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Determination of magnesium and calcium in water with ion-selective electrodes
Analytica Chimica Acta, 218 (1989) 47-59 Elsevier Science Publishers B.V., Amsterdam -
47 Printed in The Netherlands
DETERMINATION OF MAGNESIUM AND CALCIUM WITH ION-SELECTIVE ELECTRODES
IN WATER
MAGDALENA MAJ-ZURAWSKA”, MARIZEL ROUILLY, WERNER E. MORF and WILHELM SIMON* Department of Organic Chemistry, Swiss Federal Institute of Technology (ETH), CH-8092 Ziirich (Switzerland) (Received 12th August 1988)
SUMMARY The sum of the concentrations of calcium and magnesium in water samples can be determined directly with a neutral carrier-based Mg+/Ca’+-selective electrode (divalent ion-selective electrode), without addition of any auxiliary complexing agent such as acetylacetone. This approach works well, even in situations where calcium-selective electrodes do not detect the second inflection point because the calcium/magnesium concentration ratio is too high ( [ Ca2+ ] : [ M$+ ] > 5 : 1) or the sodium concentration is high. With high levels of acetylacetone (0.1 M) the divalent ionselective electrode can also be used for calcium determinations. For such measurements, however, the standard deviations obtained with the calcium-selective electrode are smaller. A theoretical description of titration curves corroborates these findings.
Recently, magnesium ion-selective electrodes based on the neutral carrier N,iV” -0ctamethylenebis (N’ -heptyl-N’ -methyl malonamide ) (ETH 4030) were described [ 11. In certain membranes, this ionophore exhibits equal selectivity for Mg2+ and Ca2+ and rejects all alkali metal and all other alkalineearth metal ions, preferring Mg2+ over Na+ and K+ by factors of up to about 10 000 [ 11. Such electrodes are interesting candidates for determinations of water hardness. The high selectivity against Na+ allows the determination of Ca2+ and Mg2+ in samples with a high sodium background, which would be especially valuable for highly polluted river water and for sea water. A determination of Ca2+ and Mg2+ under these conditions with a so-called divalent ion-selective electrode [ 21 ( Mg2 + /Ca2+-selective electrode) has not been possible previously [ 31. Here, the application of the recently described electrode [l] is reported for *Permanent address: Chemistry Department, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland.
0003-2670/89/$03.50
0 1989 Elsevier Science Publishers B.V.
48
determinations of magnesium and calcium in water and the results are compared with those obtained by using a highly selective calcium electrode. THEORY
Computer simulation of titration curves For modelling the simultaneous titration of two species M and N with a ligand L (here the titration of calcium and magnesium ions with EDTA) , the following mass-balance equations are taken into account:
Ll+ [ML1+ WLI = Ll,; WI + [ML1= WI, [N] + [NL] + [NLL] = [N],;
[L’] +n[NL:,]
= [L’],
where [X] and [X ] t are the individual and the total concentrations of species X, respectively. The two relationships containing [NE:,] cover the situation where a second complex-forming agent L’ selective for N is added to the sample solution prior to the titration (e.g., the addition of acetylacetone for complexation of magnesium ions). For simplicity it is assumed that such an additional ligand forms complexes of a given 1: n stoichiometry (stability constant j3) and is present in excess. Hence, the following approximations are obtained: [L’
I= L’ It; [NL:,l =P[Nl L’ It”
The complex formation induced by the ligand of the titrant is characterized by the respective stability constants K ML and I&, the latter being assumed to have the lower value (i.e., the end-point for the titration of species M appears first ) :
[MLI=&L[MI ELI; WLI=KNL[NI [Ll All values [X] t in the above equations correspond to the actual total concentrations at the time when a volume increment dV= V,- V, of titrant is added to the sample. They are related to the initial concentrations [Xl, of sample and titrant, respectively, as follows:
Ll,= Llo(vt-vo)Ivt; [Ml,= [WoVo/V, WI, = Plo Vo/Vt; L It = L’ lo VOW, Accordingly, the actual concentrations [X] of all species involved can be calculated as a function of the volume of titrant added, V,- VO.Combination of these relationships finally leads to the following equations as implicit solutions for [M] and [N] , respectively:
49
W13(1-W-
PWW--k)
([Ml,+ WI,- LM-
(kWl,+ WI,)
WI (l+P[L’ I;) = ( WI, + WI, - WI,) - WI + ( Wit - WI
)I&L[MI
(2)
where k characterizes the relative selectivity of the titration reaction:
k=KNLI{K~L(l+P[L’ltn))
(3)
Equation 1 is an extended version of an expression reported earlier [ 3, 41 which was derived for the compleximetric titration of calcium (M) and magnesium ions (N) without additional ligand (L’ ). In order to obtain more appropriate explicit descriptions of the titration curve near the first and second end-points (indicating the consumption of M and N, respectively), one can delete the last and the first term in Eqn. 1, respectively. In both instances the cubic equation reduces to a quadratic one. The calculated concentrations of unchelated Ca2+ and Mg2+ ions during compleximetric titrations with EDTA are shown in Fig. 1. The curves were simulated for different concentrations of the magnesium-masking ligand acetylacetone and are given as a function of the fraction titrated, F=dV/dVEP2, where dVEp2 represents the volume of titrant added at the second end-point (i.e., at the equivalence point for the sum of titrated ions). The total concentrations [Ml0 and [N],, chosen are the reported mean values of calcium and magnesium concentrations [5] in fresh water (Fig. la) and sea water (Fig. lb). The values of KML, KNL and /3 to be inserted in Eqns. l-3 are the conditional constants which depend on the pH value. In real titration experiments, the pH of the sample is buffered with Tris to ca. 8.5, as recommended for EDTA titrations with calcium-selective electrodes [ 61. It should be mentioned, however, that the ratio KNL/K ML (magnesium/calcium) has a constant value of 0.01 over a large pH range. In the present calculations, the values of KML,P&L and p (assuming n= 1) were estimated to be 108, lo6 and 250, respectively, which resulted in good qualitative agreement between the calculated and observed titration curves (see below). It becomes evident from Fig. 1 that the Ca2+ concentration curve is considerably influenced by the complex formation of Mg2+ ions with acetylacetone. An increasing concentration of acetylacetone masks the magnesium ions partly (for [L’ ],,=O.Ol in Fig. la or 0.01-0.02 in Fig. lb) or completely (for [L’ Jo> 0.05 in Fig. la) (cf. [ 61)) which leads either to two distinct inflection points (equivalence points for calcium titration and for titration of the sum of divalent ions) or to only one inflection point (calcium titration) on the Ca2+ concentration curve. The first case suggests the
50
log x
log x
I
o-
a
-2-3-
-l-
-4-
-2
-5-
_3
-6-
-4
-?-
-5
-6-
-6
-9-
-?-
-to-
-6-
0
I 0.2
0.4
1 a6
EP 1 I 0.6
EP 2 II 1.0
I 1.2
. F
b
.
