638
Anal. Chem. 1989, 6 1 , 638-640
T a b l e I. Comparison of Performance between Wire Probe a n d Photoetched Probe
coil
Q(un1oadedIa
Q(1oadedIb
photoetched probe wire probe
266 256
231 192
optimal pulse width,‘ SINd LWe 15 16
42 27
3.0 4.2
‘Q = 2n(fo/Af0,71).where fo denotes resonance frequency; b.fo,71, bandwidth at 0.71 peak height. * Q estimated with a phantom containing 100 mM bicarbonate, 10 mM ATP, 20 mM PCr, 1 mM EDTA, 1% NaN,, and 3.7% gelatin, pH 7.3. CMeasuredwith peak heights of a single scan by using a standard containing 100 mM phosphoric acid. dThe ratio of the peak height to rms noise on one scan of 100 mM phosphoric acid. eApproximate line width of 100 mM phosphoric acid in hertz. decoupled natural abundance 13C spectrum of the avocado is shown in Figure 3. The ‘H decoupling probe employed a modified concentric loop-gap resonator design for efficient proton decoupling, although this use of the coil design has not been previously reported. It is clear that considerable flexibility and precision are inherent in this fabrication technique in terms of coil sizes, shapes, width of copper foil, and interturn spacing. For example, in cases where a coil conforming to the sample shape (e.g. kidney) is desired, a photograph of the sample can be digitized as a bitmap into the computer by using a common optical scanner, and the coil can be drafted accurately on the basis of the sample profile by tracing the bitmap from the
CAD program. As many CAD programs are also capable of producing drawings based on complex calculations, this fabrication scheme can reduce the gap between theoretical designs and actual testing of such probes. Finally, although we demonstrated this fabrication techniuqe on planar coils, it can be readily extended to three-dimensional coils such as Helmholtz or solenoid by turning to three-dimensional CAD programs capable of “unwrapping” a three-dimensional design for two-dimensional transparency printing, and by wrapping the transparency over cylindrical or flexible PC boards (3) to photoetch. Perhaps the most rewarding probe designs involve the testing of coils that integrate all three approaches, a task facilitated by the fabrication method described here. Registry No. ATP, 56-65-5; Cu, 7440-50-8.
LITERATURE CITED (1) Gadian, D. G. NMR and Its Applicatbns to Living Systems; Oxford University Press: Oxford, England, 1982. (2) Tiffon, B.; MispeRer, J.; Lhoste, J-M. J . Magn. Reson. 1988, 68, 544. (3) Barker, P.; Freeman, R. J . Magn. Reson. 1085, 6 4 , 334. (4) Fukushlma, E.: Roeder, S. E. W. €xper/menta/ Puke NMR. A Nuts and Bolts Approach; Addison-Wesley Publishing Co.: London, 1981; pp 379, 380. (5) Murphy-Boesch, J.; Koretsky, A. P. J. M g n . Reson. 1083, 5 4 , 526. (6) Hyde. J. S.; Froncisz, W.; Jesmanowicz. A,; Kneeland, J. B. Med. Phys. 1987, 13, 1. (7) Chang, H.; Chew, W. M.; Weinstein, P. R.; James, T. L. J . Magn. Reson. 1087. 72, 168.
RECEIVED for review October 12,1988. Accepted November 28, 1988. This work was supported in part by NIH Grant P41RR02479.
Coupled Ion-Selective Electrode Measurement of Aqueous Carbonate and Bicarbonate Ion Activities John D. Pigott’ Laboratoire de Geologie d u Museum National d’Histoire Naturelle, 43 rue de Buffon, 75005 Paris, France, and School of Geology and Geophysics, University of Oklahoma, 100 East Boyd, Norman, Oklahoma 73019 INTRODUCTION Previous development of carbonate and bicarbonate ion selective electrodes has been hindered either by poor selectivities (e.g. chloride interference: (1-3)) or by restricted pH M COS2-for the membrane electrode ranges (C8.5 for 4 X of Herman and Rechnitz ( 4 ) ) . Nonetheless, it is surprising that the potential uses and demands for these electrodes have not as yet led to their commercial manufacture, especially with the increasing applied interest in the field of ion selective electrodes ( 5 ) . Reported herein are the theoretical development and initial experimental results of carbonate and bicarbonate ion electrodes based upon a novel use of available products. THEORETICAL DEVELOPMENT Mass Action Fundamentals. Research in field aquatic systems, principally with carbon dioxide dynamics, requires the determination of the activities of the carbonate ion. This ability to quantify C032-is fundamental to an ability to resolve saturation states of lagoons, open oceans, and pore waters with respect to a variety of calcium carbonate phases, e.g. calcite, aragonite, and a spectrum of magnesian calcites. The classic oceanographic approach (titration alkalinity, pH, apparent
dissociation constants, etc. (6))works well in open oceans where major ions are fairly conservative with respect to chlorinity. However, the surface and pore waters of estuarine to normal marine to hypersaline natural systems are not amenable to such assumptions of major ion conservation. In these cases, conventional wisdom dictates a total chemical analysis with subsequent calculations for ionic strengths and activity coefficients. However, much of the tedium, calculative procedure, and incumbent error by measuring concentrations and then indirectly assessing carbonate ion activities could be minimized by using the coupled electrode technique. First, we need K1 and K2,the first and second dissociation constants of carbonic acid, respectively (7), a t 25 “C
K, = a H C O s ~ H + / a H 2 ~ 0 ,=p K2 = ~ c o ~ ~ ~ H + /=~ 10-10.329 Hco~-
(2)
where (7) H2C03* = H 2 C 0 3+ C02(dissolved)
(3)
and a represents activity. Second, by combining eq 1 and 2, one has aco32- =
’Present address: University of Oklahoma.
