V O L U M E 20, NO. 4, A P R I L 1 9 4 8 log
CY
=
loge
log p = -log
- log Y / C Ap - 2 log w
+ log p 2 log D = log y + log Q log y = log
CY
381
(6)
(7) (8) (9)
where CY, 13, and y are introduced palameters.
If each of these three variable equations is nomographed on the same sheet, according t o the method of Davis ( I ) , and the parameters represented by reference lines, Equation 5 may be solved by drawing four lines, each representing the solution of one of these equations. The constant factor, A , is included in the nomograph by locating one scale to correspond to an arbitrary numerical solution of Equation 5. This scale location is then checked by cowparing graphic and numerical solutions of Equation 5 over different areas of the nomograph. Changes in the units in which the variables are expressed >rill only result in shifting the position of one scale up or d o ~ n without , affecting the relations between scales. The value of A in Equation 5 depends only upon the dimensions of the centrifuge bowl. The bowl dimensions of each centrifuge of the same type are, of course, the same. The value of A should, therefore, be the same for all centrifuges of the same type; in the author’s laboratory this is the Sharples Type T-66-24 1 HY, for which RI = 2.175 cm. and Rz = 0.7348 cm. A for this instrument was calculated t o be 1.61 - * using the more concm.4’ venient units of Equation 5A, the entire constant becomes 2.44 X 1012. For other centrifuges of different dimensions, Equation 10 applies:
where D2 = size of particles obtained in different centrifuge, mp D1 = size of particles obtained from nomograph, mp 1 A Z = constant for different centrifuge,4cm.
Sample Calculation. A colloidal dispersion is to be centrifuged. The following data are obtained: Viscosity of dispersion medium = 0.8 centipoise. Difference in density between particle and medium = 4.07 grams per cc. If the centrifuge is operated a t 40,000 r.p.ni. with a feed rate of 100 cc. per minute, what is the size of particle which will sediment out 9 cm. above the bottom of the bowl? ( Yl C = 30 from tabulation on nomograph.) 2.44 X 10l2(0.8) (1000) = loo nncl By calculation: D = 30 (40.000)2 . (4.07) . From nomograph: D = 99 m i ’ The, variation in these values is Tvithin t,he limits of opera.ting precision.
4
LITERATURE CITED
(1) Davis, D.S., “Empirical Equations and Nomography,” 1st ed., p. 104-14,New York, ,McGraw-Hill Book Co., 1943. (2) Fancher, G., Oliphant, S. C., and Houssiere, C , R., IND. ENG. C H E M . , A N A L . ED., 14,552-4 (1942). (3) Hauser, E. A., and Lynn, J. E., Ind. Eng, Chem., 32, 669-62 (1940). (4) Hauser, E. A., and Reed, C. E., J . Phya. Chem., 40, 1169-81 (1936). (5) Hauser, E.A, and Schachman, H. K., Ibid., 44,584-91 (1940). (6) McIntosh, J., and Seibie, F. R., Brit. J . Exptl. Path., 21,163-60 (1940), (7) Schachman, H.K., J . B i d . Chem., 143,395402 (1942). RECEIVEDMarch 27, 1947.
Kjeldahl Determination of Nitrogen without Distillation Application t o Samples Containing Phosphorus K.1LMAN MARCALI
AND
WILLIAM RIEMAN, 111
Rutgers University, New Brunswick, N . J.
TIME-saving modification of the Kjeldahl method ( 3 )
A has been published recently, in which the digested material
is diluted and adjusted to theamethyl red end point with sodium hydroxide. Thus, the flee sulfuric acid is neutralized. Then formaldehyde is added, and the ammonium ion is titrated to the phenolphthalein end point with standard 0.1 N sodium hydroxide. The chief disadvantage of this niethod lies in the interference of phosphorus. l17hen the ammonium ion is titrated from the methyl rrd end point to the phenolphthalein end point, the phosphate is converted from the primary to the secondary salt, thus introducing a positive error. A minor disadvantage is that the precipitation of sulfates of calcium and barium and of hydroxides of iron and aluminum (when these elements are present in the sample) makes the end points less distinct. This paper describes B procedure that eliminates both these difficulties.
Reagents. In addition to the reagents previously listed (S), zirconyl chloride solution, about 1.0 M is required. Dissolve 322 grams of zirconyl chloride octahydrate in 600 ml. of 1.0 N hydrochloric acid and dilute t o 1 liter with the same acid. Procedure. Weigh a sample containing about 10 milliequivalents of nitrogen. Perform the digestion and dilution as previously described (S), then transfer the solution t o a 250-ml. volumetric flask, rinsing the digestion flask with five 10-ml. portions of water. Add 15 ml. of sodium bromide, 5 ml. of zirconyl chloride, and 3 drops of methyl red. Add 10 N sodium hydroxide dropwise until the solution turns yellow, then add A- sulfuric acid dropwise
Table I. Nitrogen in Pure Organic Compounds (2% of phosphorii. added as NaaPOzl
After the usual digestion, dilution, and addition of sodium bromide, zirconylthloride is added, and the solution is brought to the methvl red end point. Zirconyl hydroxide is precipitated, carrying with it all the phosphorus as zirconyl phosphate. The solution is diluted in a volumetric flask and filtered. An aliquot portion of the filtrate is then titrated as usual with sodium hydroxide to the phenolphthalein end point in the presence of formaldehyde. This procedure will also remove calcium, barium, aluminum, and iron. The carbonate, introduced as a contaminant of the sodium hydroxide, is quantitatively precipitated with the zirconyl hydroxide (1,4). Therefore the boiling just prior to the adjustment to the methyl red end p
