Interconversions of Binary
Compositions by Simple Graphical ICUAN HAN SUN AND ALEXANDER SILVERMAN University of Pittsburgh, Pittsburgh, Penna.
Two simple graphical methods have been worked out for the interconversion of weight, volume, and mole fractions, and for conversion into these fractions ffrom compositions expressed in parts by weight, or otherwise, i n a binary system. The methods should find extensive application.
ENERALLY there are two ways of expressing composition of a system: ( a ) in parts by weight or volume, in numbers of moles, etc.; and (b) in fractions or
G
percentages by weight, volume, moles, etc. While both are valid the latter is more generally employed by the scientist. (Fractions and percentages are interchangeable and differ only by a factor of 100. Throughout the paper only fractions are considered.) The conversion of one expression to another is almost a daily routine for chemical engineers dealing with problems on absorption, distillation, etc., and for physical chemists in their studies of various physical systems. Since the conversion has always been considered a laborious or tedious process, especially for chemical engineers] several methods have been devised for the conversion of composition of a binary system either by means of charts or scales (8-6)or by graphical methods (1). The following methods, applicable to binary systems, are believed to be more comprehensive, simpler, and perhaps more accurate than previous methods.
FRACTIOK\‘OLUXE FEACTION Mole fraction from volume fraction:
hfOLE
(5)
Volume fraction from mole fraction: XA
Conversion Equations
P A R T BY WEIGHT
IvEIGHT,
MOLE,OR
Weight fraction from part by weight:
To devise universal graphical methods for the most important types of conversion, the coniersion equations are first listed and then examined: hcOLE FRACTION $ WEIGHT FRACTION Mole fraction from weight fraction:
hTOLUME FRACTION
(7)
W A -
Mole fraction from part by weight: T I
Weight fraction from mole fraction: XA
Volume fraction from part by weight:
VOLUME FRACTION e WEIGHTFRACTION Volume fraction from weight fraction:
Wn
PA
PA
-+-
= W A PA
(3)
W B
The above equations can all be summarized by the following general equations:
PB
Weight fraction from volume fraction: V A -
(4) PB
PB
PA
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June, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
683
E
As a simple example let us consider a binary system potassium oxide-silica with 70 per cent by weight of silica and 30 per cent by weight of potassium oxide. &A
+
QB
= 1 (in most
p
Given:
MsioP= 60.06 M K s O = 94.19 Wsio, = 0.70 WK~O = 0.30 To find: XsioZ(PA)and XK*O P B )
cases)
Graphical Method Knowing Q A , Q B , SA, and SB in Equation T H PROBLEM. ~ 10 or 11, how can one get P A or P i by a simple graphical method?
From Figure 2, A B = 1. Draw a vertical line through point L so that A L = WSIO, = 0.70. Plot points E and F along this line so that LE and LF correspond to MSIO, (60.06) and MGO (94.19), respectively. Connect lines AE and BF, which intersect a t point G. The horizontal coordinate of point G, which is equal to A H (0.786), gives directly the mole fraction of silica, or X S ~ OThe ~ . mole is equal to (1 - X S ~ O , ) fraction of potassium oxide, XK~O, or 0.214. loot
METHODI. On any graph paper, assign the whole length or suitable length of abscissa, CD,as unity a t the top of the paper as indicated in Figure 1. Ignore the above assignment, and plot points E (having coordinates & A and SA) and F (having coordinates Q B and 8,) in the usual manner by ohoosing any suitable scales, but considering A and B as origins, respectively. Connect A E and BF and draw a vertical line from intercept G to H . Then CH will equal P Aand DH will equal P B . The method for getting PA and Ph will be the same except that the coordinates for points E and F should be & A , S Band Q B , SA,respectively. In case &A QB = 1, as in most cases, no upper scale for abscissas is needed, but AB should be assigned as unity. Then E and F will be on the same vertical line and AG' and BG' will equal P Aand P B , respectively. Triangles AEE' and AGG' are similar and we have
I
F!
FR ACT I 0 N 100
E.
