The values of 1, t , and D are generally such that R is approximately equal to P , as is the case in the example given above, If, however, R is significantly less than P , as may happen when t is small, then P rather than R should be used in the denominator of the last term in Equation 7 to avoid an unnecessarily high estimate of the error bound. By substitution of typical values for 1, t , and D into the coefficient of dR/R in Equation 7, it can be seen that the value of this coefficient will usually be between 2.0 and 2.5. This means that for equal relative errors in 1, t , and R , the three error terms on the right side of Equation 7 have a ratio of roughly 2:1:2 when reading from left to right. A serious source of systematic error results from convective loss of diffusant from the mouth of the capillary. For example, in our laboratory we have observed that the first millimeter of water in the bore of a 1-mm diameter capillary was continually swept out by convection when the surrounding liter of water was stirred at 300 rpm with a smooth, 45-mm diameter, Teflon disk mounted perpendicular to the stirring shaft. These conditions are similar to those reported elsewhere (2). When such a loss of diffusant occurs, and it is assumed that the length of the diffusion column is the same as the bore length of the capillary, then the resulting systematic error in 1 will be such that dl is positive, i.e., the value of 1 used to calculate D is greater than the true value. Also, if CO is not determined experimentally, but is instead assumed to be the same as the analytical concentration of diffusant in the solution used to fill the capillary, then convective loss will cause CO to be in error by some positive amount; hence dR will be negative. Equation 5 shows that in the unfortunate case where dl is positive and dR negative, these errors are additive rather than compensating.
One concludes that accurate results require the use of fine bore capillaries from which convective loss is minimal. Nevertheless, the accuracy obtainable with larger bore capillaries may be entirely consistent with the needed and obtainable precision, which in some cases may not be better than 5 to 10%. The best precision reported so far is f0.5% for selfdiffusion of sodium ions in aqueous solution, obtained by Mills (7) using fine bore capillaries and special apparatus. Past use of capillaries as large as 1 mm in diameter has apparently been needed to diffuse sufficient material to satisfy the sensitivity requirements of the various techniques used to determine diffusant concentration.
LITERATURE CITED J. S. Anderson and K. Saddington, J. Cbem. SOC., S381 (1949). J. Bacon and R. N. Adarns, Anal. Cbem., 42, 524 (1970). R. N. Adarns. “Electrochemistry at Solid Electrodes”, Marcel Dekker, New York, N.Y., 1968, pp 220-222. T. A. Miller. B. Lamb, K. Prater, J. K. Lee, and R. N. Adarns, Anal. Chem., 36, 416 (1964). T. A. Miller, B. Prater, J. K. Lee, and R. N. Adarns, J . Am. Chem. SOC., 87, 121 (1965). R. A. Robinson and R. H. Stokes, “Electrolyte Solutions”, 2nd rev. ed., Butterworths, London, 1965, pp 261-264. R. Mills, J . Am. Cbem. SOC.,77, 6116 (1955).
N. C. Fawcettl Roy D. Caton, Jr.* Department of Chemistry The University of New Mexico Albuquerque, N.M. 87131 RECEIVEDfor review July 25, 1975. Accepted October 3, 1975.
1 AIDS FOR ANALYTICAL CHEMISTS Calibration of the Oxygen Polarograph by the Depletion of Oxygen with HypoxanthineXanthine Oxidase-Catalase Jordan L. Holtzman Clinical Pharmacology Section, Veterans Administration Hospital, Minneapolis, Minn. 554 17
When the oxygen polarographic or “Clark” electrode, is used to quantitate oxygen uptake, it is necessary to calibrate the electrode current against the concentration of dissolved oxygen. By far the simplest method for such calibration is to thoroughly saturate the reaction medium with air at the reaction temperature and then derive the oxygen concentration for 100% saturation from tables of solubility of oxygen in water (1). [These data can be found only in editions of reference 1, which were published prior to 1970 (51st edition).] Although this method is simple and reasonably precise, it is limited to solutions in water and cannot be used with other solvents as deuterium oxide or glycerolwater mixtures, both of which have found use in enzymatic studies. Further, the atmospheric pressure must be noted at the time of the study. Alternatively, the electrode can be calibrated by determining the stoichiometry between submitochondrial electron transport oxidation of NADH particles and the decrease in electrode current ( 2 ) .This technique requires the
preparation of these particles, which entails some effort and expertise. More important, the usual preparations of NADH are not highly purified and may contain several percent of yellow contaminants as well as an unspecified amount of water of hydration. Although these problems can be circumvented by spectrophotometrically determining the concentration of the reagent, it is desirable to begin with a pure reagent for any calibration. Recently Wingo and Emerson ( 3 ) have proposed the use of the decomposition of aqueous hydrogen peroxide by catalase for such calibrations. The primary disadvantages of this method are that the solutions must be degassed, the peroxide must be calibrated using titrimetric methods even though such methods have fallen out of favor in biochemistry laboratories, and minor contamination of the hydrogen peroxide could readily lead to its decomposition changing the calibration. In view of these considerations, 1 have recently investigated the calibration of the electrode by the depletion of ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
