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of the density is 1 X 10-jg/mL; for the semi-micro method, 2x g/mL. The results agree within 0.1% in the worst case. There may be a slight negative bias (-0.0005 g/mL) for the semi-micro method; however, the limited number of samples analyzed precludes any definite conclusion on a bias this small. Thus, the objective of finding a reasonably accurate (>0.1% accuracy) semi-micro method has been met. The method should be applicable to any body fluid.
LITERATURE CITED
Flgure 1. Cradle of sheet aluminum for holding micropipet on the analytical balance
and Tobsd is the observed temperature in "C. The value for the constant in the formula has been empirically determined for serum and does not differ significantly from the value given for distilled water.
RESULTS AND DISCUSSION T h e densities of one serum and both porcine and human blood samples were determined. Some of the samples were preserved with EDTA or heparin. Each of the results presented in Table I represents the average of a t least triplicate determinations. All determinations have been corrected t o an observed average laboratory temperature of 23 "C. For the pycnometer method, the standard deviation
Baw,N. ''D8trnbti-m of Density" in "Techniques of Organic Chemistry". Weissberger. A., Ed.; Interscience: New York, 1949; Chapter VI, pp 263-276. Altman, P. L. In "Blood and Other Body Fluids"; Dittmer. D. S.,Ed.; Fed. Am. SOC.Exptl. Bioi., Comrn. on Biol. Handbooks; Washington, D.C.. 1961; pp 12-13. Sunderman, F. W.; Boerner, F. "Normal Values in Clinical Medicine", W. B. Saunders and Co.: Philadelphia, Pa., 1950; pp 93-95. Elder, J. P. "Recent Advances in Fluid Density Measurements"; Am. Lab. 1978, 10 (4). 75. MacLeod, J. "Red-Cell Density in Certain Common Animals": 0.J . Exp. Physiol. 1932, 22, 275. Moore, N. S.,; VanSlyke, D. D. "The RelationshipBetween Plasma Specific G-avity, phsma Protein Content, and Edema in Nephritis", J . Clin. Invest. 1930, 8 , 337. Barbour, H. G.; Hamilton, W. F. "The Falling Drop Method for Determining Specific Gravity"; J . B o / . Chem. 1926, 69, 625. Philips, R. A.; VanSlyke, D. D.; Hamilton, P. B.; Dole, V. P.; Emerson, K.. Jr.; Archibald, R. M. "Measurement of Specific Gravities of Whole Blood and phsma by Standard Copper Sulfate Soluiions"; J . Bb/. Chem. 1950, 183, 305. Kenner, T.; Leopold, H.; Hinghofer-Szalkay, H. "The Continuous HighPrecision Measurement of the Density of Flowing Blood"; Pflueger's Arch. 1977, 370, 25.
RECEIVED for review December 21,1978. Accepted March 13, 1979.
Improved Accuracy in Atomic Absorption Analysis by Optimization of Optical Cell Parameters Gerald F. Dowd and John C. Hilborn" Environment Canada, Air Pollution Technology Centre, River Road, Ottawa, Canada, K 1A 1C8
Extensive use is made of the atomic absorption detector in the measurement of mercury vapor levels in the atmosphere. The active part of this detector is the optical cell and the air in the optical cell is generally considered to represent the atmosphere being sampled, but only if the mercury concentration remains constant. If it is not constant, the concentration in the optical cell will be changing continuously and will not be equivalent to the concentration in the sampled atmosphere a t any given time. This occurs because there is a finite time associated with achieving a uniform concentration in an optical cell following a step change in input and this mixing time is a function of a number of parameters. These parameters can be selected and used in instrument design to achieve a desired mixing time. We speak of mixing time because time is a parameter which can be measured, but what is really desired is to achieve a certain percentage (usually 99% or 99.9%) of the true atmospheric concentration in given time. If greater than 99% of the final concentration can be achieved quickly in the optical cell, the measured concentration more nearly represents the true atmospheric concentration, i.e., accuracy has been improved. An optical cell can be viewed as a small version of an animal exposure chamber. This fact led us to examine the equations in the literature which have been used to describe the pollutant concentration changes in an exposure chamber following a step 0003-27@0/79/@351-1578$01 .OO/O
change in input concentration (purging) as they apply to optical cells. Silver ( I ) and Nelson ( 2 ) have defined a function that relates the number of air changes in a chamber or cell and concentration. An air change means that a volume of air equal to the volume of the cell has passed through the cell. This function (Equation 1)is called the ideal mixing function as it assumes perfect and instantaneous mixing a t all times.
C1 = COe--N
(1)
C, is the pollutant concentration in the cell before the purging operation begins. C1 is the concentration of pollutant in the cell a t some time during the purging operation. N is the number of air changes. From experimental work, Silver ( I ) has reported a 97% response to a step concentration change with N values greater than 3. Brief and Church (3), working with exposure chambers, have reported that, for safety reasons, a mixing factor K should be applied to the ideal mixing formula.
