INDUSTRIAL A N D ENGINEERING CHEMISTRY
148
Vol. 15, No. 2
to find tools made in which the agitation is accomplished by applied to operations not ordinarily considered agitation, 618 a device which does not involve a variety of principles. where it is desired to dissolve a solid in a liquid in the lixiviation of ores. Still another form which agitation takes is MISCELLANEOUS TYPES well illustrated in washing an immiscible liquid with water by Various types of devices are encountered in special fields pumping the heavier, in a stream more or less broken, into which do not involve any of the principles so far discussed. the lighter, as in washing nitrobenzene with water to free Blowing a gas through a liquid mass is often used for agitation it from acid. The circulation is accomplished by a pump where the interaction of the gas with the mass is either de- of any efficient type, although usually centrifugal, in a system sired or not objectionable, as in the cases of the aeration of virtually independent of the containing vessel which draws sewage and mixing of strong mixed acids, where it is desirable liquid from the bottom of the mass and pumps it in again at to blow out oxides of nitrogen. Many combinations of fluid the top through some kind of a spray head. streams, either liquid or gas, with paddles and propellers are met in practice. The stirring of a liquid being electrolyzed ACKNOWLEDGMENT in an electrolytic cell by surrounding it with a magnetic field has been found to be very highly efficient in many electrolytic The writer wishes to acknowledge the kindness of the operations where the presence of any foreign substance in the various manufacturers who have lent us the cuts and drawelectrolyte is objectionable. The cascade principle is often ings for this article.
Effect of Agitation on t h e Rate of Solution of Crystals' By E. V. Murphree MASSACHUSETTS INSTITUTE OP
TECHNOLOGY, CAMBRIDGE, MASS.
NE OF the problems in which agitation plays an important part is the solution of crystalline materials. It is possible to develop formulas for this case in which the only unknown quantity is the specific solution rate. This constant depends upon the effectiveness of agitation, and it is possible to test out experimentally an agitator suited for this work by determining this constant for the case of a given material dissolving in a given solvent. Comparison of the constant thus obtained with that found on other equipment used for the same purpose gives a measure of the relative agitation efficiencies of the two types of equipment. Assume a definite weight of crystals of size uniform or nearly so, added to a solvent and agitated a t a uniform rate. Assume also that the volume of the solution remains substantially constant. The rate of solution is proportional to the area of crystals exposed and to the degree of agitation. Furthermore, as has been shown by A. A. Noyes,2 the rate of solution a t any particular time is proportional to the difference in concentration of the saturated solution and that of the main body of the solution. This is because the solution in absolute contact with the crystal is saturated and the crystals dissolve only by diffusion of the solute through the stationary film of liquid around the crystals. This diffusion is of course proportional to the concentration difference. Since the diffusion rate will be inversely proportional to the thickness of this film, and since this film thickness is determined by the effectiveness of agitation, being approximately inversely proportional to the velocity of the liquid past the crystal, diffusion rate-i. e., the constant which represents the specific rate of solution for unit area of crystal surface-is a good measure of agitation efficiency.
0
GENERALFORMULA NOMENCLATURE
V = volume of solution. 8 = time. c, = concentration of saturated solution as weight per unit volume. 1 2
Received January 5 , 1923. Noyes and Whitney, Z. physik. Chem., 2s (1897), 689.
c
= concentration of solution at time 8 in same units.
linear dimension of crystal a t zero time.
x0
x
= linear dimension of crystal a t time
W,= total weight W = total weight n
e.
of crystals a t time zero, of crystals a t time e. W O
number of crystals = -, ax.2
-
p
weight of one crystal. bxo* = surface of one crystal. a and b are constants, the numerical value of which depends upon the form of the crystal grains. uxo8
It is assumed that when 8 = 0 the solvent contains no solute. 1 '
dC
-
de
=
K (ca- c ) 'n b n
w, - w
n
( m , 3
=
v,
- (1x3) = V,
- 3 anx2 dx
= V dc
On substituting for c and dc, rearranging, and integrating, Equation 1 takes the form
wherekS = A.
The value of Equation 2a.
3
in this formula can be found by means of
SPECIAL CASEI-When there are not enough crystals originally present to saturate the solution, the time for comp!ete solution is found from Equation 3 by making x = 0. This gives
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1923
SPECIAL CASE11-When there are just enough crystals to saturate the solution, the time for complete solution is found from Equation 4. I n this case, however, A = 0, so the time becomes infinite. SPECIAL CASE111-When there are more than enough crystals t o saturate the solution, the time for saturation is given by Equation 3 and is infinite. SPECIAL CASEIV-When the amount of crystals is very large compared with the amount necessary to saturate the solvent, the change in surface area of the crystals may be neglected and the expression for solution rate reduces to dc = K (c,-c) B de where B = surface area. JnC“= KB8 .Hence, c,-c V This condition might well be used where it is desired to test the agitation efficiency of a given type of agitator for a thick mixture of solids suspended in liquid. Where the agitator is to be used for a relatively small amount of solids in the liquid, this condition should obviously not be employed, because it greatly changes the character of the mixture.
