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INDUSTRIAL AND ENGINEERING CHEMISTRY
The agreement in the K,, equivalents lends considerable weight to the view that the viscosity method for determining the molecular weight of linear polymers is quite reliable when suitable solvents are selected and a reliable K,, value is employed. There still remains, however, a lack of certainty that in some cases a true molecular dispersion of the polymer exists in solution. In the case of polystyrene, however, the fact that the same viscosity is obtained using different solvents is evidence that complete molecular dispersion probably is obtained. The question as to the reliability of the osmotic method as compared to the viscosity method for molecular weight determination cannot be finally settled a t this time. This is because the viscosity method is well established for the lower polymeric range, but its application must be assumed in the higher range of molecular weights where reliable independent methods are not available. Due t o experimental complications the osmotic method cannot readily be employed in the case of the lower polymers, and since the higher polymer solutions deviate widely from Raoult’s law, the results by the osmotic method are believed to be inordinately high. Outside the range of ideal solutions the molecular weight values obtained by the cryoscopic method are also too high, as shown in previous work ( 2 ) by the increase in the K,, value as the molecular weight increases. Summary 1. The cryoscopic method is not satisfactory for polystyrenes containing more than twelve styrene units in the chain on account of the failure of their solutions to obey Raoult’s law.
Vol. 34, No. 9
2. The present work has established a new K,, value of 0.45 X IO4 for benzene solutions of polystyrene to be used in the equation,
A K,, value of 0.6 X lo4 has been similarly established for benzene solutions of polyindene. 3. Increased confidence in the viscosity-molecular weight procedure is derived from the data presented for the nenK,,equivalent covering a wide range of different polymers. Literature Cited DeBoer, J H . , Trans. Faraday SOC.,32, 30 (1936). Kemp, A. R., and Peters, H., IND. ENQ.CHEM.,33, 1263 (1941) Ihid., 33, 1391 (1941). Kemp, A. R. and Peters, H., unpublished work. Mark, H., and Raff, R., “High Polymeric Reactions”, Historical Discussion, New York, Interscience Publishers, 1941. Staudinger, H., “Die hochmolekularen organischen Verbindungen”, Berlin, Julius Springer, 1932. Staudinger, H., Trans. Faraday SOC.,32, 97 (1936). Staudinger, H., Ashdown, A. A., Brunner, M., Bruson, H. A. and Wehrli, S., Helu. Chim. Acta, 12, 934 (1929). Staudinger, H., and Fischer, K., J . prakt. Chem., 157, 19 (1940). Staudinger, H., and Heuer, W., 2. physik. Chem., A171, 129 (1935). Staudinger, H., and Leupold, E. O., Helv. Chim. Acta, 15, 221 (1932). PRBBENTED before the Division of Paint, Varnish, and Plastics Chemistry at the 103rd Meeting of t h e AMBRICANCHEMICAL SOCIETY, Rlemphis, Tenn.
LEACHING CALCULATIONS A Note on the Graphical Method GILBERT FORD BINNEY Pratt Institute, Brooklyn, N . Y. It is possible to transform triangular coordinates as used in leaching calculations to ordinary rectilinear coordinates, retaining the advantages of the triangular diagram and at the same time making the plot more flexible. The methods of calculation remain unchanged; the same straight line relations and material balances hold. The use of ordinary graph paper permits selection of scales more suitable for many calculations, particularly those for which extraction is nearly complete.
ROBABLY the most straightforward calculation of various leaching operations is the graphical method of Elgin (Z), related to similar methods for liquid-liquid extraction (3, 4). A triangular diagram is used, with the advantage that each region, path, and point has physical significance easily grasped. Material balances are indicated by lengths of the various line segments, and processes and changes are easily followed and visualized. These are all
P
real advantages, particularly for the occasional user. A simple triangular diagram with calculations of a stepwise countercurrent extraction is shown in Figure 1. The graphical method of calculation in this particular case is seen to be somewhat unsatisfactory. The compositions and quantities give points and lines that are crowded together into a small area. Really precise graphical construction and evaluation become difficult. This same situation occurs in almost all cases where leaching is nearly complete and the solid product contains but little extractable matter. It has been pointed out that the crowding difficulty observed here and in similar cases can be partly overcome by working on an enlarged scale. Expansion of the scales on a triangular diagram is not without difficulty, however, for the diagram is inflexible by nature. For example, if a tenfold expansion of each coordinate were required (a not unusual case) and if the enlarged diagram were made from standard triangles pasted together, ten squared or one hundred triangles must be cut out and properly aligned. This is hardly a convenient procedure. The equilateral triangular diagram is but an adaptation of oblique coordinates for a particular purpose. Two independent variables only are involved, for the third quantity can always be found if the other two are known. Since oblique
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1942
FIGURE 1.
