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Anal. Chem. 1985. 57. 2116-2120
nificantly deplete the analyte, provided that the sample volume is large enough. Although, the final steady-state values are the same for both the electrodes, the main advantage of using HC1 instead of NH&l is much faster recovery. Changing the internal filling solution can be made using both Double Injection (microelectrode)and modified jacket electrodes. The limitation of the Double Injection sensor is in its dynamic properties, whereas the modified jacket electrode cannot use filling solutions antagonistic to the reference junction. In the case of enzyme analyses, interfering gases, if any, can be removed from the sample prior to the analysis by any of the degassing techniques, such as those developed in liquid chromatography.
CONCLUSION In order to improve the analytical performance of ammonia and urea ISEs, five out of the six steps of an individual assay have been studied. The “Double Injection Electrode” described here, built on a tip-microelectrode, improves the changing and holding of the sample, dissolution of the gas in the filling solution, pH measurement, and especially base line recovery, making the ammonia assay extremely fast (full cycle
with base line recovery less than 1 min). A new “titration” principle of a gas-ISE filling solution has been proposed and found to be useful for some analytical problems. Registry No. Ammonia, 7664-41-7; urea, 57-13-6.
LITERATURE CITED Clark, L. C.; Lyons, C. Ann. N . Y . Acad. Scl. 1962, 102, 29. Updike, S.; Hicks, G. Nature (London) 1967, 2 1 4 , 986. Guilbault, G. G.; Das, J. Anal. Blochem. 1970, 3 3 , 341. Guilbault, G. G. “Handbook of Enzymlc Analysis”; Marcel Dekker: New York, 1977. Riley, M. In ”Ion Selective Electrode Methodology”;CRC Press: Boca Raton, FL, 1979;Vol. 11, Chapter 1. Guilbault, 0. G.; Tarp, M. Anal. Cbim. Acta 1974, 7 3 , 335. Mascini, M.; Gullbault, G. G. Anal. Chem. 1977, 49, 795. Havas, J.; Guilbault, G. G. Anal. Chem. 1982, 5 4 , 1999. Hansen, E. H.; Larsen, N. R. Anal. Chim. Acta 1975, 7 8 , 459. Meyerhoff, M. E. Anal. Chem. 1980, 52, 1532-1534. Arnold, M. A. Anal. Chlm. Acta lg83, 154, 33-39. Ross, J. W.; Riseman, J. H.; Krueger, J. A. Pure Appl. Chem. 1973, 3 6 , 473-487.
RECEIVED for review November 5, 1984. Accepted May 20, 1985. The authors kindly appreciate the financial support of the Environmental Protection Agency (Grant No. R808532).
Chronopotentiometry at a Dropping Mercury Electrode: Effects of Electrode Sphericity for an Electrode Process with a Preceding Chemical Reaction Jesus Galvez* and Maria L. Alcaraz Laboratory of Physical Chemistry, Faculty of Science, Murcia 30001, Spain
Tomas Perez and Manuel H. Cordoba Laboratory of Analytical Chemistry, Faculty of Science, Murcia 30001, Spain
A theoretical study of the kinetic response for the CE mechanism in DME chronopotentiometry by using a perturbation function of the form Z ( t ) = ZoPis presented. Equations for the potential-time curves and for the transition times have been derived by taking into account the sphericity of the electrode. An experimental verification of the theory has been carried out with the Cd2+/EDTA system by using the function Z ( t ) = l o t .