V
To measure rate of solution any of the standard methods can be employed for analysis of the solution a t any specific time. If instantaneous readings are desired, it might be worth while to use conductivity methods of analysis. The general equation is applied to the following data. Since the investigator did not determine the number of particles, they were assumed to be spherical. This can introduce no serious error. The value for cs was taken as the last reading in the table. DATAPOR RATE OF SOLUTION OF KzCrzOi CRYSTAL@ Volume of solution, 4000 CC. Weight of crystals, 500 g. Size of crystals, 0.6314 cm. Temperature of solution, 23’ C. Time in Min. 0
1 5 10 15 25 40 60 80
Concn. in Equivalents per Liter 6.00 0.60 1.60 1.93 2.06 2.18 2.26 2.30 2.34
From these data the following was calculated : cg
a b
= 0.1147 g./cc. = 8.450 = 3.142 9 X
0 1 5
10
15 25 40 60
0.6314 0,5780 0.4552 0.3954 0.3654 0.3340 0.3083 0.2936
f 0.0 0.0162 0.333 0.566 0.759 1.272 1.702 3.710
n = 235 A = -0.0218 k = -0.2794 9 (calcd.) 0.0 0.5 6.3 10.6 14.5 24.0 32.5 70.0
According to Equation 3, the result of plotting f against 0 should be a straight line, and the experimental results justify this conclusion. The slope of the straight line is
- The value of K for this caseis therefore 0.366 g. per Vk
sq. em. per min. per unit concentration difference. The difference between 0 observed and calculated for one minute may be due to error in determining zero time. A small error in analysis will make a large error in the case of 0 for 40 and 60 min. It is evident that results analogous with those given here can be obtained for any similar case of heterogeneous equilibrium. H. Braude, M. I. T. thesis, June, 1913.
149
The Stability of an 0.OlIV Sodium Oxalate Solution* By Edward S. Hopkins BALTIMORE CITYWATERDEPARTMENT, BALTIMORE, MD.
In this laboratory the usual oxygen-consumed test2 is made as daily routine practice. This is an acid permanganate digestion and subsequent titration with sodium oxalate. Frequent standardization of the oxalate solution was necessary as decided deterioration was encountered after the first week of use. I n fact, upon titrating a solution 17 wks. old it required only 7.4 cc. of permanganate instead of 10 cc. This condition is well known in chemical l i t e r a t ~ r e . ~ ~ ~ The addition of 100 cc. of 1:4 sulfuric acid per liter to the oxalate solution will prevent this deterioration for a t least two months (actual experiment), even when the solution is stored in clear glass bottles on the laboratory shetf exposed to daylight. Weekly tests were made upon our laboratory solutions, and 10 cc. oxalate always equaled 10 cc. permanganate. The permanganate was checked a t the time of each titration against a weighed amount of standard oxalate and found to be correct. These laboratory solutions are stored in the usual clear glass tincture bottles with glass tube connections to the usual siphon buret and no precaution is taken to exclude light or treat them in any particular manner. This addition of sulfuric acid to a standard oxalate solution has been presented by one authority6 who discussed the behavior of an 0.1 N solution of oxalic acid, without describing storage conditions. Received December 20, 1922. “Standard Methods for the Examination of Water and Sewage, American Public Health Association,” 1920. * Blum, J . Am. Chem. Soc., S4 (1912), 129. 4 Bur. Standards. Circ. 40 (1920). 6 Treadwell and Hall, “Quantitative Analysis,” 599. 1
2
Gypsum Decision By a decree of the Federal District Court issued on January 3, the Gypsum Indiistries Association, which comprises practically all the manufacturers of gypsum products in the United States, was ordered dissolved as a combination in restraint of trade and commerce in gypsum products. The terms of the decree virtually destroy the trade association and prohibit its regular weekly or monthly meetings, a t which opportunities were offered, as the government contended, for open or illicit price-fixing by the group, for arrangements for the curtailment and limitatjon of production, and for devising other abuses which are alleged to have resulted from the meetings. In its place is substituted a nonprofit-making corporation for the joint welfare of the members, with powers limited expressly by the decree, and by its charter to certain well-defined and concededly lawful activities. The decree is said to be of far-reaching importance because for the first time in the history of the Sherman Law there is clearly set forth a code of principles governing trade associations and outlining definite restrictions, with certain provisions in this specific case for what they may be permitted to do. The main injunctive provisions of the decree prohibit agreement to fix or establish prices for gypsum products, to establish or maintain uniform prices, to advance or decrease prices, to limit or otherwise control the production of gypsum products, to fix boundaries of sales territories open only to certain members, and to effect any discrimination in prices. Activities which are held to be lawful include advancing or promoting the use of gypsum products by all legitimate means, including research, publicity, and advertisement, dealing with engineering and trade problems pertinent to the industry, carrying on educational work, maintaining a traffic bureau to furnish information, dealing with improved methods of plant and mine operation, and maintaining a credit bureau. The decree is the result of a nationwide investigation conducted by the Government, and of a Grand Jury hearing lasting more than a month, a t which a large amount of evidence was accumulated.
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