(1)
K & I ~ H ~ C O ~ * / ~ H + ~ (4)
That is, measuring the activities of the hydrogen ion and
0003-2700/89/0361-0638$01.50/0 0 1989 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 6, MARCH 15, 1989
639
Table I. Experimental Results
mL of acid added’
pH
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
11.409 10.153 9.725 9.361 8.911 7.450 6.802 6.697 6.426 5.908 1.739 1.260
aHcoa-
aCog2-
6.00 X 4.36 X 2.98 X 1.79 X 7.36 X 1.66 X 3.73 X 3.86 X 1.49 X 1.69 X 9.25 X 1.14 X
4.94 X 6.57 X 1.18 X 1.66 X 1.89 X 1.25 X 1.23 X 1.64 X 1.17 X 4.42 X 3.52 X 1.33 X
lo”’ lo-’ 10” 10” 10“ lo-’
10”’
lo-’
10” lo-”
lo-’
aH2C03*
4.31 X 1.03 X 4.95 X 1.62 X 5.21 X 9.93 X 4.34 X 7.35 X 9.89 X 1.23 X 1.44 X 3.11 X
lo-’ 10“ 10” 10”’
EmV(pH)
EmV(H2C03*)
-270.3 -195.1 -169.5 -147.7 -120.7 -33.2 5.6 11.9 28.1 59.1 308.8 337.5
-104.6 -106.2 -100.5 -80.5 -46.9 48.4 61.3 59.8 61.4 63.2 59.9 64.6
EmV(C032’)
-214.9 -138.8 -116.2 -105.0 -95.8 -58.9 -26.9 -19.8 -4.4 25.6 277.1 303.3
EmV(HC03-) -159.1 -82.2 -62.7 -62.1 -70.8 -84.6 -59.6 -51.7 -37.2 -8.1 245.1 268.8
OTo 50 mL of 0.500 M Na2C03at 25 O C , mL of 1.053 N HCl were added with constant mechanical stirring; Emvreadings were recorded after 1 min. H&O3* directly determines the activity of the carbonate ion. Similarly, one can also observe from inspection of eq (1)that the activity of the bicarbonate ion is likewise directly determinable. This manipulative procedure, omitting the conventional method of measuring by titration the carbonate alkalinity, has been employed extensively and successfully by myself and my students in a variety of natural waters using simultaneously the Orion Ross combination pH electrode and the Orion carbon dioxide electrode. Furthermore, the procedure is in part the mechanicaI basis for the described carbonate and bicarbonate ion selective electrodes. Nernst Derivations. Let us assume that the carbonate ion electrode can in principle involve eq 4,and that its electrochemical response is some Nernstian function of the behavior of its component parts, in this example an Orion Ross pH electrode and an Orion carbon dioxide electrode. For the experiment discussed in the following section, the operational response of the p H electrode a t 25 OC to earlier buffer calibration was measured to be EmV,H+ = 413 59.0 log U H + (5)
+
and that of the carbon dioxide electrode to be Solving for
uH+
we have
uH+ = 10(Ern~,~+-413)/59.0
(7)
and similarly for U H ~ C O ~we . have
aHZCO3~ = 1O(E,~,~~0~*-193/55.5
(8)
By substituting these observed Nernst electrode equations into eq 4,combining K1 and K 2 values of eq 1 and 2, and simplifying, one finds a t 25 “C: EmV,H+ - O.i%E,v,~,co,~=
-181.7 - 29.5 log
Uco32-
(9)
which provides the theoretically observable response of the logarithm of the activity of carbonate ion to be linearly related to the difference between the voltage of the combination pH electrode and 0.53 that of the carbon dioxide electrode. This voltage difference may be described, then, as that of a “differentially coupled double junction (i.e. Ross combination pH electrode)-attenuated membrane (Le. 0.53 of the voltage output of a carbon dioxide membrane electrode) carbonate ion electrode”, or Ernv,co32-= -181.7 - 29.5 log U C O ~ Z (10) Thus we shall assume eq 10 to be the predicted operational Nernst equation for which we shall test the carbonate ion electrode. Note that the predicted slope of -29.5 mV per log unit of activity is 99.7% that of a perfect Nernstian slope of -29.6 mV log unit of activity for divalent ions a t 25 “C (7).