In a previous paper (I),we developed the theory concerning the use of the perturbation function I ( t ) = IOtW+1/6 (w 2 0) for a single-transfer reaction. We adopted the expanding sphere electrode model (ES) and showed that the effect exerted by the sphericity of the electrode on the transition times may be so great that the more simple model of expanding plane electrode (EP) for the DME is not valid. On the other hand, the theory for the CE mechanism in DME chronopotentiometry has been also derived (Z), although the EP model for the DME was used. Hence, the aim of the present paper is to extend the corresponding theory for this mechanism by adopting the ES model and to make clear the influence exerted by the curvature of the electrode on the kinetic response. The theory has been tested by obtaining the rate constant values for the system Cd2+/EDTA from measurements of poten-
Table I. Notation and Definitions heterogeneous rate constants of the forward and reverse charge-transfer reaction apparent heterogeneous rate constant for charge transfer at Eo rate constants of the chemical reaction equilibrium constant of the chemical reaction ( = k 2 / k l ) constant of proportionality of electrode area time-dependent electrode area (=Aot2l3) rate of flow of mercury (3m/47rd)‘i3 spherical correction parameter (=(12Di/ (7$2))’/2t’/6)
(12Di/(7$2))’/2 (Dc/OD)
time-dependent electrode potential E(t)- E o time-dependent Faradaic current (=IOt”+1/6) constant applied rate of Faradaic current increase (eq 1) kinetic transition time for the ES model transition time for the ES model when no kinetic effects are involved Euler gamma function other definitions are conventional
tial-time curves ( E / t ) and transition times.
THEORY Notation and definitions are given in Table I. A CE mechanism is described by the scheme
0003-2700/85/0357-2116$01.50/00 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL.
kl
kf
k2
kb
B S C + n e - Z D
58
By application of the ES model (3), the corresponding differential equations are obtained. If double-layer effects are neglected, these equations can be solved by adopting the derivational pattern described in ref 1 and 2. Thus, if I ( t ) has the form ( 4 )
I ( t ) = I0tW+1/6
57, NO. 11, SEPTEMBER 1985 2117
t
0
(1)
w10
w
s
the transition time, re, is given by
-50
3 -iw
where
x=Kt
K=K,+k2
(3)
and rd,e is the transition t h e for the ES model when no kinetic effects are involved (1). In eq 2 the Gw,e(x) and R functions are defined in the Appendix. Note that if the spherical correction is neglected, we have R = 1 (see Appendix) and eq 2 is simplified to that previously derived for this mechanism by adopting the EP model (2). In turn, the corresponding relationship for the E / t curves in a dimensionless form is written as
(e( w , t ) ) - W v (w,t )lo"'@)=
-150
I
2
4
6
8
10
t/m Figure 1. Dependence of A € ( t )on t for different values of k , : Bo = 20s~',N0=0.5s-1'2,w=1/2,K=1,n~1,T~298K,a!~0.5, = 0.15 s-1'8, T , , ~= 11.04 s. Values for k , (s-') are (1) 5 X (2) 0.5, (3) 5, (4) 50, and (5)1000.
where
= 6'ot/P2,w,, 60'
= 12k?/(7Dc)
(5) (6)
nF(E(t) - E O )
(7) RT In 10 and N(w,t) and Ni*(w,t)are also given in the Appendix. For a reversible charge-transfer reaction (k, 1. Note that according eq 2 the value of k, for which re Td,e depends on K and so, if K = 1 we find re/rd,e 1 0.99 for kl 1. 3200 s-'. Figure 2 illustrates the effect of the equilibrium constant, K , on the E / t curves for kl = 5 s-l. These curves show the behavior predicted by eq 2 and 4 so that the E / t curves shift
2118
ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
Table 111. Dependence of A E ( t ) on t / r O t/r 60
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
e >
.! -w Y n .u
19.15 -0.08 -13.51 -25.04 -36.11 -47.72 -61.08 -78.50 -107.31
20.52 1.18 -12.29 -23.81 -34.84 -46.39 -59.64 -76.88 -105.37
"Normalized E / t curves for w = 5/6, kl = 3 s-l, K = 1, No = 0.4 s-5/6, Bo = 10 s-l, and .&,,c(s-1/6) = (I) 0.15; (11) 0.0. Other conditions
Q
are given in Figure 1. -I 88
I
0.1
045 -1s)
1
e..
2
d
3 n
3
t/n Figure 3. Potentlal-time curves for Bo = 20 s-', N o = 0.5 s - ~ k, l = 5 s-l,K = 1. w values are shown on the curves. Values for (&I6) are (-) 0.15 and (---) 0.0. Other conditions are given In Figure 1.
e.8
\
0
5
U
(r?