-9 0
EP 1 I 0.2
EP2 I 0.4
I 04
1 0.6
10
1.2
F
Fig. 1. Calculated concentrations of free magnesium and calcium ions as a function of the fraction titrated (F=dV/dVEp,) with EDTA. Acetylacetone present: (1) none; (2) 0.01 M, (3) 0.05 M; (4) 0.1 M; (5) 0.2 M. Magnesium and calcium correspond to (a) typical fresh-water concentrations (A4,=4~10-~ M, N0=1.6~10-4 M) and (b) to typical sea-water concentrations (Z&=7x 10e3 M, N0=3.5x lo-* M). The constants inserted in Eqns. l-3 are KNL,=250, I&,. = 10s and KNL= 106.
possibility of applying calcium-selective electrodes for the successive determination of calcium and magnesium in drinking water [ 61, whereas the second case demonstrates the applicability of Mg2+/Ca2+-selective electrodes for calcium determinations. Predicted curves forpotentiometric water hardness titration The e.m.f. response of a cell with either a calcium-selective electrode or a socalled divalent ion-selective electrode (M$+/Ca’+-selective electrode) can be described on the basis of the same semi-empirical relationship, which applies to cases with sample solutions of a given ionic strength: (4)
where 23 is the e.m.f, E0 a reference potential and s the slope of the electrode response; yj is the activity coefficient for ionj, I@$ is the selectivity coefficient of the electrode for ionj relative to Ca2+ and DL is the intrinsic detection limit of the electrode. For the calcium-selective electrode, the selectivity coefficients are 5.5 x 10m5 (Mg2+ ) and 8.7 x 10m4 (Na+ ), whereas the corresponding val-
51
togx b -2___%&!w1___
---------_____
-3-
-6-
-lO-
EP 1
I
0
0.2
0.4
0.6
0.6
EP 2.. 1.0
... 1.2
F
-6. ‘\ ‘\\.
-7~I&
‘\
DL
‘..
-0. 21
-9
-9-
-10
EP 1 I 0
0.2
0.4
06
06
EP 2 I 1 1.0
-10
I
J’ 22’ EP 1
12
F
0
EP, 2.
I
I
02
0.4
06
08
I
I
1.0
12
F
Fig. 2. Calculated concentrations of free magnesium and calcium and computer-simulated electrode response (e.m.f./s calculated from Eqn. 4) during a titration with EDTA. Magnesium, calcium and sodium concentrations are those typical of fresh water ( [Ca2+] =4X 10e4 M, [M2+] =1.6X 10e4 M, [Na+] =2.5X 10e3 M). The intrinsic detection limit (DL) of the electrodes is assumed to be 10d7 M. (a,b ) Titrations without acetylacetone; (c,d) titrations of samples containing 0.05 M acetylacetone. (a,c) Divalent ion-selective electrode (ligand ETH 4030); (b,d) calcium-selective electrode (ligand ETH 1001) . Curves: ( 1) calculated electrode response for sodium, log (Ki& [ Na ‘12); (2) calculated electrode response for magnesium, log ( K&hg [ Mg2+ ] ). Selectivity coefficients are given in the text.
52
ues for the divalent ion-selective electrode are taken as 1.0 and 1.0 x 10m3.For simplicity of the computations, it was assumed that the ratio of activity coefficients in Eqn. 4 is equal to unity, and that the intrinsic detection limit of the electrodes‘is lo-’ M. Figures 2 and 3 illustrate the computer-simulated concentration changes and the idealized electrode response for titrations of a fresh-water sample (Fig. 2) and a sea-water sample (Fig. 3). The concentration changes of Ca2+ and Mg2+ ions were calculated from Eqns. 1 and 2, respectively, whereas the sodium ion concentration was assumed to vary simply by the dilution effect. The
a .__.P!Y!___
-----_________ -l___&g
b’s? ----______
-2.
-.-.
-3 -4
-5
--..
‘\_,Iog[Mg”]
‘\
‘\
A_
‘1 \ :
-6
.,..., SF? .DL.
-7
EP
-8
::,...... \ EP
1 I
0.2
0.4
\ ‘. .‘.....,,,.,
0.6
I
2“.._ I
I
0.6
1.0
:
_7_ ,..,..,... J’?.?!.
;
\
‘.._
EP 2;
-8 1
I
F
1.2
.(. ....’ ;., \ \
0
0.2
0.4
0.6
I
0.6
1.0
1.2
F
C
__“PY!!~li!____ -----_-____
0 -1
-2 -3
-4
\ i
nls .A_
-5
=._
--._
-8
\
-.
‘\(
log
‘.._
[d
log
\,(
-6-
[d]
-.
‘I\\ EP 2 ‘\._ 1
EP 1 I 06
08
1.0
F
‘--. _
‘\\ id
-7-
z
-8.
EPl
.. . log DL
1
0
t I \. \
EP 2 I
12
‘\
-\
/2
,
J!? FL
0.4
\ -.._
-5-
‘I_
‘\ ‘\
02
‘1
‘\ , \
-6 -7
-.
02
04
06
Fig. 3. As Fig. 2, but with magnesium, calcium and sodium concentrations water: [Ca’+] =7x10m3M, [Mg2+] =3.5x10V2M, [Na+] =0.5 M.
I 08
log [C”‘.
