ANALYTICAL EDITION
40
tion tests; and to V. V. Hartman and C. A. Home for their polarizationwork in the large number of tests made by them to determine the adsorptive effect of marc.
LITERATURN CITED (1) Mints, Kartashov, and Trofimovskii, Nuulc. Zapiski Tzukrovoi Prom., 14,483 (1931). (2) Osborn, IND.ENQ.CHEM., 15,787 (1923). (3) Osborn and Brown,Facts About Sugar, 27, 434 (1932). (4) Rampler, "Die Nichtzuckerstoffe der Ruben,'' PP. 1-13, Friedrich Vieweg und Sohn, Braunschweig, 1898.
Vol. 6 , No. 1
(6) Saillard, Circ. hebd. fubr. sucre, Supplement 2255 (1932).
(6) Saillard, "RBsumB de quelques travaux francais se rapportant 8. la betterave 8. sucre et aux produits sucres des fabriques de sucre de betterave," Imprimerie de Publications Periodiques, Paris, 1932. (7) Spengler and Pear, 2. Ver. deut. Zuderind., 83, 342 (1933). (8) . , Stanek and Vondrak, 2. Zuckerind. cechoslovak. Rep., 51, 101 (1926). (9) Ibid., 52, 165 (1927), (10) Vondrak, Ibid., 57, Rundschau, 16 (1933). R ~ C ~ I V BSeptember ID 22, 1033. Presented before the Division of Sugar Chemistry et the 86th Meeting of the American Chemical Society, Chicago, Ill., September 10 to 16, 1933.
Comparison of Extraction Formulas CARROLL W. GRIFFIN,Vassar College, Poughkeepsie, N. Y.
T
H E process of extraction is frequently used for the removal of a desired compound from an impure solution of it. Thus the separation of an organic compound from an inorganic substance may usually be effected by extracting the aqueous solution with an organic solvent. A wellknown general principle for the process is that, with a given quantity of extracting liquid, the use of many fractions of the liquid leads to a more nearly complete removal of the desired compound than does the use of the entire liquid in a single extraction. Formula 1 (1)
where W = cc. of solution X o = grams of substance dissolved therein L = cc. of extracting solvent used in each extraction R = distribution ratio of the substance for the two solvents X , = grams of substance remaining unextracted after the nth extraction may be used to demonstrate the above principle and to compute the amount of substance which may be expected after a given number of operations. As n is increased in the above formula Xm, the amount of substance remaining unextracted, will diminish and approach zero as a limit (Xo, K, W , L , and n being positive). Sometimes numerical examples are used to demonstrate this, but that the conclusion is valid in general is obvious, for from Equation 1 we may say
x_.=
1 (1 + L / K W ) "
Xo
and putting L / K W = a we know that for positive values of (1 a)" = 1 + na . . . positive terms
+
+
becomes infinite as n +
X
equal 2 must, as n
xo
-+
+
+
m. m,
+
X m +< l X , or that f ' ( n ) < 0
Since the first term in the above equation is positive it is sufficient to study the sign of the remainder of the expression, i. e., that in braces. Let us make the change of variable L/KWn = u
c,)n
where, as before, XO,K, W , L, and n are positive. (In the
limit n++ U
+
$ ( u ) = --?L--
Now$(O)
l + u = 0
- In
(1
u = 0 m
and the second
+ u ) as u -+ 0 by positive values
(In general it may not be a fact that when the derivative is negative the function is negative. Here, however, the function is zero for u sero, and since its derivative is negative for u positive, it follows that the function is negative for u positive.) $'(U) =
-U (1 + u)'
Therefore $ ( u ) < 0 for u > 0. Hence the function $(u) has a graph below the axis of u for u > 0.
approach zero as a limit.
