vents than in ethanol-water solvents have been observed for the ionization of water (8, 12), but they are not what one would predict from a simple Born electrostatic model. Likewise, the differences in the effects of ethanol-water and acetone-water on the hydrolysis equilibrium constants are not predictable from such a model. Other thermodynamic data, such as transfer enthalpies and entropies, are necessary in order to draw meaningful conclusions regarding specific contributions of electrostatics, hydrogen bonding, solvation, etc. (8, 13, 18, 19).
LITERATURE CITED
- .
. io
0
.
.
40
.
.I
60
h'T % ACE'CNE Figure 2. Plots of changes in free energies (Equation 15) for ionization reactions as a function of w t YO acetone. Lines i l , i2, i3, i4, and i5 are for the ionization reactions for benzoic acid, phenol, propionic acid, acetic acid, and water, respectively. Lines h l , h2, h3, and h 4 are for the hydrolysis reactions of benzoate, phenolate, propionate, and acetate ions, respectively
order as anion size--that is, benzoate > phenolate > propionate > acetate > hydroxide. This trend is just opposite from what one would predict from a simple Born electrostatic model ( I ) if one were to assume that the protonanion interaction distance were directly related to anion size. The trend is not quite the same in acetone-water mixtures, where the effect of increased organic content on 6 is in the approximate order benzoate phenolate > propionate > acetate hydroxide. The observation that the hydrolyses show much smaller changes in 6 with increased organic content is consistent with what one would predict from simple Born electrostatics, since the hydrolysis reactions are isoelectronic processes. The greater changes in the values of d for the ionization reactions in acetone-water sol-
-
-
(1) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolyte Solutions," 3rd ed., Reinhold Publishing Corp., New York, N.Y., 1958. (2) E. Grunwald and B. J. Berkowitz, J. Am. Chem. SOC.,73, 4939 (1951). (3) E. Grunwald, J. Am. Chem. SOC.,73, 4934 (1951). (4) J. 0. Frohliger, R . A. Gartska, H. W. Irwin, and 0. W. Steward, Anal. Chem., 40, 1408 (1968). (5) R. G. Bates, "Determination of pH, Theory and Practice," 2nd ed., John Wiley & Sons, New York, N.Y., 1973. (6)P. Schindler, R. A. Robinson, and R. G. Bates, J. Res. Nat. Bur. Stand., Sect. A, 72, 141 (1968). (7) H. 0. Spivey and T. Shedlovsky, J. Phys. Chem., 71, 2171 (1967). (8) E. M. Wooiley, D. G. Hurkot. and L. G. Hepler, J. Phys. Chem., 74, 3908 (1970). (9) E. M. Woolley, J. Tomkins, and L. G. Hepler, J. Solution Chem., 1, 341 (1972). (10) E. M. Woolley and L. G. Hepler, Anal. Chem., 44, 1520 (1972). (11) E. M. Woolley and R. E. George, J. Solution Chem., 3, 119 (1974). (12) R. E. George and E. M. Woolley, J. Solution Chem., 1, 279 (1972). (13) T. Matsui, L. G. Hepler, and E. M. Wooiley, Can. J. Chem., 52, 1910 (1974). (14) K . P. Anderson, E. A. Butler, and E. M. Woolley, J, Phys. Chem., 75, 93 (1971). (15) K P. Anderson, E. A. Butler, and E. M. Woolley, J. Phys. Chem., 77, 2564 (1973). (16) K. P. Andeison, E. A. Butler, and E. M. Woolley, J. Phys. Chem., 78, 2244 (1974). (17) J. Timmermans, "The Physico-chemical Constants of Binary Systems in Condensed Solutions," Vol. 4, interscience Publishers, Inc., New York, N.Y., 1960. (18) J. W. Larson and L. G. Hepier, in "Solute-Solvent Interactions," J. F. Coetzee and C. D. Ritchie. Ed., Marcel Dekker, Inc., New York. N.Y., 1969. (19) L. G. Hepler and E. M. Woolley, in "Water-A Comprehensive Treatise," F. Franks, Ed., Vol. 3, Plenum Press, New York, N.Y., 1973. (20) E. J. King, "Acid-Base Equilibria," Pergamon Press, Inc., Oxford, England. 1965. (21) J. N. Butler, "Ionic Equilibrium, A Mathematical Approach," AddisionWesley Publishing Co., Inc., Reading, Mass., 1964.
