probably because cp2 was the controlling variable. If inactively adsorbed hydrogen affects the hydrogen overvoltage, however, these arguments do not hold, for both the AGO and the hydrogen coverage could be altered. The deviations from linearity, such as those at both lower and higher concentrations, may have been caused by any of the four mentioned variables, as well as by the particular form of the adsorption isotherm for the sulfur compound on the electrode.
ACKNOWLEDGMENT
We thank J. E. Campbell of the National Center for Urban and Industrial Health and Walter Juda of the Prototech Co. in Cambridge, Mass., for continued interest and helpful discussions. RECEIVED for review July 18, 1968. Accepted October 3, 1968. Mention of a commercial product does not imply endorsement by the Public Health Service.
Potentiometric Determinations of Calcium, Magnesium, and Complexing Agents in Water and Biological Fluids Bart van’t Riet and James E. Wynn Department of Chemistry and Pharmaceutical Chemistry, Medical College of Virginia, Richmond, Va. 23219 Calcium is determined accurately, even in multicomponent solutions, by direct titration with a solution of the tetrasodium salt of EGTA at a pH of about 8.5. A recording pH meter indicates a sharp upward break at the equivalence point, unaffected by a large excess of magnesium in the presence of citrate. Continued titration with tetrasodium EDTA of the same sample shows a break in pH at the equivalence point for magnesium. The limit of detection for both metals is 0.5 pg in samples up to 100 ml. More than 10 pg of EDTA or EGTA can be determined by addition of excess cadmium and back-titration with tetrasodium EGTA at pH 4.5 to 5.0. Reproducibility and accuracy are better than 10.5% for the samples containing more than 0.5 pmole of the metals or ligands.
DIFFICULTIES in end point detection of chelometric titrations in turbid or colored biological fluids can be avoided by potentiometric detection of the equivalence point. Schmid and Reilley ( I ) used a mercury electrode and some mercuric chelate in their samples of pure salt solutions for determination of calcium. This method, however, is limited by interferences in practical solutions-e.g., redox potential and chloride ion. Titrations of calcium plus magnesium can be done with the tetrasodium salt of EDTA under conditions that a change in pH indicates the end point. Schwarzenbach and Biedermann (2,3) did such titrations of pure salt solutions. Their results were not promising, and they discontinued this approach. A search for colored indicators was expanded and continues to the present. We shall present data showing why the pH change approach did not give better results. Conditions will be given under which sharp end points are obtained, even in urine and blood plasma, using readily available equipment. EXPERIMENTAL Apparatus. k e d s and Northrup microelectrodes, or any type of combination pH electrodes, are used in 50- or 100-ml beakers containing magnetic stirrers. The pH measurements (1) R. W. Schmid and C. N. Reilley, ANAL.CHEM., 29,264 (1957). (2) G. Swarzenbach and W. Biedermann, Helu. Chim. Acta, 31, 459 (1948). (3) A. M. Martell and Melvin Calvin, “Chemistry of the Metal Chelate Compounds,” Prentice-Hall, New York, N. Y.,1952, p 481.
