Microdetermination of .Density by the Falling-Drop Method SEYMORE HOCHBERG AND VICTOR K. LA MER, Columbia University, New York, N. Y.
determination. That tube of bromobenzene-xylene mixture is used in which drops of the unknown and of the standards for comparison require between 25 and 70 seconds to fall between marks-the longer the time the more sensitive the method. The capillary pipet (Figure 1)is made from glass tubing 3 mm. in inside diameter and a glass rod selected t o fit the tubing with very little clearance. The dimensions are not critical. The plunger is given a thick, uniform coating of a grease made by melting together, in equal roportions, powdered resin and ordinary stopcock grease. &re is taken to prevent large air bubbles in the mercury column or between the plunger and the m e r c u r y . Exact reproducibility of the drops is obtained by measuring their volume between two marks, approximately 9 cm. apart on the capillary. The drops are forced out of the pipet under the surface of the bromobeneenexylene solution. U p o n raising the pipet out of the m e d i u m the drops are broken off by the surface FIGURE 1 tension. The drops were timed by a stop watch accurate to 10.2 second. A single rinsing, using approximately 0.001 cc. of solution, is sufficient to clean the pipet.
B
ARBOUR and Hamilton describe an ingenious method ( I ) for the microdetermination of the density of an aqueous solution, based upon the rate of fall of a minute drop of the solution through an immiscible liquid of low viscosity and volatility. Using bromobenzene-xylene mixtures they obtained densities of 0.01 cc. of solution to an accuracy of +0.0001. Recently, Fenger-Ericksen, Krogh, and Ussing (2) applied the method to the determination of the deuterium content of heavy water. Using an elaborate apparatus and timing by stop watch to ~ 0 . 0 second, 2 they claim that the method is capable of an accuracy of +0.000001 in the density. Their method of calculation, however, involves an error of principle, which produces an error of 0.000022 in the numerical example they cite. In this paper is described a simpler form of apparatus and technic which is capable of determining rapidly the density of water solutions to kO.00001 using 2 drops of solution, each of 0.001- to 0.01-cc. volume. The time required for a drop of solution of unknown density to fall through 15 cm. of a bromobenzene-xylene mixture is compared with the time required by similar drops of solutions of known density. For spheres of equal size, of densities dl and dz, respectively, falling through a medium of density d', the times of fall, ti and tz, respectively, are related as follows:
Corrections When interpolating between standard solutions differing by 0.250 per cent in potassium chloride, the maximum density correction to Equation 2 is -0.00002 a t a density approximately midway between those of the standards, and decreases to zero as the density of either standard is approached.
For any given medium and a given drop size it follows that for spherical drops k a=-+d' (2) t
Difference between Interpolated Density and Density of Closest Standard 0 0.00030 0.00030 0.00060 0.00060 0.00080
Correction 0.00000 -0.00001 -0.00002
--
where d is the density of a drop, t is its time of fall over a fixed distance, and k is a constant depending upon the viscosity and density of the medium and the distance over which the drop is timed. Equation 2 is obeyed even though the drop is distorted slightly, provided an accuracy of only +0.0001 is desired (1). However, to attain an accuracy of *0.00001, it is necessary in making interpolations to apply a correction, the magnitude of which is determined by the velocity differences-and hence by the density differences-over which one interpolates.
Precision and Method of Calculation Potassium chloride solutions of the densities shown in Table I were dropped through the same solution of bromobenzene and xylene. TABLEI. MICRODETERMINATION OF DENSITY Solution number: Density a t 25,000' C.:
Experimental
Time, t
For the determination of densities of water solutions ranging
from 0.997 to 1.110 at 25' C., master solutions of potassium chloride (0 to 17 per cent separated by differences of 1 per cent) are made by weight (3). From these a series of solutions separated by steps of 0.250 per cent of potassium chloride is prepared
I I1 I11 IV V 0.99707 0.99866 1.00025 0.99787 0.99946 Sec. Sec. See. See. Sec. 55.0 29.0 20.6 37.6 24.0 55.2 29.0 20.6 37.6 24.0 55.2 29.0 20.6 37.6 24.0 55.2 29.0 20.6 37.6 24.0 55.2 29.0 20.6 37.6 24.0 . 0.0181 0.0345 0.0485 0.0266 0.0417 ~~
Mean, l / t
Calculating the density of I V from I and I1 we have:
by dilution, and preserved in glass-stoppered bottles. A series of fifteen glass tubes (35 cm. long, 7 mm. in inside diameter) containing solutions of bromobenxene and xylene graded in density between 0.996 and 1.108 is set up in a thermostat (with glass window) regulated to *0.002" C. The drops are timed between marks 10 cm. and 21j cm., respectively, below the surface of the bromobenxene-xylene mixture. To avoid undue waste of valuable solution, an orienting determination of the density is made by employing a more viscous medium, prepared from light petrolatum and dibutyl phthalate of such proportions that a drop (0.005 to 0.01 cc.) of distilled water requires 2 minutes t o fall 15 cm. through the mixture. From the preliminary result one selects the proper tube of bromobenzene-xylene to give the most accurate density
a=
o*0266- o*0181(0.99866 - 0.99707) 0.0345
- 0.0181
+
0.99707 Correction
= 0.99789
-0.00002
0.99787 The density of V, calculated from I1 and I11 by applying the correction as above, is d = 0.99745, which checks the result by weight to 0.00001. Fenger-Ericksen, Krogh, and Ussing interpolate as though the d vs. t curve were linear. A considerable error should often result. For example, using the data on page 1267 of 291
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292
their article and interpolating the density as a linear function of 1 / t , we obtain for the deuterium concentration in their sample 2.667 per cent rather than 2.645 per cent. The correction over such a short interpolation is negligible compared with the error of the incorrect interpolation.