I
1, ‘.-_
1.0
, 1.2
F
typical of those in sea
53
typical mean values observed in the respective water samples were taken as the initial calcium and magnesium concentrations, but the highest measured value was taken for the sodium concentrations [ 51. The dimensionless electrode response functions, defined as (E-l&) /s, were constructed according to Eqn. 4. In fresh-water samples the lower concentration level in the potentiometric titration curve is obviously given by the intrinsic detection limit in the case of the calcium-selective electrode (see Fig. 2 ), whereas in sea-water samples the electrode response is finally limited by Na+ interference (see Fig. 3 ). A comparison of Figs. 2a and 3a with Figs. 2c and 3c clearly demonstrates that the addition of acetylacetone to the water samples leads to a certain, but still tolerable, reduction of the potential change for the divalent ion-selective electrode at the equivalence point at F = 1 (titration of total water hardness). A clear inflection point corresponding to the titration of the calcium content is obtained for this electrode only when a relatively high concentration of the acetylacetone is present. For the calcium-selective electrode, however, the visibility of this equivalence point is considerably improved through the addition of acetylacetone, but determination of the magnesium content in sea water is generally not possible with this electrode (see Fig. 3). Accordingly, the complementary characteristics and capabilities of the divalent ion-selective and calcium-selective electrodes suggest combined applications of the two sensors. EXPERIMENTAL
The membrane preparation and the measuring technique have been described in detail [ 7 1. The membrane compositions were 1% (w/w) ionophore (ETH 1001; Fluka for the calcium-selective electrode or ETH 4030 [ 1] for the Ca2+/Mg2+-selective electrode), 33% (w/w) PVC and 65% (w/w) plasticizer (total weight 200 mg). Plasticizers used were chloroparaffin (ClP; 60% Cl; Scientific Polymer Products, New York) and o-nitrophenyl phenyl ether (oNPPE) mixed in a 1:l ratio for the divalent ion-selective electrode and dioctyl sebacate (DOS ) for the calcium-selective electrode. Potassium tetrakis (pchlorophenyl)borate (KTpClPB) was added throughout in a mole ratio of 0.7 relative to the ligand. The e.m.f.s were measured at 21 t lo C with the following cell arrangement: Hg; Hg,Cl,,KCl (satd. ) 13 M KC1 1sample 11 membrane 11 internal filling solution, AgCl; Ag. The internal filling solutions were 10m2 M magnesium chloride and lop2 M calcium chloride for the Mgz+/Ca2+-selective and the calcium-selective electrode, respectively. For the titrations with EDTA, a Titroprocessor 636/Dosimat E635 (Metrohm) was used as recommended in the special application manual (No. 125d, 1980). For the computer simulation of titration curves, the calculation and plotting
54
were done with an IBM PC AT microcomputer system using in-house software in BASIC. RESULTS AND DISCUSSION
Characterization of the ion-selective electrodes A detailed specification of the Mg2+/Ca2+-selective electrode based on the ionophore ETH 4030 has been given elsewhere [ 11. The selectivity coefficients for the most important cations in water samples are Kc& =1 and Q&a = 1.6x 10 -*. The corresponding selectivity coefficients for the calciumselective electrode are KY:& = 5.5 x 10 -’ and KgOatNa = 8.7 x 10 -*. Figure 4 shows the e.m.f. responses of the Ca2+/Mg2+- selective electrode to different Mg2+ activities in magnesium chloride solutions containing 2.5 x 10e3 M sodium chloride (typical fresh water) and 0.5 M sodium chloride (sea water), respectively. Directpotentiometric determination of water hardness Reliable determinations of total water hardness cannot be achieved by direct potentiometry, i.e., by comparison of the e.m.f. value of an Mg2+/Ca2+-selec-
ETH 4030 CIP/o-NPPE 70 mol -
%
(1:l) KTpClPB
PVC
30 mV
I -6
1 -6
I _I
I -6
I -5
1 -4
I -3
1 -2
-
Fig. 4. E.m.f. response of the divalent ion-selective electrode to different Mg2+ activities in MgCl, solutions. Sodium chloride present: (0 ) 2.5 X 10e3 M; (0 ) 0.5 M.
55
tive electrode in a water sample with a given calibration graph. Because the electrode responds to the free calcium and magnesium ion activities, the portion of calcium and magnesium ions involved in carbonate and hydrogencarbonate complexes cannot be observed directly. However, it is apparently possible to determine the non-carbonate (permanent) water hardness. Such determinations were made on artificial samples containing 3.5 x lo-’ M MgC$, 7~ 10m3 M CaCl, and 0.5 M NaCl (typical concentrations for sea water [5] ) and on drinking water from Zurich. In the second case, the non-carbonate water hardness was also determined by potentiometric titration method after the sample had been boiled, as in the conventional procedure. The result of this titration representing the sum of Ca2+ and Mg2+ concentrations was 6.27 x 10m4 M (n= 6, RSD = 1.4% ). The relative errors between the true noncarbonate water hardnesses and the values obtained by direct potentiometry were - 20 to + 14% for the artificial sea-water samples and + 20 to + 70% for the drinking-water samples. The multiple standard-additions technique partly eliminates the difficulties encountered in solutions with high background concentrations of other ions or of complexing agents, and thus facilitates the determination of the total concentration of an analyte in a complex system. This technique (with five successive known additions) was applied to determinations of the total hardness in the artificial sea water and the drinking water mentioned above. In both instances, potentiometric titration results were used for comparison. In the multiple standard-additions technique, the results were calculated from the single addition steps. The RSDs (n=5) were 3-5% for sea water and 410% for fresh drinking water. The relative errors between water hardnesses determined by titration and by standard additions were - 4.5 to - 12% and -3 to -33% for sea water and fresh water, respectively. The results of the titration were 4.26x10-’ M (n=6, RSD=0.6%) and 1.44~10~~ M (n=6, RSD = 0.2% ) in artificial sea water and fresh drinking water, respectively. Although the novel ionophore-based divalent ion-selective electrode has much better characteristics for titrations than the classical liquid ion-exchanger membrane electrodes used previously, the present results obtained by means of direct potentiometry with standard additions techniques are not more convincing than the results reported earlier [8,9]. In fact, the relative errors and standard deviations found here are similar to those obtained previously [8,9]. The failure of direct potentiometric methods can be rationalized by at least two arguments (for a discussion, see [5] ): (a) the selectivity coefficient Q&I of the divalent ion-selective electrode may deviate from the required value of unity and (b) the differences between the activity coefficients &2+ and yca2+should be taken into account (see also Eqn. 4). Potentiometric titration with EDTA Figure 5 shows examples of experimental titration curves obtained with the calcium-selective and divalent ion-selective electrodes with and without the
56 E
[mvl I
b
50I-
0
-50
_laJi, 0
0.5
10
1.5V[ml
-100 r0
0.5
1.0
1.5 V[n
Fig. 5. Experimental titration curves with the divalent ion-selective electrode (curves 1 and 3) and the calcium-selective electrode (curves 2 and 4). (a) Without acetylacetone; (b) with 0.01 M acetylacetone (curves 1 and 2 ) or 0.1 M acetylacetone (curves 3 and 4). The ion concentrations are typical of fresh water (see Fig. 2 ) .