158 *
ANALYTICAL CHEMISTRY
are made with a multispeed recording pH meter (Heath EUW 301-M). Either one of two Sargent constant rate burets is attached to the outlet which is only energized when the recorder operates. Reagents. Deionized distilled water is used in the preparation of the solutions which are kept in polyethylene containers. Ethyleneglycolbis- (betaaminoethylether) - N,N’ - tetraacetic acid (or EGTA, Eastman Cat. No. 8276) is dissolved by addition of an accurately measured volume of sodium hydroxide solution to make pH about 7.0. Its tetrasodium salt is prepared by addition of another identical volume of hydroxide, and a stock solution of 0.1M is made. Disodium ethylenediaminetetraacetate (Fisher Scientific Co.) is converted to tetrasodium EDTA with a calculated amount of 50% sodium hydroxide, and diluted to 0.1M. The proper stoichiometry is checked by titration of a standard calcium solution (see procedures). Trisodium citrate and cadmium nitrate, each about 5 x 10-3M solutions, are used. Procedures. CALCIUM.Samples preferably containing more than 20 pg of calcium are diluted to about 20 ml and adjusted to pH 8.0 to 8.6 with dilute strong acid or base. Urine and blood plasma can be titrated without further preparation. For poorly buffered samples-e.g., distilled water-and in the presence of an excess of magnesium, or when a precipitate is formed on adjustment of pH, the addition of 2 or more ml of 5 X 10-3Mtrisodium citrate is recommended. Samples containing a large excess of magnesium should be titrated in a pH region of about 8.2 or below. The titrant is 5 x to 10-3M tetrasodium-EGTA, added at a rate of 0.96 ml/min. During the titration of calcium, little change of pH is observed. The titration is discontinued after a sharp break occurs in the pH plot, and sufficient excess of titrant (about 0.5 ml) is added to allow precise interpolation. The sum of dead time and calcium content of water and citrate solution is obtained by performing a blank titration using the same amount of water and citrate as in the sample. The dead time is found by restarting the buret and recorder about 1 min after completion of the titration The distance on the plot before pH rises again represents the delay between start and response of the electrode. Blank and dead time can be determined with high precision using a high speed of the recorder. Standardization of tetrasodium-EGTA or -EDTA solutions is done by titration of a standard calcium solution ob-
I
0.5 -c
1.0
1.5
r n ~of 9.50 x 10'4M
2.0 Na,-EGTA
Figure 2. Titration of serum samples A . 0.2 ml of rat serum B. Rat serum with citrate C. 0.2 ml of human serum D. Human serum with citrate
+ml of 9 5 0
x
10-4M
Na,-EGTA
Figure 1. Titration plots of calcium with tetrasodium-EGTA, in the presence of citrate, as a function of the initial pH of sample
tained by dissolving calcium carbonate in nitric acid, and addition of 2 ml of 5 x 10-3M citrate solution. MAGNESIUM.After completion of the calcium titration, change to the buret containing 5 X to 10d3M tetrasodium-EDTA, and titrate without adjustment of pH of sample, because a break in the pH plot occurs in the same pH region as in the calcium titration. After correction for dead time, the EDTA titration represents magnesium. A less accurate but more convenient measure of magnesium in some samples can be obtained by adjustment of pH to 9.2 to 9.3 after the equivalence point for calcium is reached without addition of citrate. Continue titration with tetrasodium-EGTA. A small bend upward in pH indicates the equivalence point for magnesium. The amount of EGTA used between the final equivalence point and the one for calcium represents magnesium in the sample. Such a titration is not possible in blood plasma or samples containing citrate and other complexing agents. Also, an additional blank may be introduced by the base used for pH adjustment. EGTA or EDTA. A measured volume of excess of cadmium nitrate solution is added to the sample that should not contain heavy metals. After adjustment of pH to 4.5 to 5.0, a titration is done with tetrasodium-EGTA to a clear break in the pH plot. The titration value in absence of complexing agent is found by titration of a same volume of cadmium solution which should contain a small amount of buffering agent, such as citrate or acetate. The difference in back-titrations is equivalent to the amount of ligand in the sample. Total calcium is obtained by adjustment of pH to 8.0 to 8.6 after the end point for the cadmium titration is reached. Continue titration with tetrasodium-EGTA. Calcium is
