solution ( 2 4 ) . More recently, measurement of the conductance of a stream of deionized water after carbon dioxide absorption has been employed in C02determinations (5,6). All of these methods involved the Present address: Johnson Controls, Milwaukee, WI 53201. 0003-2700/88/035S-1766$01.50/0
physical mixing of gross amounts of gas and water, making them unsuitable for portable applications. Van Kempen and Kreuzer described a fast-responding conductometric microsensor for COzthat was constructedfrom a double-lumen catheter, the tip of which was covered by a COz-permeablemembrane (7).Conductivity electrodes placed in each lumen measured the difference in conductivity as the catheter was flushed with a constant flow of twice-distilled water. The flow of liquid in the catheter created a liquid boundary layer adjacent to the membrane, and the flux of C02 through the membrane creates a steady-state concentration gradient of COz within it. The conductometric sensor described by Himpler et al. (8) to measure carbon dioxide tensions in solution also did not require the mixing of the gas with the absorbing solution. This sensor consisted of a thin layer of water separated from the sample by a dialysis membrane. It had no provision for replacing the water in the thin layer and exhibited a slow increase in conductance with time which the authors noted, but did not explain. This increase was most likely due to the leaching of nonvolatile ionic impurities from the materials used in the cell's construction. Martinchek concurrently described a similar sensor that solved this problem (9). His sensor contained an integral mixed-bed ion exchange column. Water in the thin water layer was intermittently replaced after passage through an ion exchanger. In this study we describe a novel conductometric sensor for carbon dioxide. It consists of a thin layer of water separated from the gas phase by a hydrophobic, gas-porous membrane. This layer of deionized water is separated from a thick column of a mixed-bed ion exchanger by a thin screen that serves as the rear boundary of the thin water layer. When gaseous carbon dioxide diffuses through the membrane, a steady-state concentration gradient of dissolved carbon dioxide is estab0 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
A B
B
C
t
*
1767
.c'
A
E
zP 2
0
U
Flgure 1. Schematic representationof the continuous conductometric sensor: (A) mixed-bed ion exchanger, (e) Pyrex glass tube, (C) water-porous spacer screen, (D) thin water layer, (E) platlnlzed, gold conductivity electrodes, (F)Gore-Tex gas-porous membrane. Polypropylene screen supporting the GoraTex membrane is not shown.
lished in the thin layer of water because the mixed-bed ion exchanger functions as a sink for the ions produced by dissolved carbon dioxide. At steady state, the square of the conductance of the water layer is proportional to the partial pressure of carbon dioxide in the gas sample. Confining a water layer between the porous, hydrophobic membrane and a mixed-bed ion exchange resin yields a simple and convenient sensor for the determination of atmospheric carbon dioxide. CELL DESCRIPTION AND THEORY A representation of the continuous conductometric sensor is presented in Figure 1. The thin water layer (D)is separated from the gas sample by the hydrophobic, gas-porous membrane made of Teflon (F). Platinized conductivity electrodes (E) are deposited on the membrane face in contact with the water. The back boundary of the water layer is formed by a porous screen (C) that supports the mixed-bed ion exchanger (A). The water in the screen and the first few layers of the mixed-bed ion exchanger contributes to the effective thickness of the thin water layer. The mixed-bed ion exchanger continuously scrubs ionic species from the water layer. When gaseous carbon dioxide dissolves in the thin water layer, the equilibria
C02(aq) + H20
$H+(aq) + HCO,-(aq)
(2)
are established. Kp is the Henry's law partition constant (3.39 X M/atm), and K , is the apparent dissociation constant of C02(aq) (4.47 X lo-' M). In the range of gas-phase concentration studied (0.05-1.0%), about &96% of the dissolved carbon dioxide exists as C02(aq). COz diffuses through the membrane, the thin water layer to the screen, and into the mixed-bed ion exchanger. It acts as a sink for the dissolved carbon dioxide by removing hydrogen and bicarbonate ions, and a steady-state concentration gradient of COz(aq) is established. Figure 2 shows the development of dissolved carbon dioxide concentration profiles in the thin-layer cell. Also shown for comparison are the profiles for the pulsed thin-layer cell described elsewhere (12). All profiles were drawn assuming that no depletion of carbon dioxide occurs in the gas phase. The linearized concentration profiles are represented by the lines ABCDEi. In both cells, a step change in carbon dioxide concentration from zero to some finite value produces time-varying concentration profiles that reach a limiting value. In the pulsed thin-layer cell, profile DE, corresponds to the thin water layer being in equilibrium with COz(g). For the continuous cell, profile DE, represents the steady state in which the flux of C02(aq)through the water layer is time independent. The slope of the line DE, is proportional to the partial pressure of carbon dioxide in the gas phase.