8.4
10
10-3 0.1 0.5 1 1.5 2 3 4 5 7 10 15 20 50 100 500 1000 104
0.23 0.24 0.33 0.60 1.15 1.69 2.50 3.01 3.49 4.09 4.67 5.24 5.60 6.51 6.99 7.66 7.82 8.09
0.25 0.27 0.38 0.74 1.41 2.03 2.97 3.64 4.14 4.83 5.53 6.24 6.68 7.19 8.39 9.22 9.42 9.76
0.28 0.30 0.44 0.93 1.73 2.47 3.60 4.42 5.00 5.86 6.75 1.64 8.21 9.64 10.41 11.50 11.76 12.20
"Values of T computed from eq 24 for w = 112, K = 5, and No = 0.5 s-1/2, gnr (s&% (1)0.0; (2) 0.1; (3) 0.2.
toward more negative potentials and the transition times decreaee as K becomes greater. The influence exerted by the perturbation function is shown in Figure 3 where we have plotted E / t curves for different values of w. By comparison we have also included the corresponding curves for the EP model. Note that the behavior of these curves is similar to that obtained for a single electron transfer (1))and so, the effect exerted by the sphericity of the electrode decreases as w becomes greater. On the other hand, dependence of T , on the curvature of the electrode is shown in Table I1 where we have computed from eq 2 values of 7, for w = 1/2, K = 5, No = 0.5 d2, and different values of kl and so,c. These results make clear that if absolute values of 7 are necessary they must be obtained taking into account the curvature of the electrode. However, it is interesting to show
8.2
1
te
20
38
x r.
Flgure 4. Dependence of R(7,1rd,J" vs. xrefor w = 112 (eq 24) and [ = 0.15. K values are shown on the curves.
that the electrode model is not critical for the analysis of E / t curves if they are normalized (see Table 111),and this situation is analogous to that previously described for a single charge transfer reaction (1). Finally, in Figure 4 we have obtained working curves R( T , / T ~ , vs. ~ ) ~xIe from eq 2 which allow determination of kl and kz if the K value is known. In those cases where K is unknown we may use a fitting procedure as described below. Experimental Results. In order to verify the theory, the cadmium/EDTA redox system was chosen. This system has been studied by several workers (6-13)and it is known that under the appropriate conditions two reduction steps occur, and the first one can be represented as ki
CdHY- q Cd2+ R2
Cd2+
+ HY3-
+ 2e- is Cd(Hg)
We have obtained a great number of chronopotentiograms at the 2.17, 2.30, 2.70 and 3.02 pH values by using different EDTA/cadmium molar ratios. Under the experimental conditions used the system is not strictly of pseudo first order with respect to Cd2+. However, the experimental results (see
ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
2119
- 0.5
- 0.2
w v) V
e
-0.6
- 0.6
.
W u v)
>
ul
e v
>
W
\
c1
W
- 1.0
- 0.7 t +
Figure 5. Potential-tlme curves for the cadmium(11)-EDTA system: C W 3 = 0.2 M; m = 0.653 mgs-l; Io = 0.6 ass-'; C, = 0.54 mM; pH 2.38. CEoTA (mM) values are (1) 2.7 and (2) 0.54.
Table IV. Theoretical and Experimental Transition Times for the Cadmium(I1)-EDTA System at 25 “C”
I,, j ~ A d 0.80 0.70 0.60 0.50 0.40 0.34 0.28 0.22
Tcnld, 5
7exptb 5
0.60 0.82 1.12 1.58 2.39 3.21 4.50 6.76
0.60 0.86 1.13 1.50 2.37 3.12 4.57 6.91
.
Comparison of the 7 values computed from eq 24 with K = 20.3 and kl = 9.5 s-l and those obtained from E / t curves. = 0.2 M, CCd= 0.54 mM, CEDTA= 2.7 mM, m = 0.653 mg-s-l, pH 2.3,DC = 6.6 X lo4 c m 2 d (computed from polarographic measurements by using Ilkovic’s equation).