addition of acetylacetone to the sample. The solution measured was a mixture of calcium, magnesium and sodium chlorides, similar to fresh drinking water with a relatively high concentration of sodium ions (5 X 10d3 M). The calcium and magnesium ion concentrations were determined by potentiometric titration of separate stock solutions of calcium chloride and magnesium chloride that were mixed 1: 1. The inflection points marked on the figure were located by a microcomputer-assisted procedure, as described in the Metrohm 636 titroprocessor manual. The results of this set of titrations are given in Table 1. The addition of a relatively small amount of acetylacetone (0.01 M) allows the determination of Ca2+ and Mg2+ concentrations separately with much improved precision and accuracy when the calcium-selective electrode is used. After addition of acetylacetone (0.01 M), the sum of the Ca2+ and Mg2+ concentrations can still be determined with the Mg2+ /Ca2+ -selective electrode although the precision and the accuracy of the results are slightly reduced. In contrast, the second inflection point found for the titration curve with the latter electrode is not pronounced enough to allow the reliable determination of the calcium concentration (curve 2b). When an excess of acetylacetone (0.1 M) is added, only one inflection point is observed for both electrodes. This means that the Ca2+ concentration alone is determined because all the magnesium is masked. These experimental titration curves are in good agreement with the computer-simulated curves and with the expectations from the calibration graphs for the ionselective electrodes used. Small discrepancies in the low activity range (ca. 10m6 M) are due to different conditions for the calibration and the titration (EDTA-buffered solution in the second case). Figure 6 shows an example of titration curves recorded with calcium-selective and Mg2+/Ca2+-selective
57
TABLE I Titrationsofanartificiallypreparedwater M, [Ca”]+ [M%+]=5.6~10-‘M
sample with [Ca’+] =4X 10m4M, [MgZ+] =1.6X 10e4
Divalent ion electrode”
Calcium electrode”
[Ca”] + [Mg2+] (10-4M)
[Ca’+] + (Mg2+] (lo-’ M)
[Ca’+] (lo-’ M)
0
5.55 (0.5, -0.4) 5.56 (0.7, -0.2) 5.57 (0, 0)
5.62 (0.3, +0.9)
4.49 (0.3, + 12.4)
0.01
5.73 (0.6, +1.7) 5.63 (0.2, 0) 5.70 (0.5, + 1.2)
5.64 (0.3,
0)
3.99 (0.1, -0.3)
0.10
3.96b (0.1, - 1.7) 4.00b (0.3, -0.6) 3.98b (0.1, - 1.3)
Not observable
3.96 (0.3, -1.7)
Acetylacetone added (M)
“Mean values of three determinations with RSD ( % ) and relative error ( % ) in parentheses. bOnly the Ca2+ concentration is determined.
-1000,i
l-n 2 4 0 6 6 10 Fig. 6. Experimental titration curves for a sample solution with an ion content typical of sea water (see Fig. 3 ) and with added acetylacetone (0.01 M ) . Curves: ( 1) divalent ion-selective electrode; (2 ) calcium-selective electrode.
electrodes when acetylacetone is added to an artificial sea-water sample containing 3.5 x 10m2M MgC12, 7 x 10V3 M CaCl, and 0.5 M NaCl. They are again in good qualitative agreement with the theoretical predictions in Fig. 3. The results of this set of titrations are 4.26~ 10m2M (n=6, RSD =0.5%) for the sum of Mg2+ and Ca2+ concentrations and 7.34 x 10m3M (n= 6, RSD = 0.6% ) for the Ca2+ concentrations . Table 2 shows the results of titrations of different natural fresh-water samples from Switzerland and of sea water from Spain. Again, the same combi-
5s TABLE 2 Titrations of different natural fresh and sea watera Water
Zurich tap water (boiled) Zurich tap water
Winterthur tap water
Zurich lake
Aare river
Mediterranean sea
Rcetylacetone added (M)
Divalent ion electrode’
Calcium electrode’
[Ca”‘] + [Mg+] (lo-’ M)
(C3+]+ [Mg+] (lo-’ M)
0 0.01 0.10
-
4.83 (0.9)
0 0.01 0.10
-
0 0.01 0.10
-
0 0.01 0.10
-
0 0.01 0.10
-
0 0.01 0.10
710.6 (0.1) -
[Ca2+] (lo-‘M)
4.OOb
38.07 (0.2)
13.98 (0.2)
20.62 (0.1)
[Ca”]:
[M%+]
2.9gb
14.74 (0.3)
[Ca”‘] (lo-‘M) 2.94b
1.6: 1
-
14.73 (2.0) -
12.19 (0.3) 12.19 (0.1)
4.8: I
12.19 (0.5)
37.61 (0.3) -
26.25 (0.2) 26.37 (0.1)
2.3: 1
26.48 (0.1)
_c -
11.48 (0.9) 11.45 (0)
4.4: 1
11.39 (0.3)
_c -
17.47 (0.2) 17.45 (0)
5.5: I
17.46 (0.2)
_c -
117.2 (0.6) 114.9 (0.1)
0.2:1
-
-
-
114.6 (0.9)
“Mean value of three determinations with RSD ( W ) in parentheses. bOnly two determinations made. “The
second inflection point was not visible.
nation of a divalent ion-selective and a calcium-selective electrode was applied, and the conditions of the titration procedure were optimized according to the findings from the computer simulations in the theoretical section. This work was supported by the Swiss National Science Foundation, by Ciba Corning Diagnostics and by Eppendorf Ger%ebau, Hamburg, F.R.G. M.M.-Z. acknowledges additional support by the University of Warsaw.
REFERENCES
1
M. Miiller, M. Rouilly, B. Rusterholz, M. Maj-Zurawska, Z. Hu and W. Simon, Mikrochim. Acta, in press.
59
2 3 4 5 6 7 8 9
J.W. Ross, Jr., Natl. Bur. Stand. (U.S.), Spec. Publ., 314 (1969) 70. M. Whitfield and J.V. Leyendekkers, Anal. Chim. Acta, 45 (1969) 383. U. Hannema and G. den Boef, Anal. Chim. Acta, 39 (1967) 167,479. P.C. Meier, D. Erne, Z. Cimerman, D. Ammann and W. Simon, Mikrochim. Acta, Part I, (1980) 317. T.F. Christiansen, J.E. Busch and S.C. Krogh, Anal. Chem., 48 (1976) 1051. U. Oesch, Z. Brzozka, A. Xu, B. Rusterholz, G. Suter, H.-V. Pham, D.H. Welti, D. Ammann, E. Pretsch and W. Simon, Anal. Chem., 58 (1986) 2285. I. Sekerka and J.F. Lechner, Talanta, 22 (1975) 459. S.K.A.G. Hassan, G.J. Moody and J.D.R. Thomas, Analyst, 105 (1980) 147.