TRIANGULaR COORDINATES
and rectangular coordinates are similar, transformation of the axis angle of a triangle from 60" to 90" does not destroy fundamental properties of the plot; straight lines are still straight lines, parallel lines are still parallel, and distances along any straight line remain in the same ratio. Figure 2, on right-angle coordinates, thus corresponds exactly with Figure 1, on the more usual equilateral coordinates. Expansion of a selected portion of Figure 2 on ordinary graph paper, with scales selected to avoid crowding, is shown in Figure 3. The graphical work can now be quite precise. T H E problem worked out in these diagrams is that discussed by Baker ( I ) , who gives an algebraic solution. The numerical values plotted in the three figures are identical, but the scales used are quite different. Plotting the same numerical values permits a preliminary triangular diagram to be worked out and proper scales to be selected for the expansion without any additional conversions.
taketi off. The waxed paper contains, by weight, 25 per cent paraffin wax and 75 per cent paper pulp. The extracted paper pulp is put through a dryer to evaporate the kerosene. The pulp, which retains the unextracted wax after evaporation must not contain over 0.2 pound of wax per 100 pounds of pulp. The kerosene used for the extraction contains 0.05 pound of wax per 100 pounds of kerosene. Experiments show that the pulp will retain 2 pounds of kerosene per pound of pulp as it is transferred from cell to cell. The strong solution from the battery is to contain 5 pounds of wax per 100 pounds of kerosene. Calculate the number of cells required.'' The general method of graphical solution is to convert compositions of feeds and products to weight per cent, and locate these points and the line corresponding to wet solids passed from cell to cell (the .f line). Point K is then found as the i n t e r s e c t i o n of lines joining the feed and product for the first and last stages. The performance of a single cell is given by a stepwise path from rich solution toward the origin untii the 8 line is reached, then back FIGURE 3. EXPANDED CoORDIN.4TES toward point K to solution line. For this one cell the 8 line gives composition of solids leaving, and the solution line the composition of solution entering. This stepwise process is repeated until a composition is reached which gives the desired product on evaporation of the solvent. This is located on the fl line by connecting extracted solids with the pure solvent. The number of steps gives the number of equilibrium cells. Calculations are as follows: Material Rich solvent Fresh solvent Feed solids Exhausted solid5 (dried)
FIGURE 2.
RIQHPANQLE-TRIANGULAR
COORDINATES
The statement of the problem ia: "Two Bons of waxed paper are to be dewaxed per day by extracticm with kerosene in a continuous countercurrent extraction apparatus consisting of a number of cells. It may be assumed that equilibrium is attained in each cell before the underflow and overflow are
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Wax, Wt. % 4.76 0.06 25.00 0.20
Kerosene, Wt. % 95.24
QQ.Q5 0.00 0.00
The$ line connects 0.00 per cent wax, 66.67 per cent kerosene with points such as 4.00 per cent wax, 64.00 per cent kerosene, and so on to the apex representing pure wax. OM THE diagrams of Figures 1 and 2, the scales are such that the points for fresh solvent and product solids fall almost at the apexes. The line connecting exhausted dried solids and pure solvent is practically superimposed on the base line. It thus becomes nearly impossible t o distinguish between the individual cells on these plots. On the expanded coordinates of Figure 3 the scales have been selected so that all the points can be located. For this plot the general procedure is identical with that for the others, but &st the line corresponding t D the hypotenuse (representing solvent compositions) must be located and drawn in. Point K , corresponding to an imaginary mixture, is now best located from simultaneous equations obtained from the straight-line formula rather than graphically. The same material balances hold along any one line
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INDUSTRIAL AND ENGINEERING CHEMISTRY
1104
but obviously cannot be applied to two lines of different orientation (unless distances are measured in units of the scales). Additional calculations for expanded coordinates follow: Hypotenuse (solution line) passes through points such as 0.00 per cent wax, 100.00 per cent kerosene and 5.00 per cent wax, 95.00 per cent kerosene. Equation from feed solids and rich solvent:
70n a x
=
25.00
Baker (1). A second expansion of part of Figure 3 could have been carried out if necessary. This sample calculation was selected because it represents a condition for which graphical methods have been thought unsuitable, and because the answer is available for comparison. In general, expanded coordinates extend the range of the graphical method to cases like this where extraction is nearly complete. This seems to be particularly useful in connection with studies on continuous countercurrent extraction of solids, where ordinarily the solid produced contains very little extractable material. There is also a possibility that these same expanded coordinates might piove useful in calculations of liquid-liquid extraction.
- 0.2125 (% kerosene)
Equation from exhausted dried solids and fresh solvent:
yo wax
=
0.20
- 0.0015 (70kerosene)
Literature Cited
Solving simultaneously gives point K as the imaginary composition 0.02 per cent wax, 117.53 per cent kerosene. The answer to the problem can be seen in Figure 3. Three are rlightly more than are not sufficient, and four adequate. This is in agreement with the algebraic solution of
(1) Baker, E. M., Trans. Am. Inst. Chem. Engm., 32, 6 2 (1936).
(2) J. c.3 32, 451 (1936). (3) Evans, T. W., IND.ENG.CHnM., 26, 860 (1934). (4) H u n t e r , T. G., and Nash, -4.W., J . Soc. Chem. I n d . , 53, 95T (1934).
oints of n-A W. 0. POOL AND A. W. RALSTON Armour and Company, Chicago, Ill.
their next lower homologs. Each acid vas purified by one or more of the following methods: crystallization from suitable solvents, fractionation under vacuum in a Stedman packed column, and fractional crystallization without a solvent. The purity of a given acid n-as considered sufficient when the freezing point was in satisfactory agreement with, or was higher than, the best value reported in the literature. During the boiling point determinations the samples were
HE purpose of this paper is to report the boiling points a t various pressures of saturated n-alkyl acids containing from six to eighteen carbon atoms, inclusive. The apparatus and procedure were described in a previous paper (45). The acids were obtained from the following sources: Armour and Company, Carbide and Carbon Chemicals Corporation, and Eastman Kodak Company. Tridecylic, pentadecylic, and heptadecylic acids were synthesized from
I 50
I 100
I
I 150
I
I
I
200 TEMPERATURE,
CURVESOF FIGURE 1. VAPORPRIWSTJRE
I
I
250 OC.
n-ALmL
I 300
ACIDS
Numbers on curves refer to number of oarbon atoms in the molecule
I
I 350