RECEIVEDfor review March 10, 1975. Accepted May 12, 1975. We thank the Brigham Young University Research Division for support of part of this research.
Improved Falling Drop Method for Hemoglobin Determination C. P. Rathjen, J. E. Christner,' and R. C. Boguslaski Ames Research Laboratory, Ames Company, Division of Miles Laboratories, Inc., Elkhart, Ind. 465 14
The demonstration of the relationship between blood specific gravity and hemoglobin content (1-3) led to the development of a number of methods of hemoglobin measurement based upon specific gravity determinations. Some of these involved the behavior of liquid drops in an immiscible environment. Drops of blood added to a series of aqueous salt ( 4 ) or copper sulfate ( 5 ) solutions of graded densities were found to balance in solutions of identical specific gravity. While these methods were operationally simple, they required the preparation of a number of solutions and each determination required several sample additions. Present address, R a c k h a m A r t h r i t i s Research Unit, Kresge M e d i c a l B u i l d i n g , U n i v e r s i t y of M i c h i g a n M e d i c a l Center, A n n A r b o r , M i c h . 48104.
Two methods (6-10) were developed for the measurement of blood and plasma specific gravities with single drop samples. In the gradient tube method, mixtures of bromobenzene and kerosene were employed to establish a linear density gradient in a graduated cylinder. Drops of whole blood or serum were allowed to fall into this gradient and come to rest a t a point having an equivalent density. The specific gravity of the specimen was calculated graphically by interpolation from the positions of standards in the gradient. Alternatively, in the falling drop method, a drop of fluid was manually timed as it fell over a measured distance in a tube containing a mixture of xylene and bromobenzene. The fall time was compared to that given by drops of standard salt solutions of known densities. The specific gravity of the fluid was then calculated through use
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
1863
OVERFLOW
l.05Ok
f
I
DRAY
/
d
H WATER
Schematic representation of the column assembly in the falling drop hemoglobinometer
Flgure 1.
of an alignment chart correcting for room temperature. These methods proved tedious, inconvenient, and unsuitable for routine determinations and so have never enjoyed widespread clinical use. We wish to report a rapid and convenient method for the measurement of blood hemoglobin concentration. The procedure is based on an in-strumented method for the measurement of blood specific gravity by a modification of the falling drop approach. The method requires a single drop of blood, no dilutions or preparation of solvent mixtures, and only seconds for each determination. The precision and accuracy of the procedure are comparable with methods currently used for the measurement of hemoglobin.
EXPERIMENTAL Apparatus. The column assembly in the falling drop hemoglobinometer is depicted schematically in Figure 1. It is composed of a thermostated block surrounding a vertically supported tube, 9.0 cm long and 0.8-cm diameter, which contains a fluid immiscible with and less dense than the sample. The column was held at 39.70 f 0.01 "C by an integral cycle proportional control. The column fluid was Dow Corning 200, a dimethyl siloxane polymer with a specific gravity of 0.934 at 25 "C and a kinematic viscosity of 10 centistokes (25 "C). Procedure. A 2O-pl drop of sample was formed just below the surface of the fluid with an Eppendorf Microliter Pipet and was detached by slowly withdrawing the tip. After falling 3.5 cm, the drop interrupted a light beam aimed a t a photoconductor. This event started a timer. Further down the tube, the drop interrupted another light beam-photoconductor arrangement stopping the timer. A digital readout of the fall time was provided. The blood samples eventually resided in an immiscible layer a t the bottom of the column; thus they did not contaminate or alter the properties of the column fluid. As the volume of the aqueous layer increased, an overflow was used to maintain the oil level a t the proper height. The hemoglobin concentrations of the blood specimens which served as standards in this study were determined by atomic absorption spectrometry ( 2 1 , 12). The constants in Equation 3 (below) were calculated daily by the method of least squares from the reciprocal fall times for the standards. The hemoglobin concentration of each clinical specimen was calculated using this relationship and the corresponding fall times. All blood specimens were treated with EDTA to prevent clotting. A false result will be obtained from the falling drop procedure if an anticoagulant is used in amounts large enough to, significantly alter the specific gravity of the sample. Hemoglobin reference values for all specimens were determined from atomic absorption spectrometry on an Instrumentation Laboratory Model ILI-253 Atomic Absorption Emission Spectrophotometer. Samples of whole blood (0.1 ml) were diluted 250-fold with distilled water before being directly aspirated into the flame. Iron values were obtained by interpolation from a calibration curve derived from aqueous ferric chloride standards and were converted into hemoglobin values by assuming the iron concentration of hemoglobin to be 0.347 g/100 g hemoglobin (23). Copper sulfate specific gravity determinations were performed on whole blood and plasma according to published procedures ( 5 ) , and hemoglobin values were determined from these measurements by use of a nomogram (2). The specific gravities of all other solutions were determined using a pycnometer. Cyanmethemoglobin values were obtained according to published methods (14). 1884
0.250
0.300
0.m
bt
0.400
Reciprocal fall time vs. specific gravity ( p s ) plots for whole blood, plasma, and aqueous salt solutions
Figure 2.
