T H E JOLTRNAL O F I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
262
TABLEI-VALUES o
2g
.E
OBTAINEDBY
*
E
L
0
Vol. 8, No. 3
EXPERIMENT
2g
.a
e
‘i!
P
*
P
(n) This experiment was with water only.
densing point and t h e composition of t h e liquid and vapor phases are shown clearly b y t h e plot in Fig. I. A convenient table of results estimated from t h e curves appears in Table 11, which enables one t o determine quickly t h e approximate concentration of any alcoholwater mixture b y observation of its boiling point, with corrections for barometric pressure and exposed mercury column. I t is also possible t o tell t h e approximate composition of both liquid and vapor (or distillate) a t a n y moment during the distillation of a TABLE 11-VALUES ESTIMATED FROM CURVESIN FIG. I Boiling point O C .
78.2 78,4 78.6 z8,8 19.0 79.2
Weight a,cobol per cent in
Boiling point
liquid vapor 92 91 89 85 82 88 80 78 86 76 85
82.0 82,5 83.0 83,5 84.0 84.5
79.4 79.6
74 72
80.4 80.6
62 59 56 53 50 47
85 84
i::: 264: i i 80.2 83 80.8 81.0 81.2 81,4
45
81.8
43
82
82 81
81 80 80 80 79
O C .
Weight alcohol per cent in
Boiling point
liquid vapor 79 41 78 36 33 78 3o 77 27 76 25 75
91.5 92.0 92.5 93,0 93.5 94.0
8 85 5 .. 05
23 21
74 73
87.0 87.5 88.0 88.5 89.0 89.5
17 16
70 69 68 67 65 63 61 59 5;
:::: ;t if 91.0
15
13 12 11 lo 9
O C .
Weight alcohol per cent in liquidvapor 8 55 8 53 7 51 49 5
6
46 44
94.5 9 5.0
54
42 39
97.5
2
23 19 1s 10
;;:; 2 i;2: 98.0 98.5
99.0 99,5 100.O
1
I
0
mixture. The accuracy is, of course, less t h a n by the usual and more difficult analytical method of distillation and t h e determination of the gravity of the distillate with a pycnometer. PURDUEUNIVERSITY LAFAYETTE INDIAXA
A RAPID PYCNOMETRIC METHOD FOR “GRAVITY SOLIDS” IN CANE-SUGAR FACTORIES By HERBERTS. WALKGR
Received September 13, 1915
Since t h e introduction into sugar factory control b y Deerr’ of t h e terms “gravity p u r i t y ” and “gravity solids,” and his demonstration t h a t the determination of total solids b y t h e Brix spindle, while not absolutely accurate except in pure sucrose solutions, when applied t o juices, sugars, and molasses a t approximately the same dilution (about I j ” Brix) yielded, in consequence of consistent error, results fully as valuable for factory control work as the more tedious process of drying t o more or less constant weight, this latter method has been entirely abandoned in many factories. T h e principal objection t o t h e substitution of densimetric for direct drying methods has been t h e lack of e\Ten relative accuracy in Brix spindle readings; this: as regards accuracy of reading t h e graduations on the stem of t h e spindle, has been somewhat improved b y several devices suggested in recent years, but there still remain certain inherent errors in the method, due t o variable viscosity and surface tension of liquids, which are very difficult t o eliminate. The pycnometer is generally conceded t o be an exceedingly accurate means of determining specific gravities, b u t has thus far found little favor in cane1
Bull. 41, Agr. and Chem. Series, H. S . P. A. Expt. Station.