below) obtained by two different approaches and by using different conditions are in good agreement with those shown by other authors. So, we think that this is a valid model to corroborate the theory. Thus, in Figure 5 we show some of the chronopotentiogramsobtained for this system at pH 2.30. In turn, in Table IV we show the experimental T, values obtained from these plots for different values of 1,. The kinetic parameters (k, and K ) have been obtained by employing nonlinear regression analysis to fit the experimental T, values to eq 2. We have found K = 20.3 and kl = 9.5 s-l and these values of kl and K have been used to obtain the theoretical transition times which are also given in Table IV. In addition, these values of kl and K have been also used to obtain from an equilibrium calculation the values of kz and the dissociation constant, Kd: kz = 2.9 X lo9 L mol-l s-l, Kd = 3.3 X M. On the other hand, we have also fitted the values of E / t vs. t / r obtained at pH 2.17 to eq 8. (Note that in this case we must evaluate three parameters, E,$, K , and kl.) The resulb are shown in Figure 6 in which we have included the E ( t ) values computed from eq 8 with kl = 12.1 s-l, K = 7.87, and El/&= -0.600 V obtained from the analysis fitting (in this case kz = 2.7 X lo9 L mol-’ s-l and Kd = 4.5 X lo4 M). Note that both in Table IV and in Figure 6 the agreement with the experimental data is excellent. Finally, it is interesting to show that the values of kl,kz, and Kd are also in agreement with those obtained by other workers (see Table I1 in ref 6), and this fact indicates that DME chronopotentiometry is an appropriate technique for the study of a CE mechanism.
o
a2
0.4
0.6
0.8 117
1.0
Figure 6. Normalized E / t curve for the cadmlum(I1)-EDTA system. The full line is the experimental curve. The points are the theoretical values computed from eq 32 with K = 7.87 and k , = 12.1 s-l. , = 0.54 mM; CEDTA Conditions were as follows: CKN03= 0.2 M; C = 2.7 mM; pH 2.17; m = 0.853 mps-’; I o = 0.4 PASS-’.
APPENDIX In eq 2 the GW,Jx) and R functions are given by
fwo’).=
2r(1
+ j/2)
The GW,Jx)function has an asymptotic behavior so that for x >> 1 we have
In eq 4 N ( u , t ) and Ni*(u,t) are given by Not”
N(w,t) = P6w/7
Ni*(w,t) = (1 - fw(o)to,it1/6)N(w,t)
(A9)
Registry No. CdHY-, 69546-70-9; Hg, 7439-97-6.
LITERATURE CITED (1) Gilvez, J.; Molina, A.; PBrez, T.; Cbrdoba, M. H. Anel. Chem. 1984, 56, 887, and references thereln.
2120
Anal. Chem. 1985, 57, 2120-2124
(2) Ghrez, J.; Mollna, A. J. flecfroanal. Chem. 1983, 146, 221. (3) Heyrovsky, J.; Kuta, J. “Prlnclples of Polarography”; Academlc Press: New York, 1966; p 542. (4) Glvez, J. J. flecfroanal. Chem. 1982, 732, 15. (5) Davis, D. J. I n “Electroanalytical Chemistry”; Bard, A. J., Ed.; Marcel Dekker: New York. 1966; Vol. 1, Chapter 2. (6) Klm, M.-H.; Birke, R. L. Anal. Chem. 1983, 55, 1735. (7) Tanaka, N.; Tamamushi, R.; Kodama, M. z. phys. Chem. (Wlesbaden) 1958, 74, 141. (8) a l v e z . J.; Serna, C.; Mollna, A,; Van Leeuwen, H. P. J. Electroanal. Chem. 1984, 767, 15. (9) Aylwood, G. H.; Hayes, J. W. Anal. Chem. 1985, 3 7 , 195.
(10) (11) (12) (13)
Matsuda, K.; Tamamushi, R. Bull. Chem. SOC.Jpn. 1988, 41, 1563. Tanaka, N.; Oiwa. 1. T.; Kodama, M. Anal. Chem. 1958, 28, 1555. Schmid, R. W.; Reilley, C. N. J. Am. Chem. SOC. 1958, BO, 210. Korlta, J.; Zabransky, 2. Collect. Czech. Chem. Common. 1980, 25, 3153.
RECEIVED for review December 12, 1984. Accepted May 1, 1985. We thank the Comisidn Asesora de Investigacidn Cientifica y TBcnica for supporting this study (Project No. 321181 and 854181).
