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 thermody- namic data, such as transfer enthalpies and entropies, are necessary in order to draw meaningful conclusions regard- ing specific contributions of electrostatics, hydrogen bond- ing, solvation, etc. (8, 13, 18, 19).

LITERATURE CITED (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., - . . . . . . I

0 io 40 60

h'T % ACE'CNE

Figure 2. Plots of changes in free energies (Equation 15) for ioniza- tion reactions as a function of wt 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 > propi- onate > acetate > hydroxide. This trend is just opposite from what one would predict from a simple Born electro- static model ( I ) if one were to assume that the proton- anion 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 > propi- onate > acetate - hydroxide. The observation that the hy- drolyses show much smaller changes in 6 with increased or- ganic content is consistent with what one would predict from simple Born electrostatics, since the hydrolysis reac- tions are isoelectronic processes. The greater changes in the values of d for the ionization reactions in acetone-water sol-

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). (1 1) 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

(14) K. P. Anderson, E. A. Butler, and E. M. Woolley, J, Phys. Chem., 75, 93

(15) K P. Anderson, E. A. Butler, and E. M. Woolley, J. Phys. Chem., 77,

(1974).

(1971).

2564 (1973). (16) K. P. Andeison, E. A. Butler, and E. M. Woolley, J. Phys. Chem., 78,

2244 (1974). (1 7) 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 Trea- tise," F. Franks, Ed., Vol. 3, Plenum Press, New York, N.Y., 1973.

(20) E. J. King, "Acid-Base Equilibria," Pergamon Press, Inc., Oxford, En- gland. 1965.

(21) J. N. Butler, "Ionic Equilibrium, A Mathematical Approach," Addision- Wesley Publishing Co., Inc., Reading, Mass., 1964.

RECEIVED for 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 mea- surement 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 solu- tions and each determination required several sample addi- tions.

Present address, Rackham Ar th r i t i s Research Unit, Kresge Med ica l Bui ld ing, Univers i ty of Mich igan Med ica l Center, A n n Arbor , M ich . 48104.

Two methods (6-10) were developed for the measure- ment 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 graphi- cally 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 bro- mobenzene. 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 d

DRAY H WATER

Flgure 1. Schematic representation of the column assembly in the falling drop hemoglobinometer

of an alignment chart correcting for room temperature. These methods proved tedious, inconvenient, and unsuit- able 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 pro- cedure is based on an in-strumented method for the mea- surement 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 meth- ods currently used for the measurement of hemoglobin.

EXPERIMENTAL Apparatus. The column assembly in the falling drop hemoglo-

binometer is depicted schematically in Figure 1. I t 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 ab- sorption 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 con- centration of each clinical specimen was calculated using this rela- tionship 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 Lab- oratory Model ILI-253 Atomic Absorption Emission Spectropho- tometer. 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 concentra- tion 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 solu- tions were determined using a pycnometer. Cyanmethemoglobin values were obtained according to published methods (14).

0.250 0.300 0.m 0.400 bt -

Figure 2. Reciprocal fall time vs. specific gravity ( p s ) plots for whole blood, plasma, and aqueous salt solutions

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, tg 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 cal- culating 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 deter- mined 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 con- ducted 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 su- perimposable (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 theo- retical considerations of the behavior of immiscible drop- lets in a constricted tube.

Precision. The precision of the falling drop method was compared with the precision obtained from three conven-

1884 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, Std dev," Re1 std dev,

Method g "6 i 9 %

Copper sulfate 9.4 0.30 3.15 13.9 0.30 2.11

Cyanmet Hb 9.9 0.18 1.79 13.6 0.32 2.34 17.5 0.40 2.25

Atomic absorption 9.5 0 . l o 1.06 13.9 0.20 1.45 17.2 0.13 0.77

Falling drop 9.4 0 -09 0.95 14.4 0.11 0.76 17.6 0.11 0 -64

. . . . . . ...

0 Std dev = &where d = difference between duplicates and n = number of pairs (50).

Table 11. Comparison of the Accuracya of Various Methods for Determining Hemoglobin Concentration

Standard

Equation of the e m r

Saniple regression line/ Correlation of esti-

size, slope intercept coefficient, mate, Re1 std

Method n m b I 1 9 % d e v , %

Copper sulfate 106 0.90 1.41 0.96 0.74 6.12 Cyanmet Hb 196 0.89 1.25 0.96 0.74 6.02 Falling drop 185 1.00 0.00 0.97 0.72 5.76

a Reference procedure, atomic absorption spectrometry.

tional methods for determining hemoglobin concentration- the copper sulfate, cyanmethemoglobin, and atomic ab- sorption methods. The results from these analyses given in Table I indicate that the precision obtained from the fall- ing drop method (re1 std dev <1.0%) is comparable with that obtained from atomic absorption spectrometry and better than that obtained with either the copper sulfate or cyanmethemoglobin methods. Each mean hemoglobin value given in the table was based on duplicate determina- tions of fifty different clinical specimens, encompassing anemic, normal, and polycythemic samples. The number of polycythemic samples evaluated by the copper sulfate method was insufficient for inclusion in the table.

