ported by the fact that nitrobenzene is also bindable to PVP (13). The low efficiency of removal of the catecholamines from solution in one plate equilibria with Polyclar is most probably due to the fact that steric hindrance caused by the bulky side chains of epinephrine and norepinephrine prevents the proper alignment of these phenolics with the pyrrolidine ring. This steric hinderance lowers the energies of both hydrogen and charge transfer bonds. Recovery of the complexed phenolics from the Polyclar column using 4 M urea has been observed to proceed with near 100% efficiency. Urea is a weaker hydrogen bonder than phenols and, because of this, high concentrations were needed to force the equilibrium to favor the release of the phenolic from the polymer.
LITERATURE CITED (1) (2) (3) (4)
R. A. Anderson and J. A. Sowers, Phytochemistry, 7, 293, (1968). K. H. von Gustavson. Leder, 14(2), 27 (1963). W. D. Loomis and J. Batailla. Phytochemistry, 5, 423 (1966). R. V. Dahlstrom and M. R. Sfat, Brew. Dig., 47(5), 75 (1972). (5) R. A. Ciemens and A. J. Martineiii, Wines Vines, 39(4), April 1958.
(6) (7) (8) (9) (10) (1 1) (12) (13) (14) (15) (16) (17) (18) (19) (20)
Chem. Ind. Ltd., Britain, 1,099,722(Cl. A61K). Jan. 17, 1968. J. Burdy and W. Chernecki, Can. J. Physiol. Pharmacol., (6), 46 (1968). M. A. Kassem and A. E. M. EiNimr, Sci. Pharm., 3, 38 (1970). J. W. V. Cordice, J. E. Suess. and J. Scudder, J. Surg. Gyn. Obstet.. 97, 39 (1953). H. A. Ravin. A. M. Seligman. and J. Fine, N. Engl. J. Med., 247(24). 921 (1952). M. Freifeld, J. R. Lyons, and A. J. Martinelli, Am. Perfumer, 77(2), 25-27 (1962). R. A. Anderson and J. R. Todd, T06. Sci,, 12, 1078 (1966). P. Molyneux and H. P. Frank, J. Am. Chem. Soc., 83, 3169 (1969). T. Higuchi and R . Kuramoto, J. Am. Pharm. Assoc, Sci. Ed., 398, July 1954. D. i. Randall, E. M. Smolin, and J. P. Copes, Nature, 244, 369 (1973). B. N. Kabodi and E. R . Hammarlund, J. Pharm. Sci., 55, 1069 (1966). D. Guttmann and T. Higuchi, J. Am. Pharm. Assoc., 45, 659 (1956). H. P. Frank, S. Barkin, and F. R . Eirich, J. Phys. Chem., 61, 1375 (1957). C. D. Chriswell, R. C. Chang, and J. S. Fritz, Anal. Chem., 47, 1325 (1975). L. Chien, "An NMR Study of the Complexation of Phenol by Poiyvinyipyrrolidone"; Research Project, University of Massachusetts, unpublished, 1974.
RECEIVEDfor review July 7, 1975. Accepted October 6, 1975. This work was supported by Grant No. G P 37493X from the National Science Foundation.
1 CORRESPONDENCE Analysis of Errors in the Capillary Method for Determining Diffusion Coefficients Sir: The method of Anderson and Saddington ( I ) for determining diffusion coefficients (D) by observing the rate a t which substances diffuse from capillaries has been used to obtain D values applicable to electroanalytical chemistry. Adams and his group, for example, have clearly demonstrated the importance of determining D values independent of electrochemical techniques but under conditions used in electrochemistry, and they have used the capillary method in their work (2-5). Although the method has been described in numerous papers and has been discussed in a well-known monograph (6),to our knowledge a differential error analysis has not appeared. Such an analysis clearly shows the relative importance of the various errors that may be encountered and should prove useful to those who plan to use the method. Briefly, the experimental procedure consists of filling a capillary of length 1 with a solution of diffusant a t concentration COand then suspending the capillary vertically in a large excess of pure solvent. The capillary is closed a t the lower end but open a t the top so that material can diffuse out. Also, it is customary to stir the surrounding fluid to maintain the concentration of diffusant a t the capillary mouth as near zero as possible. After a period of time, t , the capillary is withdrawn and C, the average concentration of diffusant remaining, is determined. The diffusion coefficient is then computed from the following equation.
The total differential of R, assuming no interdependence Present address, Chemistry Department, Southwest Texas State University, San Marcos, Texas 78666. 228
ANALYTICAL CHEMISTRY, VOL. 4 8 , NO. 1, JANUARY 1976
of errors, is dR = (aR/aD)dD
+ (aR/at)dt + (aR/al)dl
(2)
The partial derivatives in Equation 2 are obtained from Equation 1 to give aR/aD = -(r2t/412)P aR/at = -(r2D/412)P aRlal = (r2Dt/213)P
(3)
where m
P = 8/r2
exp[- (2n n=O
+ 1)2~2Dt/412]
(4)
Rearranging Equation 2 followed by substitution from Equation 3 gives the following expression for the relative error in D. dD/D = 2dl/l
- dt/t
- (412/r2Dt)dR/P
(5)
From Equations 1 and 4 note that
R I P
(6)
Therefore, replacing P with R in Equation 5 gives an expression for the upper bound on the relative error in D as dDID I I2dW
+ I dtltl + 1 (412/~2Dt)dRIRI
(7)
A rough first-order approximation to the value of the error bound can be obtained by substitution of finite values for the infinitesimals in Equation 7. For example, let I At1 = 1800 sec, 1 AI\ = 0.03 cm, and 1 AR/RI = 0.01. Then for an experiment that lasts 4.3 X lo6 sec (120 hr), in 6-cm long capillaries and for which D is 1.5 X 10-5 cm2 sec-', the approximate value of the upper bound is 4%.
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
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