C1 - Coe-KN
(2)
The mixing factor allowed for nonideality of mixing and was between 0.1-0.3. Our studies of cell purging, using mercury in air concentrations measured by atomic absorption, produced data which did not conform with Equations 1and 2. However, using our 0 1979 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
co
AIR INPUT
n
1579
\ \Y
1500 V
I AMPLIFIER
RECORDER
INTEGRATOR
Figure 1. Block diagram of optical cell and accessories cell purging data, we derived functions which can be used to describe the entire spectrum of the mixing profiles which could theoretically exist in an optical cell under dynamic operation. In addition, a function was derived which describes the dynamics of our optical cell design. It is assumed that these functions would describe the behavior of gas mixtures other than mercury in air as well.
EXPERIMENTAL Apparatus. All the data presented in this report was obtained from measurements made on the cell assembly shown in Figure 1, using mercury vapor in air mixtures. These mixtures were obtained using a dynamic mercury in air generator built in our laboratory ( 4 ) based on the concept described by Nelson ( 2 )and Scheide et al. (5) or from a static mercury in air source (6). The optical cell, lamp power supply, amplifier, and signal processor were designed and built in our laboratory ( 7 ) . Emissions from a low-pressure mercury vapor lamp (8) were measured by a UV sensitive phototube after they passed through the air in the cell. The cell was 4.5 cm in diameter, 27 cm in length, and had a total volume of 423 mL. The flow rate of air through the cell was maintained at 650 mL/min. Both the phototube and the lamp were mounted inside the cell to obtain maximum contact with the air stream. Procedure. Optical cell purging was examined by first allowing mercury in air mixtures to flow freely through the optical cell until the recorder indicated a steady maximum output. Switching a valve located as close as possible to the optical cell inlet interrupted the flow of mercury in air to the cell and permitted mercury-free air to enter the cell. The change in mercury concentration in the cell with time was described by the recorder tracing of the decay curves. The behavior of mercury vapor introduced into an optical cell was used to verify our derived equation for dynamic injection approaching idealized injection. Air saturated with mercury vapor was injected into a stream of clean air passing through the optical cell. RESULTS AND DISCUSSION Dynamics. The dotted line in Figure 2 describes a function we obtained by averaging concentration measurements made during purging operations using the dynamic mercury source on our 423-mL cell a t a flow rate of 650 mL/min. The initial concentration (Co) was 230 fig of mercury vapor per cubic meter. This dotted line could not be described by the ideal mixing function. Using the mixing factor concept of Brief and Church (3)and our experimental results for decay curves, we calculated a n approximate value of K = 0.7 for our 423-mL absorption cell. The function for ea is shown in this figure. Neither the K = 1function nor the K = 0.7 function describes the dotted line in Figure 2 . Curve fitting showed t h a t this dotted line could be described by another exponential on the values of N and of u (a power of N), as shown in the figure, with a u value of 1.3 f 0.03. Note that u = 1 is identical t o the ideal gas mixing function, K = 1. Note also t h a t the u = 1.3 equation satisfies the initial conditions of the K = 0.7 equation while supporting Silver's stabilization time values. Brief (9) has further reported in 1960 on the presence of different ordered concentrations in a chamber that suggests
'"
NUMBER OF AIR CHlNGES
O()
Figure 2. Plots of number of air changes ( N )vs. percent of initial concentration (C,) reached. (A) Equation 2 when K = 0.7, (B) equation 2 when K = 1.0, (C) purging curve
r-l C1=COEXP
F"J Ioyllr\nlcI 1 ( MIXING
MIXING
FUNCTION
F] 1( INJECTION
INJECTION
Figure 3. Relationship of air flow ( F ) ,time ( T ) , and cell volume (V,) to the number of air changes (N) and the evolved function on the variable U
that the mixing factor value reflects the presence of many different concentration distributions in a chamber which is of particular interest in the application to animal toxicity studies. T h e mean time-to-death experiments, upon which many LK50 values were determined, have assumed a homogeneous gas mixture, which, in reality, may not have been the case. Figure 3 shows a relationship ( R ) defined by the cell dynamics of air flow (F),time of measurement ( T ) , and cell volume (VJ. T h e solution is shown as N , the number of air changes in the cell. On this solution we have evolved t h e function shown on a variable u having values between 1 and a. This function was the result of laboratory studies on purging operations and injection calibration. Here we see that there are three distinguishable states of u. When u = 1,we have ideal mixing; when u = 2 , we have the derivative of the error function; and when u -- m, we have ideal injection without any mixing. Between the ideal mixing and the error function, we have fractional values of u. As it is most likely t h a t a number of distanct concentration distributions exist in the cell in a dynamic mixing operation, these values may be defined on partitions of whole numbers of u. Dynamic mixing following injection calibration is close t o the u = 3 variable regardless of concentration, air flow, or injection quantity. This is of particular importance as it gives practical verification of the function when u = 3. Figure 4 is a graphic representation of the family of curves obtained when u is between 1 and a. T h e u m equation is of special interest. It represents idealized injection where there is n o mixing, viz., a highly ordered transfer of a slug of mercury through the cell. This shows that in the idealized condition a n ordered transient of mercury vapor passes through the cell in exactly two air changes.
