Rapid Determination of Specific Gravity of liquids under Pressure J. I. LACEY Hooker Electrochemical Company, 'Viagara Falls, S. Y . LIQUID FROM CYLINDER
VENT
'PLI WELDED ' SPECIAL F U
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VENT +HLRMOM€TKR
-5lGHT CLA5$ -GUARD
'LIQUID CHLORINE LEVEL
-HYDROMLTCR
Figure 1. Apparatus for Determining Density of Liquid Chlorine METHOD for the rapid determination of the specific gravity
A of a liquid under pressure at various temperatures involves
placing the sample in a high-pressure vessel that is fitted with a sight glass and reading the specific gravity by means of a hydrometer floating in the liquid. Thi. method has been used to check the densities of commercial liquid chlorine.
Apparatus. The sample was held in the case of a Fischer and Porter armored, horizontal line flow rotameter, modified as described (see Figure l ) . The metering tube, gaskets, and float were removed, the bottom outlets were blanked off, and a well line and a gas outlet were provided through the top flange. The connections were made so that either liquid or gas could be withdrawn or charged. -5, -10" to +llO" C. thermometer subdivided t o 1" C. was suspended in the rotameter case, so that the bulb and part of the stem, but mt the calibration, a-ere immersed in liquid chlorine 1% hen the vessel was half full. -10 to 200 pounds per square inch silver diaphragm pressure gage was provided on the gas phase A hydrometer was placed in the case before filling it with chlorine, and it floated in the liquid after filling. To cover the range indicated, it was necessary to use two hydrometers, 1.300 to 1.400 and 1.400 t o 1.500 specific gravity a t 60" F : the scale on each hydrometer was divided into 100 parts. When the gravity changed from 1.399 t o 1.401 it was necessary to expel the sample, change hydrometer, and then put a frebh sample into the vessel. The temperature was controlled by means of a water bath, the level of which n-as kept just below the level of the chlorine in the vessel. Procedure. A cylinder (100 or 150 pounds] of commercial liquid chlorine nas connected to the well line and inverted. Liquid chlorine was then run into the vessel until it was half full. During the filling, sufficient gas was vented to allow the liquid to enter, but no special effort was made to eliminate all air from the system. The temperature of the water bath mas raised to 50" C. and allowed to cool slowly. The testing equipment was located out of doors, and radiation to the atmosphere was the source of cooling except in the extreme lolver range, n here ice water n-as occasionally used. The temperature and specific gravity n-ereread at frequent intervals. The vessel & a smoved gently between readings to ensure a uniform liquid temperature. At the end of the determination, the instruments were checked against Bureau of Standards instruments and found to be accurate jvithin the limits to vihich they could be read. This method may be adapted to other liquids under pressure, providing the pressure does not collapse the instrument's. The liquid being tested must not appreciably attack the confining vessel or instruments. In this instance the confining vessel was a high-pressure rotameter case, but any vessel of appropriate dimensions having a suitable sight glass may be used. RECEIVED March 2 8 , 1947.
Nomograph for Particle Size Determination with the Sharples Supercentrifuge ELERISGTOX S-IUNDERS, Monsanto Chemical Company, Merrimac Division, Everett, Mass.
HE Sharples supercentrifuge has been used for the deterTmination of particle size and particle distribution in colloidal systems (2-6). Mathematical relations for calculating the size of particles sediinented out under definite operating conditions have been presented (3, 4). Since these calculations are somewhat laborious, graphical methods have been found convenient. Fancher, Oliphant, and Houssiere (2)have presented an alignment chart, but this construction does not consider several variablbs and requires a nerr chart for each system under consideration. An alignment chart has also been presented for the Svedberg ultracentrifuge (7). I t is believed, therefore, that the following nomograph, which is applicable to any system and can be applied t o centrifuges of varying dimensions with a simple correction, willsimplify these calculations still further. Hauser and Lynn (3) have developed methods for calculating the size of particles deposited by the supercentrifuge under definite operating conditions by assuming that the particles obey
Stokes' law, and that the flow parallel t o the rotatory axis streamlined. Their equation is expressed as:
where
Y
L
= vertical distance of deposition of particle of given
size in cm., measured from bottom of centrifuge bowl Q = rate of feed of suspension, cc. per second K , = function of construction of bowl and equal to:
RZ = distance from axis of rotation to bowl wall, cm.