In a like fashion, one can derive the predicted Nernstian response of a similarly constructed bicarbonate ion electrode. Recalling the Nernst equations (7 and 8) obtained experimentally for the pH and carbon dioxide electrodes, respectively, and from a rearrangement of the mass action relationship of eq 1, one has
which provides the theoretical response of the logarithm of the activity of the bicarbonate ion to be a linear function of the difference between the voltage of the pH electrode and 1.06 that of the carbon dioxide electrode. This specific voltage difference may be described as a “differentially coupled double junction-amplified membrane bicarbonate ion electrode”, or expressed by the predicted operational Nernst equation
Note that this predicted slope of -59.0 mV per log unit of activity is 99.7% of a perfect Nernstian slope of -59.2 mV per log unit of activity for monovalent ions a t 25 O C (7). This response was also experimentally tested.
EXPERIMENTAL SECTION Design. The following experiment in electrode behavior was conducted in a temperature bath at 25 f 0.1 “C using an Orion Ross combination pH electrode coupled to an Orion carbon dioxide electrode, a Fisher titrimeter (fO.01 mL), and a Fisher Accumet Ion meter (fO.l mV). To 50-mL portions of 0.500 M Na2C03, 5.00-mL incrementa of 1.053 N HCl were added. Magnetic stirring was continuous. One minute after each addition, the readings of both electrodes were recorded. In this fashion, the Na2C03 solution was acid titrated from an initial pH of 11.409 to a final pH of 1.260. The primary experiment consisted of 0.53 attenuation of the potential of the carbon dioxide electrode output (calculated mathematically in this instance from the reading) which was then subtracted from the pH combination electrode output, eq 9. The secondary experiment conducted simultaneously consisted of 1.06 amplification of the potential of the carbon dioxide electrode output subtracted as described by eq 11. RESULTS The titrated solutions were corrected for changes in dilution, in changes in ionic strength (mean-salt and Davies equations (7)), and solved for activities of bicarbonate, carbonate, and H2C03* by simultaneous solution of one mass balance, one charge balance, and two mass action equations. These activities, pH, and the observed voltages for the pH, carbon dioxide, carbonate, and bicarbonate electrodes are listed in Table I. As a point of electrode behavior reference, the performance of the commercially available Orion carbon dioxide electrode is illustrated in Figure 1. Recall from eq 6 that for the activity
640
ANALYTICAL CHEMISTRY, VOL.
61, NO. 6,MARCH 15, 1989
CARBON DIOXIDE ELECTRODE RESPONSE
\a
~
L
O l
I
,
V
I
-150
:1
4
IE-09
250
Em
, , ,.,.
-:
IE48
,
,
-
_". IE-05 1E-04 ACTIVITY Cf HZC03.