calculated from the distance between equivalence points at pH 4.5 to 5.0 and at 8. Contamination of reagents should be checked by appropriate titrations of blanks. RESULTS Optimum pH Range of Samples. Figure 1 represents a series of titration curves obtained from samples prepared by diluting 0.200 ml of 6.16 X fO-aMcalcium chloride and 2 ml of 5 x lO-3M trisodium citrate to 20 ml and adjusting an initial p H between 7 and 9. The titrations were carried out with 9.5 X 10-4Mtetrasodium-EGTA in the Sargent buret. Direct reading of the equivalent point without interpolation is possible at pH 8.6 and above. The top curve represents a sample that also contained 1.00 ml of 2.1 X 10-aM magnesiurn nitrate. At pH values of about 8.0, interference of magnesium becomes virtually nil in the presence of citrate. Without citrate, an upper limit of about pH = 8.6 is necessary in the presence of moderate amounts of magnesium, and sharp equivalence points for calcium are obtained down to pH = 7.5. Biological samples give sharper end points at lower p H regions than calcium citrate solutions, down to p H = 8.0. Figure 2 shows some examples of urine and serum titrations, as well as the effect of citrate addition to serum on the plot. Magnesium determinations can be performed, but excess of citrate must be avoided, and an initial pH of 9.2 to 9.3 is required to determine magnesium in urine with tetrasodiumEGTA. A superior end point is obtained in the titration of calcium plus magnesium with tetrasodium-EDTA at pH = 8.2 (Figure 3). Improper adjustment of the stoichiometry of the tetrasodium ligand shows up either in excessive increase or decrease of p H during the titration. However, a sharp end point is obtained anyway, provided this point remains in the optimum p H region, as shown in Figure 3, in which the tetrasodiumEDTA contained some trisodium salt. Determinations of VOL. 41, NO. 1, JANUARY 1969
b
159
3.5
50
45
9 .O
%
t
8.5
I
I
I
I
I
I
05
IO
15
20
25
30
--L
I
8 .O
-
0.5
I
I
I
1.0
1.5
2.0
ml of 9 5 0 x 1 0 - 4 M No,-EGTA
or Na,
- EDTA
Top curve, titration with tetrasodium-EGTA, pH adjusted to 9.3 after end point for calcium. Bottom curve, titration with tetrasodium-EDTA in the presence of citrate EGTA and EDTA in rat urine show clear equivalence points for excess of cadmium at pH between 4.5 and 5.0. Titration curves of cadmium and of rat urine after addition of excess of cadmium are given in Figure 4. Interpolation of the plots is facilitated by the presence of buffer, such as acetate or citrate. Direct titration of acid cadmium solutions without buffer gave ambiguous poor equivalence points (curves C and D).
0 Ca
160 Ca 160 Ca 160 Ca 160 Ca 79.5 Mg 0 Ca 82.5 Mg 40 Ca 134 Mg 134 Mg 134 Mg 80 Ca 80 Ca 80 Ca 105 Cd
210 Cd 80 Ca
Foreign ion, pg
... ... ... ... 79: 5'Mg 160 Ca 82.5 Mg 0 Ca 134 Mg 40 Ca 40 Ca 40 Ca 200 c u 300 Ba 300 Sr 800 Ca 400 Ca 210 Cd
M
No,-
EGTA
Figure 4. Determination of EGTA in rat urine
Figure 3. Determination of calcium and magnesium in 0.100 ml of human urine
Taken, pg 0 Ca
ml of 9 50 x
A. Back-titration after addition of 0.400 ml of cadmium solution to 0.100 ml of urine E . Direct titration of 0.400 ml of cadmium solution plus 2 ml of 5 X 10-3Mcitrate plus 1.0 ml of 6 X 10-3M~al~ium chloride C and D. Same as B. but without citrate
Precision, Accuracy, and Limit of Detection. In titration of a variety of prepared solutions varying in volume from 20 to 25 ml, the titrant was added at a rate of 0.96 ml/min. The speed of the recorder was varied from 5 sec/inch for samples of low calcium content to 15 or 30 sec/inch for standard solutions. Table I gives the results expressed in micrograms of calcium, magnesium, or cadmium as obtained by the various methods, the range of results of quadruple determinations, and the deviation of the average results from the amount taken. Calculations were made from distances on the chart after correction for blanks.
Table I. Titrations of Standard Solutions Citrate, rnl MethodG End point, pH Found, p g 5-8.8 1.30 2 A 10 A 8.0-9.0 1.40 7.8-8.8 158.5 0 A 2 A 8.0-8.8 160 10 A 8.2-8.8 160 2 B 8.G8.4 160 8.7-8.8 79.9 2 B 2 B 8.3-8.5 0.2 8.7-8.9 82.8 2 B 39.8 0 A 7.8-8 . O 9.3-9.5 133 0 A 8.8 134 2 B 134.5 2 C 8.6-8.8 8.8 80 5 A 7.5 80.5 2 A 7.4 80.2 2 A 4.8 105 2 D 4.9 210 2 D 4.8; 8.2 80 2 D I.
Range, pg 0.1 0.1 0.4 0.3 0.3 0.4 0.4
0.2
Error,
...
...
-1.0 Ref. 0 0 +0.5
...
