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INDUSTRIAL AND ENGINEFRING CHEMISTRY
Vol. 39, No. 2
(6) Olc!ott, H. S.,arid Plmmerson, 0. I{., I b i d . , 59,1008 (1937). (7) O l c O t t , H. 8., alld Mattill. H. A , , Ibid.. 58,1627 (1936). (8) Rienienschneider, 12. IT., Turcr, J., and Ault, W. C., Oil h Soap, 21, 90 (1944). (9) Robeson, C. E., and Baster, J. G.. J . Am. Chem. Soc., 65, 940
this paper, and to Merck & Company, Inc., and Distillation ProdUCtS, Inc., for the samples of pure tocopherols used in the course of this investigation.
(1943).
LITERATURE CITED
(10) Simons, E. J., Buston, L. O., and Colman, H. B., IND.EXG. CHEX.,32, 706 (1940). (11) Sn-ift. C. E.. Rose, IT. G., and Janiieson, G. S . , Oil h Soap, 19, 176 (1942).
(1) Berenbluni, I., and Chain, E., Biochem. J . , 32, 295 (1938). (2) Bird, 0. D., Publication 298, Univ. Microfilms, .Inn Arbor, hIich., 1941. (3) Buxton, L. O.,IND. EXG.CHEX, 34, 1486 (1942). (4) Golumbic, C., Oil & Soap, 20, 105 (1943). (5) Golumbic, C., and Mattill, H.A., J . Am. Che77~.SoC., 63, 1279 (1941).
I’RESEXTED i n part before the Division of Biologioal ChemistrJr a t the I O D t h AIeeting of t h e . ~ M E R I C A \ TC H C ~ I I CSOCIETY, AL .Itlantic City, N.J.
BATCH DISTILL
APH I
MELVIN NORD Sord and Company, Inc., Keyport,
N T H E theory of simple batch distillation of binary solutions the following, k n o m as Rayleigh’s equation, occurs:
.Y.J . ,
I
whcre Li and L, arc the number of moles (or pounds) of original charge and residue, respectively, z1 and 2 2 are the mole fractions (or weight fractions) of light component in the original charge and t’he residue, and cy is the relative volatility of the light component, which is assumed to be constant over the concentration range considered’. In order to solve Equation I, lor rl or x2, trial-and-error solution is necessary. I t is possible, however, to construct a nomograph which will solve Equation 1 without trial and error. Rayleigh’s equation may be rewritten as follows:
or
L,
z=
(3)
If
Therefore, from a graph of lnf(z) against 2, for lines of constant one can subtract In j(z2) from in f(z1)nomographically to find the ratio L2/L1, or the fraction of the initial charge which remains in the still. This is demonstrated in Figure 1. As an example of the use of the nomograph, assume 21 = 0.80, N = 2.0, and LZ/Ll = 0.044; then z 2 is found as follows: At 0.80 on the z scale, go vertically up to QI = 2.0, then horizontally over to the scale marked 2 1 , scale 3. Connect, the point on the 21 scale Tvith point 0.044 on the &/L’ scale and continue to scale 3, marked z2. Then draw a line from this point through the key point an$ continue t o scale 1, then horizontally to cy = 2.0 and vertically down to the x scale. The result is 0.36, which is the desired value of 22. This path is indicated by directed lines on the nomograph. The nomograph can be used in the reveme manner to find z‘, or it may be used to find & ~ / Lwhen I z1 and z~ are known. If more precise results are desired than can be obtained with a nomograph of moderate size, the values obtained in this way may be regarded as the first approximation in a trial-and-error solution. If it is desired to take into account variations in a,the nomograph may be applied over small enough int’ervals of concentration so that constant values of OL may be used over each interval. cy,
x,
X Z
0
.2
4
.6
.8
Figure 1. Simple Batch Distillation Nomograph
1
Perry, J. H., Chemical Engineers’ Handbook, 2nd ed., p. 1383 (1941).