FIGURE
3
+
AG' AE' GG' EE' BG' - = - = BF' @ GG' FF' -E---
&A
SA SB
Substituting Equations 12 and 13 in Equation 10,
+
Calling CD unity, it is obvious that
PA = OH PB = (1
- P A ) = DH
METHOD11. This method applies only when Qr QB = 1 in Equations 10 and 11. Assign CD as unity which is parallel to the abscissas as shown in Figure 3. Plot points C and E on the ordinate so that: AC = S A and A E = 8,. Connect ED and locate point F on line CD so that CF = Qr
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INDUSTRIAL AND ENGINEERING CHEMISTRY
(consequently DF = Q B ) . Extend line A F until it intersects line ED a t G. C H , the horizontal coordinate of point G, equals P A . (The above applies also for S A > S B ) . Triangles FGH and A C F are similar; therefore, GH
AC
FH
GH
=mor-=
CH -
SA
GH= _D H _ CE cD
or-=SB
GH
- SA
&A
&A
1
- CH
(16)
1
Combining Equations 15 and 16 by eliminating GH, and solving for C H ,
Vol. 34, No. 6
Since in most cases the significant figures for compositions go t o only about four places, a graph paper about 50 X 60 cm. in size will ensure accuracy equal to numerical calculations. If an ordinary graph paper (8.5 X 11 inches) is used, the accuracy equals that of the slide rule. These methods have been applied to actual problems and found to require less than half the time necessary to carry out the conversion by slide-rule calculation. Because of their simplicity these graphical methods introduce less error than numerical calculation. Although only parts by weight have been considered in method I, it is obvious that parts by volume or numbers of moles can be treated similarly if desired.
Nomenclature molecular weight p = density W = weight fraction V = volume fraction X = mole fraction M
=
..-.~---
T i = run n r t hv woivht Ir' I
The same example as in method I is used and the graphical solution is shown in Figure 3, from which we find
Aclrnowledgmen t The application of method I by Tong Yee in an actual problem led the writers to the development of method 11. They are indebted t o Tong Yee.
A C = Msio, = 60.06 ( S A ) A E = M K ~ O= 94.19 Sa) CF = wsio, = 0.70 LA,
with the following result: Xsion = CH
= 0.786
Q = a quantity which may be W , V, X , or U S = a uantity which may be 114, p (Mlp),( p / M ) , or unity P = a fraction which may be W , $, or X Subscripts A and B = components A and B, respectively, in binary system A-B
(PA)
Literature Cited
The method of finding P i of Equation 11 will be similar.
Discussion Although method I offers wider scope of application, method I1 is preferable when many conversions of a given type are t o be carried out simultaneously.
(1) Baker, J. S., Chem. & Met. Eng., 45, 155 (1938). (2) Bridger, G.L.,Ibid.,44,451 (1937). (3) Byerlv. W.. J. Chem. Education,18,465 (1941). (4) Nevi& H.G.,Chem. & M e t . Eng., 39, 673-5 (1932). (5) Patton. T.C.,Ibid.,41, 148-9 (1934). (6) Underwood, A.J. V., Trans.Inst. Chem. E ~ Q T 10,112-52 s., (1932) I
CONTRIBUTION 447 from the
Department of Chemistry, University of Pitta-
burgh.
CHRONIC TOXICITY OF DERRIS ANTHONY 8%.AMBROSE', FLOYD DEEDS, AND JAMES B. MCNAUGHT
Food Research Division, Bureau of Agricultural Chemistry and Engineering, U. S. Department of Agriculture, and the Departments of Pharmacology and of Pathology, Stanford University School of Medicine, San Francisco, Calif.
I
N THE search for effective substitutes for lead arsenate and fluorine compounds as insecticides, the investigation of potential health hazards traceable to spray residues is an essential and indispensable part of the program. The determination of possible health hazards is especially important in the case of substitutes which show promise and are likely to find widespread use. I n view of the promising results being obtained with derris as an insecticide, the toxicity data of Haag (6) and Ambrose and Haag ( I , 8, 3) are important, and the additional data obtained recently in this laboratory should be of interest. The literature on derris was reviewed in the earlier papers by Haag and Ambrose. Haag (6) reported the acute toxicity, in terms of the minimal lethal dose, of rotenone by 1 Present
KY.
addrese, Univeraity of Louisville Sohool of Medicine, Louiaville,
various routes of administration in guinea pigs, rabbits, dogs, cats, pigeons, frogs, and albino rats, and presented data on the chronic toxicity, over a limited period of time, to dogs, rabbits, and guinea pigs. Ambrose and Haag ( I ) reported: the acute toxicity of whole derris administered gastrically to rabbits, rats, guinea pigs, and dogs; the acute toxicity of aqueous extracts of derris given gastrically to rats and rabbits, and intravenously+ intramuscularly, and subcutaneously to rabbits; the acute toxicity of the acetone soluble fraction of derris; the lethal dose of an olive oil extract of derris given gastrically to rats and rabbits; and the irritant properties of derris applied l,ocally, and its anesthetic effects on nerve tissue and the mucous membranes of the mouth. Ambrose and Haag (2) also presented data on the comparative toxicities in rabbits, rats, and guinea pigs of rotenone, deguelin, toxicarol, dehydrorotenone, and dihy-