IE-06
lE-03
IE-02
IE4I
Figure 1. Experimental output of the Orion carbon dioxide electrode at 25 OC as a function of H2C03* activities (see text for description of solution chemistry). Regression line for electrode performance includes only the activity range between 4.95 X lo-' and 7.35 X and excludes data points either below or above these ion electrode sensitivities. 50
s -200
CARBOWAE ION ELECTRWE WSPONSE T
ti
b
-250 lE-07
3
1E-96
b
193 + 55 5 log WC03'1 r - 0 9 9 n.6
,...,;
IE-07
BICARBOWATE ION ELECTRWE RESPOWSE
300
,
lE45
IE-04
1E-03
lE-02
ACTIVITY ff C03-
Flgure 2. Experimental output of the attenuated coupled double junction-membrane carbonate ion electrode at 25 OC as a function of C03*- activities (see text for description of solution chemistry). Regression line for electrode performance includes only the activity and excludes data points range between 1.69 X lo-' to 4.36 X below these ion electrode sensitivities. range between 4.95 x IO4 and 7.35 x this electrode's slope was statistically regressed to be 55.5 mV per log unit of dissolved carbon dioxide ( r = 0.99, n = 6), or 94% Nernstian. Data points outside this range of optimal electrode response are also shown. The carbonate ion electrode response is illustrated in Figure 2. For a carbonate ion activity range of 1.69 X to 4.36 x or approximately 4 orders of magnitude, and at the extremely broad pH range of 5.91-10.15 the electrode responded statistically ( r = -0.99, n = 9) with a slope of -34.0 mV per log unit of carbonate ion activity ( r = -0.99, n = 9). The observed Nernst equation is E,, = -207.3 - 34.0 log aCo3z(13) which is about 15% higher a slope than that theoretically predicted (eq 10) or 85% that of a perfectly Nernstian response. Operational precision at the f0.1 mV level is f2.9%. Figure 3 illustrates the behavior of the bicarbonate ion electrode as a byproduct of this experiment. Though the experiment was designed to principally evaluate the carbonate electrode, thus biasing on purpose the solutions toward high and low bicarbonate activities, the performance of the bicarbonate electrode was comparable. Excluding the errant 178.3 mV data point, the statistically ( r = -0.99, n = 11) observed Nernst equation is The -66.5 mV per log unit of bicarbonate ion activity slope is about 13% higher a slope than that predicted (compared to eq 12) or 88% that of a perfectly Nernstian response. Operational precision a t the f O . l mV level is f1.5%. Therefore, the response of the bicarbonate electrode to the broad 6.57 X to 1.33 X lo-' range of bicarbonate activities
IE-07
IE-06
lE-05
IE-04
IE43
lE-02
IE-01
ACTIVITY of HC03-
Figure 3. Experimental output of the attenuated coupled double junction-membrane bicarbonate ion electrode at 25 "C as a function of HC03- activities (see text for description of solution chemistry). Regression line for electrode performance excludes errant -159.1 mV datum. tested is slightly better than that of the carbonate ion electrode.
DISCUSSION The experimental data for the carbonate ion electrode and bicarbonate ion electrode should be viewed as encouraging and perhaps possibly stimulating to further technological development. These coupled specific ion electrodes exhibit approximately 85% of a Nernstian response to carbonate ion activities and 88% of a Nernstian response to bicarbonate ion activities between and activities of carbonate and bicarbonate ions, a t 25 "C, and at pH values from 5.9 to 10.2. Operational precision for the carbonate and bicarbonate electrodes is limited a t the f0.1 mV level to f2.9% and =k1.5%,respectively. Therefore, the theoretical and experimental responses of the two electrodes are similar, the pH ranges broad, and the response ranges selective yet also broad. Although mechanically this electrode design is not as asthetically pleasing as a refined manufactured model might someday be, it does work and offers immediate benefit to those aquatic scientists who require carbonate and bicarbonate ion measurements now. Operationally, to make these selective ion determinations, one needs only to couple (mathematically or electronically) the combination pH electrode and carbon dioxide electrode as described by the left sides of eq 9 and 11and follow standard calibration-measurement procedures. ACKNOWLEDGMENT I thank James Ross of Orion and Patricia K. Bettis for encouragement in developing the coupled-electrode technique, Jeff Silfer for help in the experiments, and Der-Duen Sheu for editing an early draft. The discussed theoretical background of ion activity measurements by electrodes benefited from early thermodynamic discussions with R. Garrels, L. S. Land, A. Lerman, and F. T. Mackenzie. The applied environmental uses and conceptualization of a carbonate ion electrode were an outgrowth of research collaboration with Karl Van Keuren, Jefferson E. Laughlin, Douglas G. Neese, and Nancy I. Trumbly. LITERATURE CITED (1) Grekovich. A. L.; Materova, E. A.: Garbuzovz, N. V. Zh. Anal. Khim. 1983, 78, 1206. (2) Coetzee, C. J.; Freiser, H. Anal. Chern. 1969, 4 1 . 1128. (3) Ross, J. W. I n lon-Selectlve Electrodes; NBS Spec. Publ. 314 Durst, R. A,. Ed.; National Bureau of Standards: Washington, DC, 1969: Chapter 2. (4) Herman, H. 0 . ; Rechnitz, G. A. Science 1974, 184, 1074. (5) Solsky, R. L. Anal. Chem. 1988, 6 0 , 106R. (6) Pigott. J. D.: Land, L. S. Mar. Chern. 1986, 355. (7) Stumm. W.; Morgan, J. J. Aquat. Chem. 1981, 780 pp.
RECEIVEDfor review July 11, 1988. Accepted December 8, 1988.
