I.\-DUSTRIAL
July, 1925
AAVD EXGINEERING CHEMISTRY
The results of the analyses are given in Table I, and it is seen that (1) no appreciable loss of calcium results through the use of persulfate, and ( 2 ) there is no serious contamination of the lime or magnesia by manganese. The behavior of uranium, titanium, and vanadium under these conditions was also tested as follows: Solutions were prepared containing about 0.15 gram Fe203 to which were added in the first series 0.005 gram of VZOS;in the second series 0.005 gram of TiOz; and in the third series 0.005 gram of [TO3. After precipitation made by the method given above, the filtrates showed no trace of titanium or uranium
745
and only a very faint trace of vanadium. Apparently, under these conditions the presence of persulfate had no disturbing action on the precipitation of these elements by ammonia. Chromium, if present, will be found in the filtrates and may be removed before the precipitation of calcium.3 It is believed that this modification of the Blum method will be found simple in manipulation, and it is evident from the foregoing results that it is satisfactory for the precipitation of manganese in the ammonia precipitate, and for the elimination of its interference in the determination of lime and magnesia.
Solubilities of Sulfur Dioxide and Ammonia in Water’ By T. K. Sherwood XASSACHUSETTS INSTITUTE OP TECHNOLOGY, CAMBRIDGE, MASS,
experimental points on such a plot drawn to a large scale. Those figures in parentheses are from extrapolated portions of the curves, shown dotted on the plot. Table
SOLUBILITY OF SO, IN W4TLR
I2
5
11
10
d 9
3
ga 7e a. ~6
R 6
5
3 4 3
2 I
0
Is
x)
5 10 P4RTUL PRESSURE 5oeM M Hy.
s
sit’s or s where
p
H K
+
water are not included as they were evidently from the same sources, and check excellently those given by Zeisberg2 in r‘t recent article. I n the treatment of the data on the solubility of sulfur dioxide, it is assumed that the dissociation is constant a t any particular temp e r a t u r e , and that Henry’s law applies to t h e undissociated solute. On the basis of ~, these assumptions it has been shown3 that
I-Solubility
of Sulfur Dioxide in W a t e r
c,
SOLUBILITY OF SO, IN WATER
200
vi
IS0
I
= H,b m p = Hd; C H = grams SO2 dissolved in 1000 grams water = partial pressure SO*, mm. mercury
+
Henry’s law constant = dissociation constant of t h e HpSOs
=
0
0
: :: N
100
vi
Therefore, the data were collected in the form of a plot of The best straight line was drawn through .s/dFversus the points on this plot, and the curve and Table I of s versus p are from points taken from this line. The data on the solubility of ammonia have been plotted on logarithmic paper to reduce the curvature of the resulting line, and to obtain a constant percentage error in plotting. The data in Table I1 are from the best line through the
5
dF
1
Received March 26, 1925.
2
Chem. M e t Eng , 32, 326 (1926).
8
Haslam, Hershey. and Keen, THISJ O U R X ~ L ,16, 1226 (1924).
50
PARTIAL PRESSURE SO2 M.M. Hq.
0
I
I S D U S T R I A L ,450 ESGIAVEERISG CHEMISTRY
746
p
1000 900 800
700
600 500 400 300 250 200 150
103 (0
50 40 30 25 20 16 12 10
c
PARTIAL PRESSURE XHa, MM.H G -
100 c
200
PARTIAL PRESSURE
NH, IN M.M. MERCURY
of A m m o n i a i n W a t e r
T a b l e 11-Solubility Grams ?;Hq/1000 grams water ‘00
-
c
300
c
400 C ,
500 C ,
Acknowledgment 600 C,
Thanks are due C. E. Lanyon, W. K. Lewis, and R. G. Whitman for references and suggestions.
94!
is5 636 500 380 2ij 190 119 S9.5 64 42.7 25.1 17.7 11.2
987 780 600 439 301 190 144 103.5
iO.l 41.8 29.9 19.1 16.1 11 3
1-01. 17, Xo. 7
Bibliography 943 686 470 298 227 166 114 69.6 50.0 31.7 24.9 18.2 l5,O
12.0
S o l u b i l i t y of Sulfur Dioxide 719 434 352 260 179 110 79.7 51.0 40.1 29.6 24.4 19.3 15.3 11.5
692 534 393 273 167 120 76.5 60.8 45 (37.6) (30.0) (24.1) (18.3) (15.4)
825 596 405 247 179 115 91.1 67.1 (55.7)
S34 5S3 361 261 165 129.2 94.3 77 (44.5) 61 (35,s) 48.7 (26.7) 36.3 (22.2) 30.2
1-Scbonfeld, A n n . , 96, 1 (1853). C-Sims, Ibid., 118, 340 (1861). 3-Roozeboom, Rec. trau. chim.,3, 29 (1884). 4-Lindner, Monafsh., 33, 646 (1912). j-Freeze, Wochbl. Papierfabr., 51, 861 (1920). 6-Smith and Parkhurst, on file, M. I. T. Research Laboratory of Applied Chemistry. 7-Watts, I-Raoult, 2-Carius,
J . Chem. Soc. (London),2, 88 (1864). S o l u b i l i t y of A m m o n i a A n n . chim. phys., 1, 262 (1874). A n n . , 99, 144 11856).