47 Printed in The Netherlands
DETERMINATION OF MAGNESIUM AND CALCIUM WITH ION-SELECTIVE ELECTRODES
IN WATER
MAGDALENA MAJ-ZURAWSKA”, MARIZEL ROUILLY, WERNER E. MORF and WILHELM SIMON* Department of Organic Chemistry, Swiss Federal Institute of Technology (ETH), CH-8092 Ziirich (Switzerland) (Received 12th August 1988)
SUMMARY The sum of the concentrations of calcium and magnesium in water samples can be determined directly with a neutral carrier-based Mg+/Ca’+-selective electrode (divalent ion-selective electrode), without addition of any auxiliary complexing agent such as acetylacetone. This approach works well, even in situations where calcium-selective electrodes do not detect the second inflection point because the calcium/magnesium concentration ratio is too high ( [ Ca2+ ] : [ M$+ ] > 5 : 1) or the sodium concentration is high. With high levels of acetylacetone (0.1 M) the divalent ionselective electrode can also be used for calcium determinations. For such measurements, however, the standard deviations obtained with the calcium-selective electrode are smaller. A theoretical description of titration curves corroborates these findings.
Recently, magnesium ion-selective electrodes based on the neutral carrier N,iV” -0ctamethylenebis (N’ -heptyl-N’ -methyl malonamide ) (ETH 4030) were described [ 11. In certain membranes, this ionophore exhibits equal selectivity for Mg2+ and Ca2+ and rejects all alkali metal and all other alkalineearth metal ions, preferring Mg2+ over Na+ and K+ by factors of up to about 10 000 [ 11. Such electrodes are interesting candidates for determinations of water hardness. The high selectivity against Na+ allows the determination of Ca2+ and Mg2+ in samples with a high sodium background, which would be especially valuable for highly polluted river water and for sea water. A determination of Ca2+ and Mg2+ under these conditions with a so-called divalent ion-selective electrode [ 21 ( Mg2 + /Ca2+-selective electrode) has not been possible previously [ 31. Here, the application of the recently described electrode [l] is reported for *Permanent address: Chemistry Department, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland.
0003-2670/89/$03.50
0 1989 Elsevier Science Publishers B.V.
48
determinations of magnesium and calcium in water and the results are compared with those obtained by using a highly selective calcium electrode. THEORY
Computer simulation of titration curves For modelling the simultaneous titration of two species M and N with a ligand L (here the titration of calcium and magnesium ions with EDTA) , the following mass-balance equations are taken into account:
Ll+ [ML1+ WLI = Ll,; WI + [ML1= WI, [N] + [NL] + [NLL] = [N],;
[L’] +n[NL:,]
= [L’],
where [X] and [X ] t are the individual and the total concentrations of species X, respectively. The two relationships containing [NE:,] cover the situation where a second complex-forming agent L’ selective for N is added to the sample solution prior to the titration (e.g., the addition of acetylacetone for complexation of magnesium ions). For simplicity it is assumed that such an additional ligand forms complexes of a given 1: n stoichiometry (stability constant j3) and is present in excess. Hence, the following approximations are obtained: [L’
I= L’ It; [NL:,l =P[Nl L’ It”
The complex formation induced by the ligand of the titrant is characterized by the respective stability constants K ML and I&, the latter being assumed to have the lower value (i.e., the end-point for the titration of species M appears first ) :
[MLI=&L[MI ELI; WLI=KNL[NI [Ll All values [X] t in the above equations correspond to the actual total concentrations at the time when a volume increment dV= V,- V, of titrant is added to the sample. They are related to the initial concentrations [Xl, of sample and titrant, respectively, as follows:
Ll,= Llo(vt-vo)Ivt; [Ml,= [WoVo/V, WI, = Plo Vo/Vt; L It = L’ lo VOW, Accordingly, the actual concentrations [X] of all species involved can be calculated as a function of the volume of titrant added, V,- VO.Combination of these relationships finally leads to the following equations as implicit solutions for [M] and [N] , respectively:
49
W13(1-W-
PWW--k)
([Ml,+ WI,- LM-
(kWl,+ WI,)
WI (l+P[L’ I;) = ( WI, + WI, - WI,) - WI + ( Wit - WI
)I&L[MI
(2)
where k characterizes the relative selectivity of the titration reaction:
k=KNLI{K~L(l+P[L’ltn))
(3)
Equation 1 is an extended version of an expression reported earlier [ 3, 41 which was derived for the compleximetric titration of calcium (M) and magnesium ions (N) without additional ligand (L’ ). In order to obtain more appropriate explicit descriptions of the titration curve near the first and second end-points (indicating the consumption of M and N, respectively), one can delete the last and the first term in Eqn. 1, respectively. In both instances the cubic equation reduces to a quadratic one. The calculated concentrations of unchelated Ca2+ and Mg2+ ions during compleximetric titrations with EDTA are shown in Fig. 1. The curves were simulated for different concentrations of the magnesium-masking ligand acetylacetone and are given as a function of the fraction titrated, F=dV/dVEP2, where dVEp2 represents the volume of titrant added at the second end-point (i.e., at the equivalence point for the sum of titrated ions). The total concentrations [Ml0 and [N],, chosen are the reported mean values of calcium and magnesium concentrations [5] in fresh water (Fig. la) and sea water (Fig. lb). The values of KML, KNL and /3 to be inserted in Eqns. l-3 are the conditional constants which depend on the pH value. In real titration experiments, the pH of the sample is buffered with Tris to ca. 8.5, as recommended for EDTA titrations with calcium-selective electrodes [ 61. It should be mentioned, however, that the ratio KNL/K ML (magnesium/calcium) has a constant value of 0.01 over a large pH range. In the present calculations, the values of KML,P&L and p (assuming n= 1) were estimated to be 108, lo6 and 250, respectively, which resulted in good qualitative agreement between the calculated and observed titration curves (see below). It becomes evident from Fig. 1 that the Ca2+ concentration curve is considerably influenced by the complex formation of Mg2+ ions with acetylacetone. An increasing concentration of acetylacetone masks the magnesium ions partly (for [L’ ],,=O.Ol in Fig. la or 0.01-0.02 in Fig. lb) or completely (for [L’ Jo> 0.05 in Fig. la) (cf. [ 61)) which leads either to two distinct inflection points (equivalence points for calcium titration and for titration of the sum of divalent ions) or to only one inflection point (calcium titration) on the Ca2+ concentration curve. The first case suggests the
50
log x
log x
I
o-
a
-2-3-
-l-
-4-
-2
-5-
_3
-6-
-4
-?-
-5
-6-
-6
-9-
-?-
-to-
-6-
0
I 0.2
0.4
1 a6
EP 1 I 0.6
EP 2 II 1.0
I 1.2
. F
b
.