Coated Piezoelectric Quartz Crystal Monitor for Determination of Propylene Glycol Dinitrate Vapor Levels B. D. Tumham, L. K. Yee, and G. A. Luoma* Defence Research Establishment Pacific, FMO Victoria, British Columbia, Canada VOS IBO
Coated plezoelectrlc quartz crystal microbalances have been studled as potentlal selectlve and sensltlve defectors for a wlde range of toxlc vapors, yet (due to technlcal problems assoclated wlth frequency stablllty and selectlvlty) the only major ctnnmerclal application has been the detectlon of water vapor levels. The present artlcle descrlbes the development of a worklng monitor using a plezoelectrlc quartz crystal mlcrobalance for the detectlon of propylene glycol dlnltrate (PGDN), a hlghly toxic compound used as a propellant In torpedoes. The dual crystal deslgn of the present devlce contalnlng a trap for PGDN on the reference crystal elhnlnates many of the frequency stablllty and selectlvlty problems associated wlth these detectors and produces a detection llmlt of better than 0.05 ppm In a m a l l llghtwelght portable device. The device Is hlghly selectlve for PGDN over all normal atmospherlc contamlnants and Is lnsensltlve to humldlty changes.
Propylene glycol dinitrate (PGDN) is a commonly used propellant for torpedoes. It must be handled in all servicing shops and production facilities and presents a health hazard to exposed workers (1). Studies on inhalation of vapors by numerous animal species including a single report on humans suggest that a few hours of exposure to concentrations as low as 0.1 ppm can produce symptoms such as headaches and nausea (2-7). Exposures to higher concentrations cause more serious effects such as the production of methemoglobin (7). The present TLV for PGDN in Canada is 0.02 ppm, while in the U.S.it is 0.05 ppm. Therefore, effective means of monitoring very low levels of PGDN vapors must be available to avoid exposure of workers to toxic levels. Several physical properties of PGDN increase both its potential as a hazardous material and the difficulty in its detection. First, the maximum concentration of PGDN vapor obtainable in an environment is -90 ppm at 20 OC, and PGDN also does not mix readily with air (1). Therefore, concentrations from a spill can buildup slowly in localized Present address:
C a p i t a l A p p l i e d Research a n d Technolog
Ltd., Discovery Park, U n i v e r s i t y of Victoria, Victoria, BC,Cana& vaw 2 ~ 2 . 0003-2700/85/0357-2120$01.50/0
areas. Second, it decomposes at temperatures above 160 “C, making its analysis by gas chromatography using heated injectors difficult. Finally, it easily penetrates through many organic polymers and adsorbs on most surfaces, making accurate determination of concentrations difficult. Because of these properties no portable instruments which can effectively monitor PGDN concentrations for extended periods exist (1). The use of coated piezoelectric crystals for the detection of specific toxic vapors has been studied extensively (8-13). Coating materials for the detection of a large variety of atmospheric pollutants including sulfur dioxide in combustion emissions, ammonia, and organophosphorus pesticides have been investigated. However, field-usable instruments have not been produced for any of these applications due to a number of engineering difficulties in producing coated piezoelectric crystal detectors. The lone exception is the Du Pont Model 303 moisture analyzer (8). In principle, the function of the detector is simple. A quartz crystal is coated with a material which will specifically adsorb, absorb, or react with the compound to be detected. The crystal is then allowed to oscillate at its natural frequency which can be monitored to an accuracy of better than 0.1 Hz. When the crystal coating interah with the specific compound, the weight of the crystal increases which causes a decrease in oscillating frequency roughly according to Sauerbrey’s equation (14)
hF = (-2.3
X
106)F(AMs/A)
where AF is the change in oscillating frequency (Hz), F is the oscillating frequency of the quartz crystal (MHz), AMs is the change in mass of the crystal, and A is the area of the interaction with the coatings (cm2). This equation predicts that crystals with high oscillating frequencies will produce a greater frequency change and that a small coated area is desirable. However, to obtain durability and frequency stability at a reasonable price, crystal oscillating frequencies of about 10 MHz are preferable, and the coated area must be large enough to interact quickly with the desired compound. With these compromises, sensitivities (in the parts-per-billion range) to the various toxic gases mentioned above have been obtained (8-13).
The major problems associated with coated piezoelectric crystal detectors arise from adapting them for field usage and Publlshed 1985 by the Amerlcan Chemlcal Soclety
