INDUSTRIAL AND ENGINEERING CHEMISTRY
1434
screened pulp were obtained from jack pine sawdust than from the chips. It is apparent from these data that jack pine is not pulped as readi1y.m is aspen by the nitric acid process. The substitution of sodium carbonate for the sodium hydroxide in the alkaline treatment had a deleterious effect on the resultant pulps, as shown in Table 11. Apparently the reaction products from the action of alcoholic nitric acid on wood are not as soluble in sodium carbonate as in the sodium hydroxide solution. When sulfur dioxide and lithium bisulfite were substituted for the nitric acid in both ethyl and n-butyl alcohols, no pulped residues were obtained after the sodium hydroxide treatment. This indicates that the nitric acid acts as an oxidizing rather than as a hydrolyzing agent.
Literature Cited
VOL. 29, NO. 12
(5) Horvhth, E., and fiber, G., Cellulosechem., 12, 85 (1931). (6) Klein, A. S., Papier-Fabr., 27, 325 (1929). (7) Kleinert, T., and Tayenthal, K., 2. angew. Chem., 44, 788 (1931). (8) Krais, P . , Papier-Fabr., 29, Fest- u. Auslands-Heft, 71 (1931). (9) Kiirschner, K., and Hoffer, A., Tech. Chem. Papier u. ZellstofFabr., 26, 125 (1929); Chem.-Ztg., 55, 161, 182 (1931). (10) Lynch, D. F. J., and Goss, M. J., IND.ENQ.CHEM.,24, 1249 (1932). (11) Payne, J. H., Ibid., 26, 1339 (1934). (12) Routala, O., and Sev6n, J . , Cellulosechem., 7, 113 (1926). (13) Schaarschmidt, A., and Nowak, P., Ibid., 13, 143 (1932). (14) Shimoda, I., Cellulose Ind., 12, 13 (1936). (15) Ibid., 12, 71 (1936). (16) Solechnik, N. Y., Bumazhnaua Prom., 14, No. 4, 30 (1935). (17) Suida, H., and Sadler, H., Papier-Fabr., 25, Fest- u. AuslandsHeft. 93 (1927). (18) Suide, H., Sadler, H . , and Noss, F., Ibid., 27, Fest- u. AuslandsHeft, 71 (1929). (19) Ibid., 28, 363 (1930).
(1) Aronovsky, S.I., and Gortner, R. A., IND.ENQ.CHEM., 28, 1270
(1936). (2) B a d , E. H., and Blondel, C. M. J., British Patent 391 (Feb. 16, 1861). (3) Hachihama, H., Onishi, M., and Takemura, W., J . SOC.Chem. Ind., Japan, 38, suppl. binding, 690 (1935). (4) Ibiu., 39, suppl. binding, 239 (1936).
RECEIVED August 12, 1937. Presented before the Division of Cellulose Chemistry at the 94th Meeting of the American Chemioal Society, Rochester, N . Y . . September 6 to 10, 1937. Paper No. 1528, Journal Series, Minnesota Agricultural Experiment Station. S. I. Aronovsky was Cloquet Wood Products Fellow, Vniversity of Minnesota; the fellowship was established b y the Northwest Paper Company of Cloquet, Minn.
Calculation of the N u m b e r of Theoretical Plates for a Rectifying Column BARNETT F. DODGE Yale University, New Haven, Conn.,
JOHN R. HUFFMAN‘ Columbia University, New York, N. Y.
T
HE usual means of estimating the number of theoreti-
cal plates for a given separation of two liquids is the McCabe-Thiele graphical method. When the number of plates is very large, as is the case with certain hydrocarbon separations and especially with isotopes, this method is tedious and apt to be inaccurate if carried out with the usual, smallscale diagram. The purpose of this paper is to call attention to the method proposed by Lewis (S) some years ago which has been completely supplanted by the later method of McCabe and Thiele (4, but which has distinct advantages in the case of a large number of plates. This method was given in the first edition of Walker, Lewis, and McAdams’ book (7) but was omitted from the second. The usual material balance on a rectifying column, coupled with the assumption of constant heat content of the vapor and liquid streams throughout the column, leads to the following equation for rectification above the feed level: Y,
+ jj 1
xn+l
(%e
- yn)
1 Present address, Department of Chemical Engineering, New York University, University Heights, New York, N. Y.
Subtracting xn from both sides, xn+ 1
- x,
=
yn
- x*
-
B1
(2,
- Yn)
(2)
x n + l - xn is the enrichment per plate and may be written Ax/ An. When the number of steps is large, Ax/An = dx/dn very closely. Finally we may write : dn
z=
~n
- xn
1 - B1
(2,
-~
n )
(3)
Similarly for the section below the feed level: dm dy =
Ym
- Xm
1 -+P0 (Ym -F F __
- 2),
(4)
Equations 3 and 4 can be rearranged to 5 and 6, respectively: An =
lxc lxfYn
dX 1
- xn. - E
(2,
(5)
- Yn)
dx
Am =
- zn
~ r n
- FF~- P
- xw)
( ~ m
(6)
I n the originaI application of these equations, as given by Lewis (S), and in the text by Walker, Lewis, and McAdams (‘ithey ‘),were integrated graphically; but in the case of an
DECEMBER, 1937
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ideal solution, which would be a valid assumption in many cases of hydrocarbon separation and certainly in all cases of isotope separation, the algebraic integration is relatively simple. Thus for an ideal solution a t constant temperature, CYX
(7)
y=l-x+CYx
and for the constant-pressure distillation of an ideal solution, a, which is the ratio of the vapor pressures of the two pure components, is substantially constant and an average value may be used. Substitution of Equation 7 in 5 and rearrangement (with the subscripts dropped for simplicity) leads to:
where A = R(l - a ) B = R(CY- 1 ) = -xc
c
- X,(CY
I)
+
CY
Integrating and substituting limits: An = 2.303
2Axf 2Ax,
[
2R 2v’BZ
+
- 4AC d B z - 4AC
{log
2Ax, 2Axf
+B +B
-
-\/B2 - 4AC