379
ANALYTICAL CHEMISTRY SEUYWTATION DISTANQ f QNTRIFUQ
- CM?
FACTOR- Y/C
b
as
- REFERENCE LINE ..
EEZ ssss
qs30
lo00
MK)
- -
FEED RAlE 0
nI
rl-r
. 29
0
VISCOSITY OF DISPERSION MEDIUM-
0000
l l
I
3ooeoo
CENTIPOJSES
CC. PER MINUTE
I l l l l I
I
-
EOUIVALENTSPHERIGALDIAMETER OF PARTICLES -D- MlLLlMICmS 40 ! o " 0 7 0 8 0 loo 1!omBDo Joo 00 8coo BODDO0 180017mPQD I
I
80
I
I
I
I
sI
4 35 3 2.5 I
I
1
~
1 1 ~ 1 )'1 ~I l1 I ~1 ( ) I 12 109 8 7 6 -5
1
30 25 20 I7 S
$0
6I
I
I
eI
1.71.5 1.2 1.0 1
1
1
1
distance from axis of rotation t o oveifiow weir, m i . viscosity of dispersion medium, poises equivalent spherical diameter of particle sedimented out a t Y , em. angular velocity of rotation, radians per second difference in density between dispersed particlw arid dispersion medium, p1 p2 density of dispersed particles, grams per cc. density of dispersion medium, grams per cc. distance from axis of rotation a t which a given particle will begin to sediment out toiyard bowl wall, cm
-
For a given suspension, and fixed operating conditions, Equation l becomes:
I.
= I.'(XO,
Di
(4)
Under these conditions, since I' depends only on Y o , the ternis in the brackets in Equation 1, called C, can be given values for each value of Y and a curve of C vs. Y drawn (3). The tabulation of Y LS. Y / C shown on the nomograph has been taken from this curve, 18 K1 in Equation 1 are called A , a ~011If the factors
- R:)
stant, Equation 1 hecomes:
y 'C'
=
.LL/3
D2 w 2 10
R.P.M+ 1000
1
1
1
OB ,
I
I
os os a4 I
,
,
I
AP
-
0 . n 1 7 . 1 ~~n
43 I
I
I
I
I
.io
T , , ! , j
GRAMS PER CC.
Since a value of I'/C for every value of Y may be given, Equation 5 is one of six variables and may be nornographed (1). In the accompanying nomograph, the calculations have been simplified further by conversion t o more convenient units of the variables in Equation 5. This conversion was accomplished as follows:
Y
F
=
~2
d q (centipoises) Q (cc. per minute) (millimicrons2) w2 (revolutions2 per minute21 AP (grams per cc.) ' 1 poise
1 cc. per second
100 centipoises
60 cc. per minute
X
1 millimicron2 X (10-7)2 cm.2
(3)
but is implicit in X c and unsolvable except bj a family of curves, determinants, or an alignment chart. However, under conditions of narrow particle size range and appropriate feed rate, D no longer tends t o he an independent variable and Equation 3 approaches: 1- = . f ( S n )
I
I
I
RWRENCe LINE
DENSITY UFPERENCE-
(Rg
1
I
I S D
Y - REFERENCE LINE
ROTATORY RATE-W
T
I
1 1 1 1
100'10M)56e5
1
5)
I'
c=
1.52 X 1012A?Q D 2w 2 Ap
where 1) is expressed in centipoises Q is expressed in cc. per minute L) is expressed in millimicrons w is expressed in r.p.ni. Ap is expressed in grams per cc Y is expressed in cni. C is expressed in cm.2
(5.4)
s
The method of noniographing referred to ( I ) includes only equations containing up t o five variables, but may be extended to plot six variables as follows: Equation 5 may be reduced to four equations of three variables carh:
V O L U M E 20, NO. 4, A P R I L 1 9 4 8 log
CY
=
log p =
- log Y / C -log Ap - 2 log w
loge
+ 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 , affecting shifting the position of one scale up or d o ~ n without 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.
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