Accuracy. The accuracies of the three methods for mea- surement of hemoglobin were evaluated by comparing the results obtained on clinical specimens from each of the methods with those supplied by the atomic absorption method. Atomic absorption is gaining wide acceptance as an analytical method for metal analysis in biological sam- ples. I t has been shown to be an accurate method for mea- suring hemoglobin ( 2 1 , 12) and is inherently specific be- cause it is based on the atomic properties of iron. A sum- mary of the findings given in Table I1 indicate that all three methods have comparable accuracy. Figure 3 gives a comparison of the results obtained by the falling drop and atomic absorption methods. The correlation between the two sets of data was very satisfactory; the correlation coef- ficient was 0.97. The regression line had a slope of one, and a zero intercept; the dotted lines in the figure represent the 95% confidence limits.

NORMAL RANGE

r = 0.91 n= 185 S(y)=0.72g%

, I I 1 I

5 IO 15 gm% Hb (FALLING D R B )

. I . I

L

Figure 3. Correspondence of the results from the falling drop and atomic absorption methods

When compared to current methods for the measure- ment of hemoglobin, the instrumented falling drop proce- dure possesses a number of advantages. I t is rapid; each de- termination can be carried out in only a few seconds, and it is also convenient because the method uses only one drop of whole blood and does not require dilutions. The colori- metric (e.g., cyanmethemoglobin), atomic absorption, and specific gravity (copper sulfate) methods require either dilutions or preparation of a number of solutions and mul- tiple additions of sample. The instrumented falling drop method eliminates these requirements, while retaining ac- curacy and precision comparable to that obtained from these procedures.

LITERATURE CITED (1) C. T. Ashworth and W. D. Tigertt, J. Lab. Clin. Med., 26, 1545 (1940-

(2) D. D. vanSlyke. R. A. Phillips, V. P. Dole, P. B. Hamilton, R. M. Archi-

(3) C. T. Ashworth and G. Adams, J. Lab. Clin. Med., 26, 1934 (1940-41). (4) C. S. Roy, J. Physiol. (London), 5, ix (1884). (5) R. A. Phillips, D. D. vanSlyke, P. B. Hamilton, V. P. Dole, K. Emerson,

(6) C. F. Jacobsen and K. Linderstrom-Land, Acta Physiol. Scand., 1, 149

( 7 ) 0. H. Lowry and A. B. Hastings, J. Bid. Chem., 143, 257 (1942). (8) 0. H. Lowry and T. H. Hunter, J. Biol. Chem., 159, 465 (1945). (9) H. G. Barbour and W. F. Hamilton, Am. J. Physiol., 69, 654 (1924).

(10) H. G. Barbour and W. F. Hamilton, J. Blol. Chem., 69, 625 (1926). (1 1) A. Zettner and A. Mensch, Am. J. Clin. Pathol., 48, 225 (1967). (12) A. Zettner, Am. J. Clifl. Patho/., 50, 514 (1968). (13) R. L. Search, "Hemoglobin". "Diagnostic Biochemistry", McGraw-Hill,

New York, N.Y., 1969, p 270. (14) H. Mattenheimer, "Micromethods for the Clinical and Biochemical Labo-

ratory," Rev. ed., Ann Arbor Science Publishers, Ann Arbor, Mich., 1970, p 88.

(15) S. Hochberg and V. K. Lamer, lnd. Eng. Chem., Anal. Ed., 9, 291 (1937).

(16) N. Bauer and S. 2. Lewin, "Determination of Density", "Techniques of Organic Chemistry-Physical Methods of Organic Chemistry." 3rd ed., Vol. I, Part I, A. Weissberger. Ed., interscience Publishers, Inc., New York, N.Y., 1959, p 171.

41).

bald, and J. Plazin. J. Biol. Chem., 183, 349 (1950).

Jr., and R. M. Archibald, J. Biol. Chem., 183, 305 (1950).

(1940).

RECEIVED for review May 5,1975. Accepted June 16,1975. This paper was presented in part a t the 165th Meeting of the American Chemical Society, Dallas, Texas, April 1973.

ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975 1865