-9 0
EP 1 I 0.2
EP2 I 0.4
I 04
1 0.6
10
1.2
F
Fig. 1. Calculated concentrations of free magnesium and calcium ions as a function of the fraction titrated (F=dV/dVEp,) with EDTA. Acetylacetone present: (1) none; (2) 0.01 M, (3) 0.05 M; (4) 0.1 M; (5) 0.2 M. Magnesium and calcium correspond to (a) typical fresh-water concentrations (A4,=4~10-~ M, N0=1.6~10-4 M) and (b) to typical sea-water concentrations (Z&=7x 10e3 M, N0=3.5x lo-* M). The constants inserted in Eqns. l-3 are KNL,=250, I&,. = 10s and KNL= 106.
possibility of applying calcium-selective electrodes for the successive determination of calcium and magnesium in drinking water [ 61, whereas the second case demonstrates the applicability of Mg2+/Ca2+-selective electrodes for calcium determinations. Predicted curves forpotentiometric water hardness titration The e.m.f. response of a cell with either a calcium-selective electrode or a socalled divalent ion-selective electrode (M$+/Ca’+-selective electrode) can be described on the basis of the same semi-empirical relationship, which applies to cases with sample solutions of a given ionic strength: (4)
where 23 is the e.m.f, E0 a reference potential and s the slope of the electrode response; yj is the activity coefficient for ionj, I@$ is the selectivity coefficient of the electrode for ionj relative to Ca2+ and DL is the intrinsic detection limit of the electrode. For the calcium-selective electrode, the selectivity coefficients are 5.5 x 10m5 (Mg2+ ) and 8.7 x 10m4 (Na+ ), whereas the corresponding val-
51
togx b -2___%&!w1___
---------_____
-3-
-6-
-lO-
EP 1
I
0
0.2
0.4
0.6
0.6
EP 2.. 1.0
... 1.2
F
-6. ‘\ ‘\\.
-7~I&
‘\
DL
‘..
-0. 21
-9
-9-
-10
EP 1 I 0
0.2
0.4
06
06
EP 2 I 1 1.0
-10
I
J’ 22’ EP 1
12
F
0
EP, 2.
I
I
02
0.4
06
08
I
I
1.0
12
F
Fig. 2. Calculated concentrations of free magnesium and calcium and computer-simulated electrode response (e.m.f./s calculated from Eqn. 4) during a titration with EDTA. Magnesium, calcium and sodium concentrations are those typical of fresh water ( [Ca2+] =4X 10e4 M, [M2+] =1.6X 10e4 M, [Na+] =2.5X 10e3 M). The intrinsic detection limit (DL) of the electrodes is assumed to be 10d7 M. (a,b ) Titrations without acetylacetone; (c,d) titrations of samples containing 0.05 M acetylacetone. (a,c) Divalent ion-selective electrode (ligand ETH 4030); (b,d) calcium-selective electrode (ligand ETH 1001) . Curves: ( 1) calculated electrode response for sodium, log (Ki& [ Na ‘12); (2) calculated electrode response for magnesium, log ( K&hg [ Mg2+ ] ). Selectivity coefficients are given in the text.
52
ues for the divalent ion-selective electrode are taken as 1.0 and 1.0 x 10m3.For simplicity of the computations, it was assumed that the ratio of activity coefficients in Eqn. 4 is equal to unity, and that the intrinsic detection limit of the electrodes‘is lo-’ M. Figures 2 and 3 illustrate the computer-simulated concentration changes and the idealized electrode response for titrations of a fresh-water sample (Fig. 2) and a sea-water sample (Fig. 3). The concentration changes of Ca2+ and Mg2+ ions were calculated from Eqns. 1 and 2, respectively, whereas the sodium ion concentration was assumed to vary simply by the dilution effect. The
a .__.P!Y!___
-----_________ -l___&g
b’s? ----______
-2.
-.-.
-3 -4
-5
--..
‘\_,Iog[Mg”]
‘\
‘\
A_
‘1 \ :
-6
.,..., SF? .DL.
-7
EP
-8
::,...... \ EP
1 I
0.2
0.4
\ ‘. .‘.....,,,.,
0.6
I
2“.._ I
I
0.6
1.0
:
_7_ ,..,..,... J’?.?!.
;
\
‘.._
EP 2;
-8 1
I
F
1.2
.(. ....’ ;., \ \
0
0.2
0.4
0.6
I
0.6
1.0
1.2
F
C
__“PY!!~li!____ -----_-____
0 -1
-2 -3
-4
\ i
nls .A_
-5
=._
--._
-8
\
-.
‘\(
log
‘.._
[d
log
\,(
-6-
[d]
-.
‘I\\ EP 2 ‘\._ 1
EP 1 I 06
08
1.0
F
‘--. _
‘\\ id
-7-
z
-8.
EPl
.. . log DL
1
0
t I \. \
EP 2 I
12
‘\
-\
/2
,
J!? FL
0.4
\ -.._
-5-
‘I_
‘\ ‘\
02
‘1
‘\ , \
-6 -7
-.
02
04
06
Fig. 3. As Fig. 2, but with magnesium, calcium and sodium concentrations water: [Ca’+] =7x10m3M, [Mg2+] =3.5x10V2M, [Na+] =0.5 M.
I 08
log [C”‘.