M a r . , 1916
T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
sugar factories, owing probably t o real or fancied difficulty of manipulation a n d t o t h e extra calculation involved. By means of a few simple modifications, however, a pycnometer determination may be made almost as easily as a n ordinary Brix t e s t , a n d with no calculation other t h a n looking u p t h e Brix in a specific gravity table. A I O O cc. pycnometer with ground-in thermometer a n d capillary side a r m is'used; since all determinations are made a t room temperature, t h e cap of t h e side a r m is thrown away a n d t h e a r m itself cut q f f two or three millimeters above t h e graduation mark, thus facilitating rapid filling t o a definite volume. All calculations could be eliminated b y making a pycnometer t o contain exactly I O O g. water a t a given s t a n d a r d temperature, such as 17. j", Z O O , 2 7 . j" (weighed in air), or 4 " (weighed in vacuum), according t o t h e tables one intends t o use. T h e weight of t h e liquid in t h e pycnometer would t h e n be I O O times its density as compared with water a t t h a t temperature, a n d if a t a r e were made t o just balance t h e e m p t y pycnometer, t h e n t h e weights required t o balance t h e pycnometer filled with sugar solution would indicate t h e density of t h a t solution without calculation; Brix could t h e n be obtained from t h e tables, applying t h e same correction used for Brix spindles in case t h e determination were not made a t exactly standard temperature. It is, unfortunately, difficult t o obtain a pycnometer of exactly a desired capacity; one a little t o o large m a y be reduced b y grinding in t h e thermometer with emery powder, a rather tedious though not difficult process; b u t a bottle of t o o small capacity is difficult t o enlarge with accuracy. I n such cases it is easiest so t o regulate t h e t a r e t h a t t h e additional weights required t o balance t h e pycnometer full of water a t s t a n d a r d temperature shall be exactly I O O g., irrespective of t h e t r u e volume of t h e pycnometer, i. e., if pycnometer contains I O I g. water at standard temperature a n d weight of t a r e equals weight of pycnometer, t h e n Pycnometer water = t a r e I O I g. Increasing weight of t a r e b y I g., Pycnometer water = t a r e I O O g., a n d with pure water this pycnometer a n d tare will always indicate a density b y direct weighing of I . oooo. With dilute sugar solutions, a pycnometer as much as I cc. "off" in capacity will give densities with very little error, b u t when working with more concentrated solutions a small correction must be made t o t h e observed weights, since t h e I cc. excess capacity which, in t h e case of pure water, was compensated for b y t h e I g. heavier tare, will now weigh more t h a n I g. I n t h e above case of a I O I cc. pycnometer with t a r e adjusted for pure water, if i t be used with a solution of r.3000 density, t h e extra I cc. weighs of course 1.30 grams, while only I g. has been compensated for b y t h e excess weight of tare. Knowing t h e capacity of a pycnometer, i t is a simple m a t t e r t o make a table of corrections t o be applied a t different densities. Such a table for a pycnometer
+ +
+ +
263
containing I O I cc. ( a cc. here being considered t o b e t h e volume occupied b y I g. of water a t t h e temperat u r e taken as a standard for t h e density tables it is desired t o use) would be as follows: Weights used-grams.. . . Cor. to wts. (subtract).. . .
100 0.00
101 0.01
105 0.05
110 0.10
120 0.20
130 0.30g.
According t o t h e amount of change in t a r e needed t o give a weight of I O O g. with pure water, a table such as t h e above can be easily constructed for a n y pycnometer; t h u s , if it contain 100.30 g. water a t standard temperature, make t a r e equal weight of pycnometer 0.30 g., a n d t h e correction table for different densities is t h e one given above multiplied b y 0.30. The following is a n example of pycnometer calibration :
+
47.40 grams Weight of Pycnometer.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weight of Pycnometer water at 29' C . . . . . . . . . . . . . . . . 146.93
+
Weight of water..
...................................
99.53 grams
Assuming t h a t this pycnometer is t o be used with I 7 . 5 "/I 7. j " tables, a n d t h a t t h e average temperature a t which i t is t o be used approximates t h a t of calibration, the change of volume due t o expansion of glass may be neglected a n d t h e weight of water contained at 17. j" (or its volume in terms of " 1 7 . 5 " cc.") may be considered t o be 99.j3 X (density a q . 1 7 . 5 " t density aq. 29") or 99.53 X (0.99872/0.99598) = 99.80. If a t a r e is t h e n made t o equal weight of pycnometer minus 0 . 2 0 g., or 4 7 . 2 0 g., t h e weights needed t o balance pycnometer full of water at 1 7 . j" will be roo g., t h u s giving density direct. T h e correction for densities greater t h a n 1.0000 will be: Weights used. . . . Correction (add),
100 0.00
101 105 0.002 0 . 0 1
110 0.02
115 0.03
120 0.04
125 0.05
130 g. 0.06g.