229
Table 11. Determination of Volume of Incubation Vessel. Total Hypoxanthine = 473 nmol
Table I. Determination of [ O,] by Hypoxanthine-Xanthine Oxidase-Catalase [Hypoxanthine] = 110.9 phf
* SEM
Ei
Ef
[O,I P M
Av
4.375 4.365 4.375
2.075 2.07 5 2.090
211.0 211.3 212.3
211.5
t
0.4
oxygen by the oxidation of hypoxanthine in the presence of xanthine oxidase and catalase ( 4 ) : hypoxanthine
+20 2
xanthine oxidase
+ catalase
2 H202 + 2 HzO hypoxanthine
+0 2
-
uric acid
+ 2 H20
EXPERIMENTAL The oxygen concentration was determined with a YSI 5331 electrode (Yellow Springs Instruments, Yellow Springs, Ohio) and recorded on a 5-MV servorecorder (Esterline Angus, Indianapolis, Ind.). All uptakes were run in KC1-tris-MgCl2 buffer (0.15 M-0.05 M-0.005 M ; pH 7.4). Hypoxanthine, milk xanthine oxidase (X4875) (6.9 units per ml), and liver catalase (C-40) (14400 units per mg) were obtained from Sigma Chemical Corp. (St. Louis, Mo.) and used as obtained. The buffer was maintained at 37 O C under air and stirred with a magnetic stirrer. The hypoxanthine was weighed i n t o a 50-ml volumetric flask to give a concentration of 5 m M (0.681 gh.1 in buffer. The solution must be warmed to completely dissolve this reagent. The concentration was confirmed by determining the absorbancy a t 250 nm ( t = 10.7 mM-' cm-') ( 5 ) , with ratios of A250/A260 = 1.32 and A280/A260 = 0.09 ( 5 ) .The agreement between the spectrophotometric and gravimetric determinations was within 0.5%.In view of the recent widespread acceptance of direct readout spectrophotometers without slide wires, it is of the utmost importance t o check the calibration of such spectrophotometers with a neutral density filter (Optical Industries Inc., Costa Mesa, Calif.) previously calibrated on a null instrument. To determine the oxygen concentration, 5 ml of buffer was added to a jacketed incubation vessel maintained a t 37 "C. The hypoxanthine (120 pl of a 5 m M solution; final concentration, [hypoxanthine] = 120 pM) was added along with the solution of catalase (10 p1 of a 1% solution) and the solutions were thoroughly mixed. The cell was capped and allowed to equilibrate. The initial deflection on the chart was recorded (Ej) and the reaction was begun by the addition of the xanthine oxidase (100 pl). When the readings no longer changed, the chart recording was taken as the final millivolt reading ( E d . The oxygen concentration was then: [hypoxanthine] [021 = E i X [hypoxanthine] =
Ei - E f
F
where F is the fractional decrease in electrode current. The effective volume of the incubation cell was similarly determined except that the buffer was added to the cell, the cell was capped, and then the hypoxanthine (100 p1) and the catalase were added through the injection port. When the current reading stabilized, the xanthine oxidase was added. The volume of the cell ( V )
230
Ef
Vol, m l
Av
4.400 4.425 4.365 4.375 4.350
1.950 2.050
4.02 4.17 3.90 3.95 3.95
4.00
ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
1.860
1.900 1.885
* SEM
i
0.05
was then:
V = Fmol hypoxanthine -= Ei [OZI Ei - E f
+ 2 H202
+02
uric acid
Ei
pmol hypoxanthine FW21
RESULTS AND DISCUSSION This method gave highly reproducible values for [Oz]. In a typical study, the [ 0 2 ] equals 211.5 M M (Table I). On the day of this run, the atmospheric pressure was 758 Torr and the concentration should have been 211 p M ( I ) , which was close to the observed value. These results clearly indicate that the oxidation of hypoxanthine in this system has a 1 : l stoichiometry with the uptake of oxygen. Similarly, I observed a highly reproducible value of 4.00 ml for the volume (Table 11). The actual volume was 4.17 ml f 0.05 ml (N = 3), as determined by removing the incubate with a calibrated pipet. The difference between these two determinations may well be due to the fact that the volume in the injection port on the cell does not participate in the reaction, but is determined when the volume is directly measured. In conclusion, this method would appear to be a valid and convenient method to determine both the concentration of the dissolved oxygen and the effective volume of the incubation vessel. This method has the advantages over other methods in that the reagents are commercially available, inexpensive, and stable for years. Of particular importance, the primary reagent, commercial hypoxanthine, is a highly pure compound which, both from other studies (5) and my present data, does not appear to be even hygroscopic. Hence, this compound may prove to be a reasonable primary standard. LITERATURE CITED (1) "Handbook of Chemistry and Physics", 44th ed., C. D. Hodgman, R. C. West, R. S. Shankland. and S. M. Selby, Ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1962,p 1706. (2) R . W. Estabrook, "Methods in Enzymology", Vol. X, S. P. Colowick and N . 0. Kaplan, Ed, Academic Press, New York, N.Y., 1967, p 41. (3) W. J. Wingo and G. M. Emerson, Anal. Chem., 47, 351 (1975).
National Research Council, "Specifications and Criteria for Biochemical Compounds", National Academy of Sciences, Washington, D.C., 1972, p 117. (5) National Research Council, "Specifications and Criteria for Biochemical Compounds", National Academy of Sciences, Washington, D.C., 1972, p
(4)
171.
RECEIVEDfor review July 21, 1975. Accepted October 17, 1975.