I
1, ‘.-_
1.0
, 1.2
F
typical of those in sea
53
typical mean values observed in the respective water samples were taken as the initial calcium and magnesium concentrations, but the highest measured value was taken for the sodium concentrations [ 51. The dimensionless electrode response functions, defined as (E-l&) /s, were constructed according to Eqn. 4. In fresh-water samples the lower concentration level in the potentiometric titration curve is obviously given by the intrinsic detection limit in the case of the calcium-selective electrode (see Fig. 2 ), whereas in sea-water samples the electrode response is finally limited by Na+ interference (see Fig. 3 ). A comparison of Figs. 2a and 3a with Figs. 2c and 3c clearly demonstrates that the addition of acetylacetone to the water samples leads to a certain, but still tolerable, reduction of the potential change for the divalent ion-selective electrode at the equivalence point at F = 1 (titration of total water hardness). A clear inflection point corresponding to the titration of the calcium content is obtained for this electrode only when a relatively high concentration of the acetylacetone is present. For the calcium-selective electrode, however, the visibility of this equivalence point is considerably improved through the addition of acetylacetone, but determination of the magnesium content in sea water is generally not possible with this electrode (see Fig. 3). Accordingly, the complementary characteristics and capabilities of the divalent ion-selective and calcium-selective electrodes suggest combined applications of the two sensors. EXPERIMENTAL
The membrane preparation and the measuring technique have been described in detail [ 7 1. The membrane compositions were 1% (w/w) ionophore (ETH 1001; Fluka for the calcium-selective electrode or ETH 4030 [ 1] for the Ca2+/Mg2+-selective electrode), 33% (w/w) PVC and 65% (w/w) plasticizer (total weight 200 mg). Plasticizers used were chloroparaffin (ClP; 60% Cl; Scientific Polymer Products, New York) and o-nitrophenyl phenyl ether (oNPPE) mixed in a 1:l ratio for the divalent ion-selective electrode and dioctyl sebacate (DOS ) for the calcium-selective electrode. Potassium tetrakis (pchlorophenyl)borate (KTpClPB) was added throughout in a mole ratio of 0.7 relative to the ligand. The e.m.f.s were measured at 21 t lo C with the following cell arrangement: Hg; Hg,Cl,,KCl (satd. ) 13 M KC1 1sample 11 membrane 11 internal filling solution, AgCl; Ag. The internal filling solutions were 10m2 M magnesium chloride and lop2 M calcium chloride for the Mgz+/Ca2+-selective and the calcium-selective electrode, respectively. For the titrations with EDTA, a Titroprocessor 636/Dosimat E635 (Metrohm) was used as recommended in the special application manual (No. 125d, 1980). For the computer simulation of titration curves, the calculation and plotting
54
were done with an IBM PC AT microcomputer system using in-house software in BASIC. RESULTS AND DISCUSSION
Characterization of the ion-selective electrodes A detailed specification of the Mg2+/Ca2+-selective electrode based on the ionophore ETH 4030 has been given elsewhere [ 11. The selectivity coefficients for the most important cations in water samples are Kc& =1 and Q&a = 1.6x 10 -*. The corresponding selectivity coefficients for the calciumselective electrode are KY:& = 5.5 x 10 -’ and KgOatNa = 8.7 x 10 -*. Figure 4 shows the e.m.f. responses of the Ca2+/Mg2+- selective electrode to different Mg2+ activities in magnesium chloride solutions containing 2.5 x 10e3 M sodium chloride (typical fresh water) and 0.5 M sodium chloride (sea water), respectively. Directpotentiometric determination of water hardness Reliable determinations of total water hardness cannot be achieved by direct potentiometry, i.e., by comparison of the e.m.f. value of an Mg2+/Ca2+-selec-
ETH 4030 CIP/o-NPPE 70 mol -
%
(1:l) KTpClPB
PVC
30 mV
I -6
1 -6
I _I
I -6
I -5
1 -4
I -3
1 -2
-
Fig. 4. E.m.f. response of the divalent ion-selective electrode to different Mg2+ activities in MgCl, solutions. Sodium chloride present: (0 ) 2.5 X 10e3 M; (0 ) 0.5 M.
55
tive electrode in a water sample with a given calibration graph. Because the electrode responds to the free calcium and magnesium ion activities, the portion of calcium and magnesium ions involved in carbonate and hydrogencarbonate complexes cannot be observed directly. However, it is apparently possible to determine the non-carbonate (permanent) water hardness. Such determinations were made on artificial samples containing 3.5 x lo-’ M MgC$, 7~ 10m3 M CaCl, and 0.5 M NaCl (typical concentrations for sea water [5] ) and on drinking water from Zurich. In the second case, the non-carbonate water hardness was also determined by potentiometric titration method after the sample had been boiled, as in the conventional procedure. The result of this titration representing the sum of Ca2+ and Mg2+ concentrations was 6.27 x 10m4 M (n= 6, RSD = 1.4% ). The relative errors between the true noncarbonate water hardnesses and the values obtained by direct potentiometry were - 20 to + 14% for the artificial sea-water samples and + 20 to + 70% for the drinking-water samples. The multiple standard-additions technique partly eliminates the difficulties encountered in solutions with high background concentrations of other ions or of complexing agents, and thus facilitates the determination of the total concentration of an analyte in a complex system. This technique (with five successive known additions) was applied to determinations of the total hardness in the artificial sea water and the drinking water mentioned above. In both instances, potentiometric titration results were used for comparison. In the multiple standard-additions technique, the results were calculated from the single addition steps. The RSDs (n=5) were 3-5% for sea water and 410% for fresh drinking water. The relative errors between water hardnesses determined by titration and by standard additions were - 4.5 to - 12% and -3 to -33% for sea water and fresh water, respectively. The results of the titration were 4.26x10-’ M (n=6, RSD=0.6%) and 1.44~10~~ M (n=6, RSD = 0.2% ) in artificial sea water and fresh drinking water, respectively. Although the novel ionophore-based divalent ion-selective electrode has much better characteristics for titrations than the classical liquid ion-exchanger membrane electrodes used previously, the present results obtained by means of direct potentiometry with standard additions techniques are not more convincing than the results reported earlier [8,9]. In fact, the relative errors and standard deviations found here are similar to those obtained previously [8,9]. The failure of direct potentiometric methods can be rationalized by at least two arguments (for a discussion, see [5] ): (a) the selectivity coefficient Q&I of the divalent ion-selective electrode may deviate from the required value of unity and (b) the differences between the activity coefficients &2+ and yca2+should be taken into account (see also Eqn. 4). Potentiometric titration with EDTA Figure 5 shows examples of experimental titration curves obtained with the calcium-selective and divalent ion-selective electrodes with and without the
56 E
[mvl I
b
50I-
0
-50
_laJi, 0
0.5
10
1.5V[ml
-100 r0
0.5
1.0
1.5 V[n
Fig. 5. Experimental titration curves with the divalent ion-selective electrode (curves 1 and 3) and the calcium-selective electrode (curves 2 and 4). (a) Without acetylacetone; (b) with 0.01 M acetylacetone (curves 1 and 2 ) or 0.1 M acetylacetone (curves 3 and 4). The ion concentrations are typical of fresh water (see Fig. 2 ) .