The above case should be clearly distinguished from that in which the quantity of extracting liquid is not unlimited, as is always true in practice. While in this case, too, sub- ' division of the available liquid into many portions is advantageous, the limit of the process is not zero. If, in such a case, we consider L cc. as the total volume of extracting liquid and that it is to be subdivided into n equal parts, and these successively used, the formula obviously should be written
so that
The first term (in braces) becomes u1 + -In ( 1 u ) , so that we study the sign of
LY
Therefore -and its (1
following differentiation, note that L is now a constant.) Proceeding on the basis that if the first derivative is negative the function is decreasing we seek to establish that
Thus also f ' ( n ) < 0 and in particular f(n or
+ 1)
Xm+1
< f ( n ) = Xn
Xm+r < X n
Whereas X, in Equation 1 approaches zero as n increases towards plus infinity, such is not true of X , of Equation 2. In the latter case X, obviously cannot approach the limit zero since in this case the total quantity of liquid, L, is finite. We evaluate this limiting constant as follows: Starting with Equation 2 we may write
I N D U S T R I A L A N DY’E N G I N E E R I N G C H E M I S T R Y
January 15, 1934
+
which takes the form 0/0 as n --f a. Therefore, differentiating both numerator and denominator limit
limit
+m
Thus
n-
and
limit n+
+
- ~ / K ~
rn X O
The limiting value, e - - L / R W , may also be established thus: limit n + + m
-
[
KW KW+L/n
limit n++-
1‘ -
~~
limit +
[(I + L / K $ 7 n ) K W n / L ] - L ’ K W
However, the former method is necessary in order to show that f ( n )continuously-i. e., steadily or monotonically-decreases to its limiting value.
SUMMARY Two formulas used in the process of extraction are compared as concerns variables involved, especially with reference to the limits of extraction with an infinite and with a finite quantity of extracting liquid. These limits have been evaluated.
In -n x =-L X O KW
K n= e
41
ACKNOWLEDGMENT The writer is indebted to W. T. Read, W. E. Byrne, and H. S. White for criticizing the manuscript. LITERATURE CITED
= e-L/KW‘
(1) Taylor, “Treatise on Physical Chemistry,” pp. 485-7, Van Nostrand, 1931. RECEIVED September 15, 1933.
Determination of Small Quantities of Nitrobenzene in Oils C. E. ANDING,JR.,B. ZIEBER, AND w. M. MALISOFF, The Atlantic Refining Company, Philadelphia, Pa.
0
CCASIOXS arise in which it becomes necessary to of the oil present, as was expected. The color of the oils determine small amounts of nitrobenzene in petroleum precluded any hope of success by colorimetric methods. oils. An outstanding instance is the process (4) for Variant a therefore was chosen. Under that head stannous the refining of lubricating oils by extraction with nitro- chloride, titanous chloride, and titanous sulfate were chosen benzene. where both the refined oil and the extract must be for consideration as reducing agents less likely to be affected freed from small amounts by a n y t h i n g t h a t may be of residual nitrobenzene. A present in the oils. comparative study of various Titanous chloride was soon methods h a s been m a d e , ruled out on account of the selecting as the most promisformation of chloramines ( 8 ) . ing the reduction with standA comparison of the action ard solutions of titanous salts of stannous chloride (6) and and back-titration with ferric titanous sulfate with reflux alum. (1) showed superiority of the It was felt that the known latter. Using known soludifficulties of nitrogen detertions of pure nitrobenzene the minations by combustion in a u t h o r s have been able to a furnace or by a Kjeldahl obtain 98 per cent reduction procedure would be accentuw i t h 20 p e r c e n t excess ated in the case of heavy oils. titanous solution, w h e r e a s A n o t h e r major line of apeven 150 per c e n t excess proach lay in the reduction of stannous chloride gives only n i t r o b e n z e n e to aniline. 80 per cent reduction. The Two variants of this would r e d u c t i o n with s t a n n o u s be (a) reduction with an exchloride is much slower as cess of r e d u c i n g a g e n t well. followed by the determinaFigures 1,2, and 3 represent tion of the excess, or (b) rethe apparatus developed for duction followed by the dethis determination. t e r m i n a t i o n of a n i l i n e . 1Jnder procedure b one might PROCEDURE consider diazotization, The procedure finally dec o l o r i m e t r i c methods, or C veloped is as follows: bromometric methods. FIQUFIE1. ASSEMBLEDAPPARATUS A sample of oil not exceedActual tests, however, showed sulfate storage F . Condenser in@;6 grams is weighed in the that side reactions take place AB .. Titanous Carbon dioxide wash tower with spiral G. Set-up in boding poaition boiler, and 10 cc. of xylene, with nitrous acid, bromine, or c. Carbon dioxide +ea K. H. Turbine Titanous buret 25 CC. of methanol, and 25 cc. D . Carbon dioxide inlet similar reagents on account E . Boiling flask of 40 per cent sulfuric acid are