CONTINUOUS SENSOR WATER LAYER SCREEN
GAS
f- DISTANCE
Flgure 2. Time-dependent linearized concentration profiles for the continuous thln-layer cell and for the pulsed thin-layer cell.
The time, T, required to achieve a steady-state concentration profile has been considered by Crank (11) and is
T
0.45L2/D
(3) where L is the thickness of the water layer and D is the diffusion coefficient of COz(aq) in the water layer. For our cell, the exact dimension of the water layer is unknown, as the screen, the adhesive layers used in cell construction, and the ion exchange particles all contribute to the characteristic thickness of the water layer. However, the effective thickness can be estimated from the observed response time using eq 3. The square of the equilibrium conductance is proportional to the partial pressure of carbon dioxide in the gas phase for a thin-layer conductometric cell (12). A solution for the steady-state conductance of our continuous conductometric sensor as a function of Pco, has not been derived rigorously. However, since (a) the conductance across a microscopic volume element in the thin water layer is proportional to the square root of the carbon dioxide concentration in the volume element and (b) the concentration of carbon dioxide at every point in the thin layer of solution is proportional to Pco21/2, then (c) the conductance across a microscopic volume element will be proportional to the square root of the partial pressure of carbon dioxide and (d) the total conductance will be proportional to Pco;l2. Thus the same power dependence between conductance and Pco, exists for the equilibrium thinlayer cell design (12) and the continuous cell design. Flow cell designs will also obey this power relationship. N
EXPERIMENTAL SECTION Instrument and Apparatus. The operational amplifer circuit used to measure solution conductance and the recording devices are described elsewhere (13). The apparatus used to proportion the stock gases and control flow rate of sample gas to the conductometric cell is also described in ref 13. Reagents. Water used in all experiments was type I reagent grade water obtained from Milli-Q reagent grade water system (Millipore Corp., Bedford, MA). The ion-exchange bed was prepared from analytical grade mixed-bed ion exchanger, AG-
1788
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
Alo
I GAS INLfT F l p e 3. Exploded vlew of construction of continuow conductometric sensor: (A) glass tubing, (B) mixed-bed ion exchanger, (C) Densil adhesive, (D) polyproylene screen, (E) Gore-Tex sensing membrane with conductivity electrodes.
501-X8(D),20-50 mesh size (Bio-Rad Laboratories, Richmond, CA). Stock gases of carbon dioxide were supplied as custom mixture grades (Union Carbide, Linde Division) and were as follows: 5% and 1.01% C02 in air. Membrane. The gas-poroussensing membrane was 0.004-in. L. Gore and Gore-Tex poly(tetrafluoroethy1ene)sheeting (W. Associates, Inc., Elkton, MD) onto which a gold resinate solution (8300, Engelhard Industries, East Newark, NJ) was heat cured to produce porous gold electrodes. These electrodes were then platinized. The detailed preparation of the electrodes on the membrane is given in ref 13. Conductance Cell. The body of the continuous conductometric sensor was made of Pyrex tubing, 3 / 4 in. o.d., 0.5 in. i.d. An exploded view of the construction is shown in Figure 3. The cell was constructed by cutting a 6-7-in. length of the tube into two equal lengths (A). The ends of the tube from each cut were polished flat using 600-grit silicon-carbide paper and water. A 0.75-in.-diametar piece of polypropylene screen (D)was affixed onto each polished end using several rings of a pressure-sensitive silicone transfer adhesive (C) (Densil, Dennison Manufacturing Co., Framingham, MA). Enough adhesive rings were used to produce a thickness of 0.004 in. The screen affixed to the upper tube served as a porous restraint for the mixed-bed ion exchanger (B). The screen on the lower tube acts to support the sensing membrane made of Teflon (E). The membrane (E) was interposed and sealed between the upper and lower tube using rings of the Densil adhesive. As the two tubes were pressed together under hand pressure, the Densil adhesive penetrated the pores of the screens and membrane forming a water-tightseal. The mixed-bed ion exchanger (B) was placed into the upper tube to a level of about 1 in. Water was added to a level of approximately 2 in. About 10-20 min was required for the background conductance to stabilize after the addition of fresh ion exchanger. Sample gases were introduced into the lower tube through 6-mm-0.d. Pyrex tubing inserted to a distance of 0.25 in. from the sensing membrane. The gas proportioning apparatus used to prepare the sample gases was described in ref 13. RESULTS AND DISCUSSION Transient Response. Figure 4 shows the conductance transient produced for a step change in partial pressure of C02 from 0 to 0.5% and 0 to 0.05% (near ambient). The conductance rapidly rises and becomes constant as the steadystate flux is established through the water layer. For a step change to 1.0% COz the time required to reach 98% of the steady-state conductance was approximately 90-95 s. On the following step change to Nz, the conductance decreased by 98% in about 170-180 s. The flow rate of sample gas was 0.5 L min-I, and the maximum partial pressure was 0.93%. Dependence of Conductance on PCw The change in the square of the conductance with partial pressure of carbon
t
0.5% C02
TIME
Figure 4. Conductance vs. time for step change in partial pressure of carbon dioxide for continuous conductometricsensor: gas flow rate = 0.5 L min-'.