addition of acetylacetone to the sample. The solution measured was a mixture of calcium, magnesium and sodium chlorides, similar to fresh drinking water with a relatively high concentration of sodium ions (5 X 10d3 M). The calcium and magnesium ion concentrations were determined by potentiometric titration of separate stock solutions of calcium chloride and magnesium chloride that were mixed 1: 1. The inflection points marked on the figure were located by a microcomputer-assisted procedure, as described in the Metrohm 636 titroprocessor manual. The results of this set of titrations are given in Table 1. The addition of a relatively small amount of acetylacetone (0.01 M) allows the determination of Ca2+ and Mg2+ concentrations separately with much improved precision and accuracy when the calcium-selective electrode is used. After addition of acetylacetone (0.01 M), the sum of the Ca2+ and Mg2+ concentrations can still be determined with the Mg2+ /Ca2+ -selective electrode although the precision and the accuracy of the results are slightly reduced. In contrast, the second inflection point found for the titration curve with the latter electrode is not pronounced enough to allow the reliable determination of the calcium concentration (curve 2b). When an excess of acetylacetone (0.1 M) is added, only one inflection point is observed for both electrodes. This means that the Ca2+ concentration alone is determined because all the magnesium is masked. These experimental titration curves are in good agreement with the computer-simulated curves and with the expectations from the calibration graphs for the ionselective electrodes used. Small discrepancies in the low activity range (ca. 10m6 M) are due to different conditions for the calibration and the titration (EDTA-buffered solution in the second case). Figure 6 shows an example of titration curves recorded with calcium-selective and Mg2+/Ca2+-selective
57
TABLE I Titrationsofanartificiallypreparedwater M, [Ca”]+ [M%+]=5.6~10-‘M
sample with [Ca’+] =4X 10m4M, [MgZ+] =1.6X 10e4
Divalent ion electrode”
Calcium electrode”
[Ca”] + [Mg2+] (10-4M)
[Ca’+] + (Mg2+] (lo-’ M)
[Ca’+] (lo-’ M)
0
5.55 (0.5, -0.4) 5.56 (0.7, -0.2) 5.57 (0, 0)
5.62 (0.3, +0.9)
4.49 (0.3, + 12.4)
0.01
5.73 (0.6, +1.7) 5.63 (0.2, 0) 5.70 (0.5, + 1.2)
5.64 (0.3,
0)
3.99 (0.1, -0.3)
0.10
3.96b (0.1, - 1.7) 4.00b (0.3, -0.6) 3.98b (0.1, - 1.3)
Not observable
3.96 (0.3, -1.7)
Acetylacetone added (M)
“Mean values of three determinations with RSD ( % ) and relative error ( % ) in parentheses. bOnly the Ca2+ concentration is determined.
-1000,i
l-n 2 4 0 6 6 10 Fig. 6. Experimental titration curves for a sample solution with an ion content typical of sea water (see Fig. 3 ) and with added acetylacetone (0.01 M ) . Curves: ( 1) divalent ion-selective electrode; (2 ) calcium-selective electrode.
electrodes when acetylacetone is added to an artificial sea-water sample containing 3.5 x 10m2M MgC12, 7 x 10V3 M CaCl, and 0.5 M NaCl. They are again in good qualitative agreement with the theoretical predictions in Fig. 3. The results of this set of titrations are 4.26~ 10m2M (n=6, RSD =0.5%) for the sum of Mg2+ and Ca2+ concentrations and 7.34 x 10m3M (n= 6, RSD = 0.6% ) for the Ca2+ concentrations . Table 2 shows the results of titrations of different natural fresh-water samples from Switzerland and of sea water from Spain. Again, the same combi-
5s TABLE 2 Titrations of different natural fresh and sea watera Water
Zurich tap water (boiled) Zurich tap water
Winterthur tap water
Zurich lake
Aare river
Mediterranean sea
Rcetylacetone added (M)
Divalent ion electrode’
Calcium electrode’
[Ca”‘] + [Mg+] (lo-’ M)
(C3+]+ [Mg+] (lo-’ M)
0 0.01 0.10
-
4.83 (0.9)
0 0.01 0.10
-
0 0.01 0.10
-
0 0.01 0.10
-
0 0.01 0.10
-
0 0.01 0.10
710.6 (0.1) -
[Ca2+] (lo-‘M)
4.OOb
38.07 (0.2)
13.98 (0.2)
20.62 (0.1)
[Ca”]:
[M%+]
2.9gb
14.74 (0.3)
[Ca”‘] (lo-‘M) 2.94b
1.6: 1
-
14.73 (2.0) -
12.19 (0.3) 12.19 (0.1)
4.8: I
12.19 (0.5)
37.61 (0.3) -
26.25 (0.2) 26.37 (0.1)
2.3: 1
26.48 (0.1)
_c -
11.48 (0.9) 11.45 (0)
4.4: 1
11.39 (0.3)
_c -
17.47 (0.2) 17.45 (0)
5.5: I
17.46 (0.2)
_c -
117.2 (0.6) 114.9 (0.1)
0.2:1
-
-
-
114.6 (0.9)
“Mean value of three determinations with RSD ( W ) in parentheses. bOnly two determinations made. “The
second inflection point was not visible.
nation of a divalent ion-selective and a calcium-selective electrode was applied, and the conditions of the titration procedure were optimized according to the findings from the computer simulations in the theoretical section. This work was supported by the Swiss National Science Foundation, by Ciba Corning Diagnostics and by Eppendorf Ger%ebau, Hamburg, F.R.G. M.M.-Z. acknowledges additional support by the University of Warsaw.
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1
M. Miiller, M. Rouilly, B. Rusterholz, M. Maj-Zurawska, Z. Hu and W. Simon, Mikrochim. Acta, in press.
59
2 3 4 5 6 7 8 9
J.W. Ross, Jr., Natl. Bur. Stand. (U.S.), Spec. Publ., 314 (1969) 70. M. Whitfield and J.V. Leyendekkers, Anal. Chim. Acta, 45 (1969) 383. U. Hannema and G. den Boef, Anal. Chim. Acta, 39 (1967) 167,479. P.C. Meier, D. Erne, Z. Cimerman, D. Ammann and W. Simon, Mikrochim. Acta, Part I, (1980) 317. T.F. Christiansen, J.E. Busch and S.C. Krogh, Anal. Chem., 48 (1976) 1051. U. Oesch, Z. Brzozka, A. Xu, B. Rusterholz, G. Suter, H.-V. Pham, D.H. Welti, D. Ammann, E. Pretsch and W. Simon, Anal. Chem., 58 (1986) 2285. I. Sekerka and J.F. Lechner, Talanta, 22 (1975) 459. S.K.A.G. Hassan, G.J. Moody and J.D.R. Thomas, Analyst, 105 (1980) 147.