0.2
+0.25
0.2 1.o
-0.5
0.4 0.3
-0.75 0
+0.4 0
+0.25 +0.3 0 0 0
A, Ca by titration with Naa-EGTA; Mg by titration with same reagent (pH 9.2-9.4). B, Ca same as in A, followed by Mg titration with Naa-EDTA. C, Ca plus Mg with Naa-EDTA in one aliquot; Ca as in Method A in other aliquot. D, Cd with Naa-EGTA at pH 4.5-50; Ca by continued titration at pH 8.0-8.8. 5
160
ANALYTICAL CHEMISTRY
Table 11. Comparison of Results in Practical Solutions Sample Human urine Human plasma City water, Richmond, Va. Atlantic Ocean, Eastern Shore
Human plasma, +162 pg of EDTA Human plasma, +190 p g of EGTA Human urine, +162 pg of EDTA Human urine, +190 pg of EGTA
Titration method" B B B B B B A B B A C D D D D
Sought Ca Mi3
Ca Mi3 Ca Mg
Mg Ca Mg Mg Mg
EDTA Ca EGTA Ca EDTA Ca EGTA Ca Ca
Magnesium nitrate crystals A Same as in Table I. Perkin Elmer, Model 303, in presence of lanthanum, in addition EDTA for sea water.
The presence of citrate caused a slight increase in the recorded use of EGTA and EDTA. Recrystallization of the EGTA did not change this increase significantly. Standardizations of EGTA and EDTA were always done in the presence of citrate. Table I1 presents results of practical solutions by the titration methods and by atomic absorption. In addition, the quantitative recovery of complexing agents from blood plasma and urine samples was verified. The limit of detection under our experimental conditions is below 0.5 pg calcium or magnesium. This amount of calcium could be detected in 100 ml of deionized water after leaving it in a borosilicate flask for one week. The detection limit for EDTA and EGTA is about 10 pg, and a range of 4 pg is obtained. Interferences. As both EDTA and EGTA are strong complexing agents for multivalent metals, some of these metals are titrated with calcium, even in the presence of masking agents such as citrate. Citrate eliminates interference of copper and iron, but not of zinc. A small excess of cyanide masks the last metal, but the calcium titration should be carried out above pH = 8.6 with citrate added to prevent interference of magnesium. Table I shows some examples of solutions containing strontium and barium which usually interfere in titrations of calcium. If titrations are carried out to an equivalence point at pH 7.5 or below, calcium is determined without difficulty in 'the presence of up to 350 pg of total barium and strontium in the presence of citrate. Solutions of high buffer capacity in the optimum pH range for titrations give a poorly defined end point. A maximum of 0.5 mmole of phosphate is allowed for precise end point detection for calcium at pH 8.6 or above. Therefore, a phosphate/calcium mole ratio of lo00 is allowed in the determination of 20 pg of calcium. Although magnesium can be determined by titrations of aliquot samples, one with EDTA and one with EGTA, the
Titrations
Found, in ppm, by Atomic absorptions
143 92 79 20 18.2 2.89 2.78 381 1180 1170 1178 164 79 190 79 162 143 192 143 123
143.3 90.4 78.5 19 18.2 2.91 2.91 381.5 1131 1131 1131
... 78.5
... 78.5
... 143.3
... 143.3 106
difference between equivalents used may be small compared to the total titrations. It is more convenient to titrate magnesium with EDTA in a sample in which calcium has been titrated with EGTA to slightly beyond the equivalence point. A large excess of EGTA obscures the end point of the EDTA titration, because it reacts partly with magnesium, causing a rise in pH before the equivalence point. The last entry in Table I1 shows that traces of calcium can be determined in a large excess of magnesium. The titration is carried out in solutions containing sufficient citrate to complex magnesium. Samples of 0.50 and 1.00 g of magnesium nitrate crystals were used in the titrations. DISCUSSION
The suggested titration methods for calcium and magnesium give titration plots from which equivalence points can be determined with high precision. The reason for the favorable plots is the essentially complete complexation at the equivalence point in the relatively high pH region, shown in Figure 1 for calcium, in contrast with pH regions shown previously (2). Major advantages of the method are apparent in samples containing a large excess of magnesium over calcium. Even trace amounts of calcium can be determined in magnesium nitrate, although the high titration value, compared to atomic absorption, may indicate the presence of heavy metals which are determined with calcium. The titration method gives closer to accepted values for magnesium in sea water than atomic absorption does, and good agreement is found for calcium by the two methods. Sometimes it is necessary to perform titrations at lower pH than at optimum range. In such cases precise interpolation is facilitated by the presence of a small amount of buffer. Therefore, biological fluids can be titrated over a wider pH region than pure salt solutions. In addition, interference of up to 350 pg of total strontium and barium can be avoided by titration at pH 7.5 or below, and the sum of these metals can be found later by titration at a higher pH. VOL 41,
NO. 1, JANUARY 1969
161
Simplification of apparatus is possible in titrations of relatively larger amounts of calcium. Manual titrations can be carried out using a regular pH meter as the indicator. Sharp end points are obtained if 10+M or stronger titrants are used. A color indicator is less suitable because strict requirements are imposed on the stoichiometry of the titrant because the pH of the sample is not allowed to change significantly during the titration.