After looking u p t h e Brix corresponding t o a n y density, t h e customary Brix correction for temperat u r e of observation must of course be made. I n case t h e laboratory temperature prevailing were as high as t h a t just noted, i t would perhaps be more convenient t o use tables calculated for 17. 5 " / 2 7 . s o , in which case t h e calculation of tare a n d correction table would be t h e following: Weight water content a t 27.5' = 99.53 X (0.99641/0.99598) = 99.57 g. Weight tare should be 47.40 - 0.43 = 46.97 g. Wts. used.. 100 101 102 105 110 115 120 125 130 g. Cor.(add) 0.00 0 . 0 0 4 0 . 0 0 9 0 . 0 2 0 . 0 4 0 . 0 6 0.09 0 . 1 1 0 . 1 3 g .
Where it is desired t o use a pycnometer for juices or solutions of always t h e same approximate density, t h e correction for this density may be incorporated in t h e tare. I n case t h e above pycnometer were t o be used solely with solutions of about I 5 " Brix or I , 06 density, t h e correction could be added automatically b y making tare 0 . 0 2 g. lighter t h a n for pure water, i. e., 46.95 g. instead of 46.97 g. Densities around I j a Brix would t h e n be obtained b y direct weighing, with absolutely no correction other t h a n t h a t for t e m perature subsequently applied t o t h e Brix reading. T h e calibration of a new pycnometer, including adjustment of a t a r e (best made from a small bottle weighted with shot) a n d construction of a correction table, can easily be done in less t h a n a n hour; t h e calibration of a new Brix spindle at three points on t h e stem, which is just as necessary, takes considerably more time t h a n this.
264
T H E J 0 U R N A L 0 F I N D U S T RI A L A N D E N G I N E E R I N G C H E M I S T R Y
Vol. 8, N O , 3
An ordinary determination of density of a juice or H = lbs. of hulls to be made to the ton of seed 0 = lbs. of oil to be pressed out per ton of seed diluted molasses consists simply of filling t h e pycnomeC = lbs. of cake to be made to the ton of seed ter t o t h e mark a n d weighing t h e centigrams on a n y Then: ordinary sugar balance, which requires from 3 t o j A (2000 - 20J + 0 0.04b - 1.002L) - 20OOg -. minutes, hardly more time t h a n is needed for an ac- II - 1.002A -1(0.01A-0.01)-g/~(3.331-0.67)-0.3 curate determination by means of t h e Brix spindle. (2Of - 0.04b - jj + 0.002L). As regards accuracy, a n error of more t h a n 0 . 0 1 c = 2000- ( H + 0 + L + V ) g r a m in weighing is unusual; this, a t 1 5 ’ Brix, correY = b (20 L - H(1.0067 - 0,03331) sponds t o 0 . 0 2 3 ’ Brix, or about one-fourth t h e average error in reading a Brix spindle. l0OY =
+
(1 -
--)
V 2000-L
6)-
D E P A R T M E N T OF S U G A R TECIJNOLOCY COLLEGE OF H ~ i v a r r , H o h - o L n r , a HAWAII
(2000-2Of-
SEED ANALYSIS %y
SAHUM
E. KATZ
Received August 30, 1915
T h e chemical analysis of cotton’ seed is of interest a n d value t o oil mill operators only when accompanied b y a table showing t h e available yield of products t h a t may be expected from each t o n of seed. The following formulae are offered as a method for calculating t h e theoretical yield of products per ton of seed, based on t h e results of a chemical analysis of t h e seed. As t h e derivation of t h e formulae is rather lengthy, it. is omitted. Let a = per cent kernels in whole seed b = hulls in whole seed f = per cent oil in whole seed g = per cent ammonia in whole seed Z = per cent oil lost in the hulls, as made in the mill, due to imperfect separation p = lbs. of oil left in cake L = lbs. of lint removed in delinting I‘ = lbs. of waste due to mots, dirt, loss in moisture, etc. .4 = per cent ammonia desired in the cake 0.2 per cent be assumed to be the average per cent of oil naturally found in the hulls as made in the.mill 0.3 per cent be assumed t o be the average per cent of ammonia naturally found in the hulls as made in the mill Y = Ibs. of hulls, which are necessary to mix with the kernels in order to dilute the cake t o the desired per cent of ammonia z = per cent of r in the uncooked and unextracted meats.