I-\\'DCSTRIdL d S D E-17GISEERIA17G CHEJIISTRY
July, 1923
3-Perman, J . C h o n . SOL.(London), 83, 1168 (19031. 4-Watts, I b i d , 2, 88 (1864). 5-Sims, A n n . , 118, 345 (1861) 6-Roscoe and Dittmar, I b i d . , 112, 349 (1859). 7--Cragoe, Myers, and Taylor, J . A m . Chem. Soc.., 42, 220 (1920).
717
8-Mallet, A m . Chem. J . , 19, 807 (1897). 9-Mollier, Milt. Forschungsarbeifen, 1909, Heft 63-64, 10-Smits and Postma, Verslag. .-lkad. TT7efenshnppen, 23, l l i (1914). 11-Doyer, Z . p h y s . C h e m . , 6 , 486 (1890). K-Gaus, Z. anorg. Chem., 26, 236 (1900).
Rectifying Column Calculations' With Particular Reference to N Component Mixtures By E. V. Murphree THESOLVAY PROCESS Co., SYRACVSE, h7.E'.
viewpoint, calculation simplifications this is the method generally Rectification consists esThe concept of the theoretical plate does not offer a sentially in the trarlsfer of used today.3 Lewis' has satisfactory basis of calculation for rectifying columns an approximate material between a gas when the mixture being rectified contains more than method of calculation for phase and a liquid phase. components, and even for some calculations on cases ill Tvhich the rate of I t is therefore a special case ' two binary mixtures its use is not satisfactory. change of compositioll of the ' o f a b s o r p t i o n . The leas A method of calculation for actual plates which can liquor from plate to plate of volatile components are ahbe used for mixtures of any number of components ideal is l sorbed and the more volatile is developed from the absorption equations. His method considerably ' liberated. The equations A means of expressing the efficiencies of rectificasimplifies the calculations. for the rates of material tion of the volatile components is given. transfer are of the following It should only be used, 1 type? however. when the rate of change is small. I n actual columns, equilibrium between vapor and liquor is seldom realized, and consequently the number of plates needed time of contact of liquor and vapor to perform a given separation in a n actual column is usually where 8R' = = quantity of component one transferred to gas phase greater than the number calculated for the ideal column. The for a n area of contact of A ratio of the number of ideal plates to actual plates or the numk , = conductivity of gas film for component one k , = conductivity of liquid film for component one ber of ideal plates equivalent to one actual plate for a given d = area of contact of liquid and vauor column is called the plate efficiency of that column. This i> P, = partial pressure of component &e a t vapor-liquid a n average value. interface The plate efficiency for many cases gives a satisfactory P, = partial pressure of component one in main body of gas basis for the comparison and design of fractionating column;. CL = concentration of component one in main body of I t is probably a function of several variables, the most iniporliquid tant of which seem to be the type of plate, the substances beC, = concentration of component one a t vapor-liquid ing fractionated, and in some cases the temperature. Peinterface ters5 first showed the variation of plate efficiency with the K h e n the liquid film resistance is negligible in comparison material being separated. The author has seen tests on a with the gas film resistance or when the partial pressure is a given type of column which gave plate efficiencies varying from less than 0.1 up to 0.8, depending on the particular linear function of the concentration, Equation 1 reduces to: dll' substances being fractionated. _ de - Ku "I ( P L - Pd (2) I n certain types of rectification the concept of the ideal where K , = a n over-all conductivity for component one column does not offer a satisfactory basis of talculation. P L = partial pressure of component one in equilibrium K h e n the plate efficiency is small, it is rather unsatisfactory with liquid not to be able to trace the liquor from plate to plate of the For cases in which the gas film resistance is negligible in coniactual column. This is especially true when liquor or vapor is added or withdrawn from the column on other than the ternii- parison with the liquid film resistance Equation 1 reduces to
1
j
1
3
* a
Recelled March 19, 1925 La Rectification de I Alcool. ' 1893, Parr, Lewis THISJ O U R ~ A L 1 , 522 (1909) Ibrd , 14, 492 (1922) / b i d 14, 476 (1921)
. -
where K , = a n over-all conductivity for component one C, = concentration of liquid in equilibrium with the vapor 8
Leais a n d Whitman, THISJ O V R N A L , 16, 12i.5 (1924).