ACKNOWLEDGMENT The authors thank Charles O'Rear for the atomic absorption measurements, and Henry P. Lau for interference studies. RECEIVED for review September 7,1967. Accepted August 29, 1968. One of the authors (J. E. W.) is a National Institutes of Health trainee, Training Grant 2T1-GM-484. Work performed under National Institutes of Health Contract AM09427-02.
1 NOTES Gas Chromatographic Analysis of Pyruvic and a-Ketoglutaric Acids Norman E. Hoffman and Thomas A. Killinger Todd Wehr Chemistry Building, Marquette University, Milwaukee, Wis. 53233 CONVERSION of pyruvic and a-ketoglutaric acids to their methyl esters by acid-catalyzed methanolysis or reaction with diazomethane can lead to two products. Simmonds, Pettitt, and Zlatkis (I) in a thorough study have shown that, in addition to the desired ester, the ketal ester is formed in methanolysis and a glycidate ester is formed with diazomethane. These authors have reviewed previous investigations of the gas chromatography of pyruvic and a-ketoglutaric acids ( I ) . In addition to competing reactions during its formation, at least in the case of pyruvic acid, the methyl ester presents a handling problem. Because of its relatively high volatility, a sample containing the ester can be fractionated prior to gas chromatography. We report an approach to the gas chromatography of these keto acids that relies on the formation of quinoxalones (Equation l).
NE
H
Infrared and nuclear magnetic resonance spectral studies of these heterocyclics showed they existed, to the limits of detection, entirely in the keto form and not in the hydroxyquinoxaline enol form. This derivative has the advantages of rapid formation, low volatility, and a large number of reduced carbons and, therefore, greater detectability using flame ionization. Furthermore, the quinoxalone's mild acidity permits pH control for separation from basic, neutral, or strongly acidic constituents of biological samples. EXPERIMENTAL
Apparatus. A Barber-Colman Model 5000 gas chromatograph equipped with a hydrogen flame ionization detector was used. The chromatographic columns were 6-foot U-tubes packed with 80/100 acid-washed Chromosorb W coated either with 13 SE-30 or 1 OV-17. (1) P. G. Simrnonds, B. C . Pettitt, and A. Zlatkis, ANAL.CHEM., 38, 163 (1967).
162
ANALYTICAL CHEMISTRY
Reagents. Quinoxalones of pyruvic and a-ketoglutaric acids were prepared by mixing a solution of 60 mmol of sublimed o-phenylenediamine in 100 ml of 10% acetic acid with a solution of 30 mmole of keto acid in 30 ml of water ( 2 ) . The precipitated quinoxalone was filtered after 15 min, washed with water, dried, and recrystallized from methanol. Under the dilute solution conditions found in biological samples, pyruvic and a-ketoglutaric acids can be converted to quinoxalones in 100% yields. Standard solutions prepared to concentrations known to better than 1 contained about 0.1 g solute/lO ml dry pyridine. Solutes were 3-methyl-2-quinoxalone (from pyruvic acid), 3-(2-carboxyethyl)-2-quinoxalone (from a-ketoglutaric acid), 6-methyl-2-naphtho1, and p-nitrophenyl phenyl ether. Procedure. The above-mentioned pyridine solution of quinoxalone was mixed in varying amounts, 5-50 p l , with 20 p1 of the pyridine solution of either the naphthol or nitro ether mentioned above. To this was added 200 pl of bis (trimethylsilyl) acetamide (BSA) and 50 p1 of pyridine. (2) D. C . Morrison, J . Amer. Chern. SOC.,76,4483 (1954).