Table I. Dependence of Conductance vs. Flow Rate of Sample Gasn gas flow ratell mi&
conductance/S
0.02
20.75 20.59 20.1 19.84
0.5 1.0
2.0 "Pco, = 1.0%, t = 24 "C.
dioxide yielded a straight line with a slope of (3.49 f 0.0469) x S2/% and an intercept as (0.0261 f 0.0233) X S2. The maximum partial pressure studied was -1%. The conductance signal equivalent of the nitrogen blank is 0.002% COz.Thus ambient levels (0.03-0.04%)are readily measured. Gas Flow Rate Requirement. After the steady state is established, the flux of carbon dioxide through the water layer becomes constant. There exists a minimum gas flow rate necessary to supply the water layer with this amount of carbon dioxide. This minimum gas flow rate can be estimated as follows. The steady-state flux, J, of carbon dioxide through the water is given by eq 4, where C,, is the aqueous concentration
(4) of carbon dioxide a t the membrane surface and Cx=L = 0, because at x = L the solution is assumed to be in contact with ion-exchange beads. By use of a value of L = 0.020 cm (0.008 in.), the area of the membrane, and the constants from eq 1 and 2, the estimate of the required volumetric flow rate of sample gas was found to be -0.05 mL min-'. Thus gaseous diffusion can maintainthe required steady-state flux of carbon dioxide without a significant concentration gradient developing on the gas side of the membrane. This predicted insensitivity to gas flow rate is the result of the relatively small values of Kp and K,, which govern the solubility of carbon dioxide in water. To test this conclusion, the dependence of the steady-state conductance on gas flow rate was studied and the results are given in Table I. There is a detectable decrease over the gas flow range 0.02-2.0 L min-l, -4%. We attribute this conductance decrease to increased evaporative cooling of the thin layer at higher gas flow rates. Ion-Exchange Bed Life. In time, the ion-exchange beads immediately adjacent to the screen become exhausted by reaction with hydrogen and bicarbonate ion originating from dissolved carbon dioxide. As a result, the concentration gradient, DE,, shown in Figure 2, extends further into the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
1769
Table 11. Spacer Materials Used to Support the Mixed-Bed Ion Exchanger material name and description
manufacturer
thickness, in.
characteristics
polypropylene screen (PP5-100-149) nylon screen (HC-3-110) nylon screen (Nitex ASTM 3-325-44) uni-pore polycarbonate filtration membrane Zitex fibrous TFE filtration membrane
Tetko, Inc., Elmsford, NY Tetko, Inc., Elmsford, NY Tetko, Inc., Elmsford, NY Bio-Rad Laboratories, Richmond, CA ChemDlast, Inc., Wavne, NJ
0.008 0.004 0.003 0.006-0.007 0.005
34% open area 42% open area 31% open area 5
pore size
30-60 Dore size
Table 111. Response Characteristics of the Different Cells Using Different Spacer Materials conductance, S
response time, s
spacer
NZ
1% coz
t50
t90
t98
polypropylene screen nylon screen nylon screen (Nitex ASTM 3-325-44) Uni-Pore Zitex filter membrane no spacer
1.41 1.33 1.40 0.961 1.33 1.31 9.40
22.55 21.09 21.58 12.27 14.05 18.35 41.30
5 5-7 3-5 4-6 2-5 3-5