RESULTS AND DISCUSSION The specific gravity of a liquid such as blood is related to its reciprocal fall time through a column of an immiscible liquid of prescribed length by the expression given in Equation l(15, 16). PB =
m(l/t~+ ) b
(1)
In Equation 1, p~ is the specific gravity of blood, t g is the fall time over a fixed distance, b is a constant related to the density of the column fluid, and m is a constant related to such variables as column fluid viscosity, column geometry, and the dynamics of the particular fluid system employed. A similar equation (Equation 2) has been developed for calculating blood hemoglobin concentration from the specific gravity of whole blood (1-3).
HbB = 4 8 0 ( p ~- 1.026)
(2)
In Equation 2 , HbB is the concentration of hemoglobin in blood expressed in gramdl00 ml. If the expression for the specific gravity of blood given in , Equation 1 is substituted into Equation 2 for p ~ Equation 3 is obtained where C and C' are constants.
HbB = C(l/tg) 4-
c'
(3)
This expression relates blood hemoglobin concentration in a simple fashion to the reciprocal fall time for blood through a column of an immiscible liquid of prescribed length. The constants in Equation 3 were empirically determined from the fall times of the blood specimens which served as standards. Since calibration with salt solutions would be more convenient in routine use, a study was conducted to ensure that the results were independent of the viscosity of the sample. Standard curves generated from plasma, whole blood, or salt solutions were essentially superimposable (Figure 2), indicating saline solutions could serve as standards for the method. Efforts are currently under way to derive values for C and C' based upon theoretical considerations of the behavior of immiscible droplets in a constricted tube. Precision. The precision of the falling drop method was compared with the precision obtained from three conven-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
Table I. Comparison of the Intra-Assay Precision of Various Methods for Determining Hemoglobin Concentration Mean Hb, Method
Std dev,"
g "6
Copper sulfate
i
Atomic absorption Falling drop
0
Std dev = &where
NORMAL RANGE
9 %
9.4 13.9
0.30 0.30
...
...
9.9 13.6 17.5 9.5 13.9 17.2 9.4 14.4 17.6
0.18 0.32 0.40
1.79 2.34 2.25 1.06 1.45 0.77 0.95 0.76 0 -64
...
Cyanmet Hb
.I . I
Re1 std dev,
3.15 2.11
0 .lo 0.20 0.13 0 -09 0.11 0.11
r = 0.91 n= 185 S(y)=0.72g%
d = difference between duplicates and
n = number of pairs (50).
, Table 11. Comparison of the Accuracya of Various Methods for Determining Hemoglobin Concentration
Method
Copper sulfate Cyanmet Hb Falling drop
Correlation of esti-
size,
slope intercept
coefficient, mate,
Re1 std
19%
dev,%
b
L
(FALLING D R B )
emr
regression line/
m
I
15
Figure 3. Correspondence of the results from the falling drop and atomic absorption methods
Saniple
n
I 1
IO
gm% Hb
Standard Equation of the
I
5
I
106 0.90 1.41 0.96 0.74 196 0.89 1.25 0.96 0.74 185 1.00 0.00 0.97 0.72 a Reference procedure, atomic absorption spectrometry.
6.12 6.02 5.76
tional methods for determining hemoglobin concentrationthe copper sulfate, cyanmethemoglobin, and atomic absorption methods. The results from these analyses given in Table I indicate that the precision obtained from the falling drop method (re1 std dev