Conclusions A simple apparatus and technic are described with which the density of water solutions may be measured rapidly to =+=0.00001, using for each deterniination 2 drops of solution
VOL. 9, NO. 6
each containing 0.001 to 0.01 cc. For heavy water this corresponds to an accuracy of ~ 0 . 0 1per cent calculated as D20.
Literature Cited (1) Barbour and Hamilton, J. Biol. Chem., 69, 633 (1926). (2) Fenger-Ericksen, Krogh, and Ussing, Biochem. J.,30,1264 (1936). (3) International Critical Tables. Vol. 111, p. 87, New York, Mc-
Graw-Hill Book Co. RECEIVED April 2, 1937.
Paper as a Medium for Analytical Reactions I. Improvements in the Spot Test Technic BEVERLY L. CLARKE
AND
H. W. HERMANCE, Bell Telephone Laboratories, New York, N. Y.
F“
’ IGL (1) has described methods of making analytical tests on single drops of liquids, which are classified under the term “spot tests.” The drop may be placed, for example, on suitable absorbent paper, where it spreads uniformly until the surface forces are balanced. The wet area is then treated with a drop of the reagent, and the reaction produces an identifiable colored product. A variation is to place the two drops side by side on the paper, so that reaction occurs along a line formed where the spreading boundaries meet.
A
B
C
BY CAPILFIGURE 1. THREETYPEBOF SEPARATIONS LARY SPREADING
A. Seaaration by precipitation of one component
Ions separated: F e (2y) and Ni ( 5 7 ) Paper impregnant: BaCOs F e 0H)a precipitated Ft center. Ni washed to periphery and detected by immersing paper in dimethylglyoxime solution B. Separation based on difference in solubility of reaction products Ions Reparated: Ag 27) and Cu (37) Paper impregnant: &dS Black AgzS precipitates a t center; brown CuS, having higher solubility product, y c i p i t a t e s in outer zone C. Separation based on ifference in colloidal behavior Ions seoarated: Cu (67) and Fe (37) Paper rmpre nant: ZnzFe(CN)fl . Red CurFe(8N)G fixed strongly a t center: Fea[Fe(CN),e]a, not readily fixed, diffuses outward with solution, giving blue peripheral zone
Because the sensitivity of such a test, with a given reaction, is determined by the smallest quantity of reaction product per unit paper area that the observer can just detect, any modification in the technic that tends to concentrate this product by restricting the area of reaction will lead to increased sensitivity. Thus Hahn ( 3 ) points out the advantage gained when the solution under test is introduced into the paper through the fine tip of a capillary tube. The test drop then enters a t a single point, precipitation or adsorption of the reaction product taking place in the immediately surrounding region, where it remains fixed in the fibers while the clear liquid spreads radially outward by capillarity. A concentration of the colored product, which would otherwise be spread over the whole area originally wetted by the test drop, is obtained, rendering minute quantities distinctly visible.
The present article deals with improvements in both sensitivity and reproducibility brought about by the use of a capillary buret and thin, close-textured papers impregnated with reagents having low solubility in the liquids under test. To afford better control of the conditions of test, a special buret assembly is described, which permits delivering to a small area of the reagent paper, through a capillary orifice, a measured microvolume of solution, a t a controllable rate of flOW.
The slow capillary spreading of the solution from a central point in the meshes of an impregnated paper, combined with differences in solubility, reaction rate, and colloidal properties, may work to effect the separation of two or more substances. Elementary reasoning would lead one to expect that, of several substances precipitable in a given paper, the most insoluble would be the first to form around the point where the liquid is introduced, the other products precipitating concentrically around this in the inverse order of their solubilities. Experimentally this is not always attainable because of numerous interfering effects, but when conditions are favorable the process of simultaneously detecting two or more ions is a simple one. In some cases the separation is better accomplished by precipitating only one of the substances, a t the point of introduction, by the fixed impregnant. The other remains in solution and diffuses outward. After drying, a small quantity of wash liquid, again introduced a t the center, carries any of the soluble ion remaining in the central portion of the spot to the concentric peripheral ring and there concentrates it. By dipping the dried spot in a second reagent the color reaction characteristic of this substance is brought about. Colloidal properties may aid in effecting separations, as, for example, when one of two substances precipitated is strongly adsorbed by the fibers and therefore fixed near the point of precipitation, while the other diffuses outward with the liquid. Regardless of the factors on which a given separation depends, the effect is enhanced by reducing to a minimum the area over which the solution enters the paper. In many cases, control of the rate of spreading, possible with the capillary buret, aids materially. Figure 1 shows a photograph of capillary separations using the technic herein described. Figure 2 shows a comparison of effects with and without the buret. Thus the localization of reaction products through the action of capillarity makes possible the attainment of increased sensitivity as well as the simultaneous recognition of substances. However, if the precipitating reagent contained in