1
v-L-
2000-
H
C may also be calculated by t h e formula p + 0 04b-11.002L)
If i t be agreed t o consider t h e numerical values 0 . 7 per cent for I , 7 5 lbs. for L , a n d j 7 lbs. for p , as standard values, then the above given formulae may be considerably simplified. They t h e n appear as follows: =
+ 0.04b) - 2000g - 1.66g/a - 0.3
A(1981.85 - 20f
C = 1925
0 9954
- ( H + 0 + V) (1981.85
r = b (20
- 20f
&)-
-
)’
-
1925
’
+ 0.04b).
75 - 0.983H
100 r z=-1925 - H - V
The formulae for Y a n d z are especially valuable t o t h e superintendent. Knowing t h e percentage of hulls which should be mixed with t h e kernels, a n d comparing i t with t h e percentage obtained b y an actual test on t h e meats, he is enabled t o tell whether t h e proportions of kernels a n d hulls in t h e meats are correct or not, before t h e meats are carried t o t h e crushing rolls. CHEMICAL
LABORATORY, E A G L E COTTON OIL MERIDIAN, B f I s s I s s r P P r
COMPANY
ADDRESSES
THE USE OF DIAGRAMS IN CHEMICAL CALCULATIONS By HORACE G. DEMING Received M a y 15, 1915
The use of charts or diagrams for the solution of arithmetical problems is well known to the engineering profession, and several books have been written on the subject.’ Thus we have the graphical representation of forces and moments, Kutter’s formula for the flow of water, indicator diagrams for steam engines, and vector diagrams for the diagrammatic representation or graphical solution of problems in alternating current theory. In metallurgy we have diagrams for the representation of the composition of slags; in chemistry the familiar rectangular and triangular diagrams for the representation of the phase relations between the members of two-component and three-con1ponent systems ; and, in chemical technology, diagrams for ’the calculation of mixtures for the manufacture of cement. In spite of such scattering instances of the use of graphical 1 d’Ocagne, “Trait6 de Nomographie,” Paris. Gauthier-Villars; Peddle, “The Construction of Graphical Charts,” New York: The McGrarv-Hill Book Co.; Turner, “Graphical Methods in Applied Mathematics,” London: Nacmillan and Co.
methods in industrial chemistry, it appears’ that chemists do not in general take advantage of the really remarkable opportunities that the use of diagrams presents for the quick solution of chemical problems met in every-day work; and but little systematic study of the possibilities of the graphical method in chemistry has ever been published.’ The diagrams that are here presented are selected from among a large number devised by the writer with a view to illustrating some of the principal computations that may be solved by graphical means; they indicate a t the same time what a great variety of problems are susceptible to such treatment, and what diverse types of diagrams may be used. It is hoped that those presented may suggest others better adapted to the individual needs of the readers of THISJOURNAL; for this reason it will be necessary to mention the mathematical principles on which the construction of the different types of charts is based; but, since we are concerned rather with general principles than with details of execution, we can do no more than refer to many interesting charts that differ from those here given in but a few particulars. 1 But see a series of articles b y Piickel, 2 . physik. Chem.. Vols. 10 to 14. Of somewhat different scope is Kremann, “Leitfaden der graphischen Chemie,” Berlin: Geb. Borntraeger, 1910.