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
gration, only the negative slope of this curve can be considered a true function of N into concentration. Note that these dots follow the injection curve in the region where this curve is a true function. This clearly shows that the absorption cells' response to an injection can be defined by the u = 3 equation.
2
1
NUMBER OF 1IR CHANGES
3
IN)
Figure 4. Graphic representation of the derived function for u values between 1 and a
u-3
-
INJECTION
CONCLUSIONS Based on our derived functions, in order to achieve a step response greater than 99% of maximum concentration in a measurement time of 15 s, a cell volume of 30 mL coupled with an air flow of 600 mL/min is required. Other air flows and cell volumes can be selected as required. The equation in Figure 2 applies to the cell described above. Whether or not it applies to cells of other geometries cannot be stated with certainty. Further purging experiments are recommended. The derived equation should apply equally well to situations where the gas entering the optical cell is not pure diluent, but some concentration of pollutant in air which is greater or less than the concentration existing in the cell. This follows because the mixing time is a function of cell volume and flow rate, but not concentration. The time for concentration buildup and concentration decay will be the same if flow rate and cell volume are constant. Most optical cells have the lamp and phototube mounted outside the cell and it should be possible to establish mixing time for this configuration equally well by using the concepts presented here. For the same optical cell, varying flow rate may influence the mixing process and, consequently, the u value and the shape of the curve (Figure 4). I t is recommended t h a t our derived equation be used as a starting point for the estimation of mixing time, knowing cell volume and flow rate, but that the true function be derived from purging experiments as described above. LITERATURE CITED
NUMBER Of hlR CHANCES
(
N)
Figure 5. Similarity between curves for injection response (solid line) and the derived function when u = 3 (dots). Initial concentration (C,) and concentration sometime later (C,)
Figure 5 shows the similarity between an injection response curve (solid line) and the u = 3 curve (dots). The concentration scale, shown on the y axis, was obtained from a dynamic source calibration of the absorption cell. The Co point of 45 pg/m3 was obtained by calculating the cell response to 19 ng of mercury. T h e x axis is the number of air changes, as previously mentioned, a relationship between air flow, time, and cell volume. The absorption cell response to a 19-ng injection of mercury is shown by the solid line. Because of measurement inte-
Silver, S. D. J . Lab. Cfin. Med. 1946, 31, 1153-61. Nelson, G. 0. "ControlledTest Atmospheres", 1st ed.;Ann Arbor Science Publishers Inc.: Ann Arbor, Mich., 1971, Chapter 6. Brief, R. S.; Church, F. W. Ind. Hyg, J . 1960, 239-44. Dowd, G. F.; Hilborn, J. C., presented at the 174th National Meeting of the American Chemical Society, Chicago, Ill., 1977. Scheide, E. P.; Alvarez, R.; Greifer, 9.; Hughes, E. E.;Taylor, J. K. "A Mercury Vapor Generation and Dilution System", National Bureau of Standards publication NBSIR 73-254, 1973. Findlay, W . J.; Li, K.;Dowd, G.; Hilborn, J. C., presented at the 173rd National Meeting of the American Chemical Society, New Orleans, La., 1977. Dowd, G. F.; Corte, G. L.; Monkman, J. L. J. Air Pollut. Control Assoc. 1976, 26, 678-79. "Specifications for PEN-RAY Lamps", U. V. Products Inc., San Gabriel, Calif. Brief, R. S. Air Eng. 1960, 2, 40-41.
RECEVIED for review February 9,1979. Accepted April 2,1979.
Possible Errors in Energy Dispersive X-ray Spectrometry Due to Raman Scattering P. J. Van Espen, H. A. Nullens, and F. C. Adams" Department of Chemistry, University of Antwerp (VIA), Universiteitsplein 1, 6-26 10 Wilrijk, Belgium
Shortly after the discovery of Raman scattering of visible light in 1928 ( I ) , an intensive search was conducted to find a similar effect for X-rays. Although the phenomenon had already been predicted in 1923 ( 2 ) ,conclusive evidence for its existence could not be obtained until 1959 ( 3 , 4 ) . The effect can be described as follows: an incident photon with energy hvo ejects an electron from one of the inner shells of the atom, 0003-2700/79/0351-1580$01 .OO/O
giving it a kinetic energy E,; the remaining energy can be detected as a photon having an energy hv, with
hv = hvo - Ek
- Eb
(1)
where E b represents the binding energy of the electron. T h e kinetic energy of the ejected electron can vary between zero and hvo- E,; therefore, when monochromatic X-rays interact 1979 American Chemical Society
