INDUSTRIAL AND ENGINEERING CHEMISTRY
998
normally high rates in comparison with the other three elements studied, so that apparently chemical affinity plays a greater role than the atomic weight of the diffusing element. On the other hand, it may be that even at the temperature of molten iron some of the diffusing molecules contain more than one atom, so that the atomic weight may not be a true measure of the relative mobility of the molecules. At any rate, it is evidently not safe to predict the relative diffusion rate of an element through a metallic bath from its position in the periodic table. CONCLUSIONS The rate of diffusion is much faster a t the beginning of a test than later. The distance to which a measurable amount of an element will diffuse in 30 minutes is almost as great as it will be in 3 hours. The reason is that as diffusion progresses the gradient becomes less steep. The rate of diffusion a p parently follows the same laws as heat conduction along an insulated rod. If a deep, undisturbed bath of metal was in contact with a bath of slag, desulfurization would almost cease after a relatively short time. Any movement of a dis-
Vol. 24,
KO.9
solved substance through a liquid is largely governed by agitation. Hixson and Crowell ( 1 ) state: “ . . . . . . . .stirring takes those layers which at the start had relatively small interfacial-contact area with the less concentrated solution and low-concentration gradients, and stretches them out into very thin convoluted strata with great contact areas and high concentration gradients.” Hence it is seen that, in those metallurgical processes in which the chemical elements such as sulfur, phosphorus, silicon, carbon, or manganese are being transferred to or from a molten bath of iron, it is extremely important that adequate agitation be maintained in t,he bath, for the amount of material transferred by straight diffusion is extremely small. LITERaTURE CITED (1) Hixson, A. W., and Crowell, J. H., IND. EXG. CHEM., 23, 928 (1931). (2) Ingersoll, L. R., and Zobel, 0. J., “Introduction to Mathematical Theory of Heat Conduction,” Equation 37, p. 78, Ginn,1913. RECEIVED April 19, 1932. Published by permission of the Director, U. S. Bureau of Mines. (Not subject to copyright.)
Relation between Fineness of Limestone Particles and Their Rates of Solution FIRMAN E. BEAR,American Cyanamid Company, New York, X. Y., AND LILBURNALLEN,Ohio State University, Columbus, Ohio
A
LL other factors being equal, the rates of solution of different-sized particles of limestone of a given origin should be proportional to the surfaces exposed to the solvent. It follows from this that all surfaces should be dissolved off a t equal rates-that is, the diameters of all particles should be reduced by equal amounts during any given period of time. If a limestone particle of a given size is made to dissolve just within a given length of time, a larger particle placed in the same solvent for the same period of time should have been reduced in diameter by an amount equal to the diameter of the smaller particle. If D is the diameter of the larger particle and d that of the smaller particle, the percentage dissolved from the larger particle a t the time when the smaller is completely dissolved should be O3 - (D - d)a, assuming both particles are of the same shape and have the same physical and chemical characteristics. PERCENTAGES OF EACHLARGER TABLEI. THEORETICAL LIMESTONE SEPARATE DISSOLVED AT EXACT TIMESOF COMPLETE SOLUTION OF STANDARD SEPARATES SCREEN MESH
3-4 4-6 6-8 8-10 10-14 14-20 20-28
28-36 35-48 48-65 66-100 100-160 150-200
DIAMETER
DISsOLVED 150-200 mesh 45-65 mesh standard standard
Cm.
%
0.5690 0.4010 0.2840 0,2010 0.1410 0.1000 0.0710 0.0503 0.0356 0.0251 0.0178 0.0126 0.0089
4.7 6.7 9.5 12.8 17.8 24.6 33.2 44.4 57.8 73.0 87.5 97.5 100.0
% 12.8 17.8 24.6 33.2 44.4 57.8 73.0 87.5 97.5 100.0
100.0 100.0
100.0
Assuming this equal reduction in diameter of all particles in a given sample of pulverized limestone whose particles range
from 3 to 200 mefih in size, and taking the average diameter of the particles retained on each unit of the Tyler standard screens, Table I gives the fractional decomposition of all particles a t the time the average-sized particles passing a 150mesh screen and retained on a 200-mesh screen are completely dissolved. Similarly, fractional decomposition values are given for the exact time of complete solution of 48-65 mesh material. Since the diameter of the average particle of any screen separate of the Tyler standard screens is d 2 times the diameter of the average particle of the next smaller screen in the series, the percentage decomposition values always bear exactly the same ratio to the one next above or below, no matter where in the series one cares to set the point of complete solution. Thus when, for example, the average particles of the 20-28 mesh separate are completely dissolved, 97.5 per cent of the average of those of the 14-20 mesh separate will be in solution. METHODFOR EVALUATING PULVERIZED LINESTONE
PRODUCT To evaluate any grade of pulverized limestone in terms of 150-200 mesh material of the same origin, and assuming that the time factor is that of the completion of solution of the average-sized particle of the above screen, one multiplies the percentage of each separate by the percentage decomposition of that particle size at the given time. It will be observed, in the case in which the evaluation is in terms of, and at the time of complete solution of the 150-200 mesh particles, that the percentage decomposition of particles less than 200 mesh in size is set at 100. At that time all particles less than 200 mesh would also have been completely dissolved. If one chooses as the standard the 48-65 mesh material, the percentage efficiency of the grade of limestone given in Table 11, at the time of the complete solution of the average-sized
I IL' D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
September, 1932
999
Samples of these stones were pulverieed and the products particles of that mesh, is 63.42 per cent. I n this case all particles smaller than 48-65 mesh have a percentage de- divided by the use of standard screens into the several separates previously indicated. ?\Tot knowing the rate of solution of composition value of 100. The reciprocals of the fractional decomposition values of limestone particles in the above soil, it was decided arbitrarily Table I represent the quantities of the different separates to use the 48-65 mesh material as the standard with the required to equal in neutralizing effect the unit weight of the thought that particles of high-calcium stone of this size would standard 150-200 and 48-65 mesh txoducts, at the exact time mobablv be comdetelv . -dissolved a t the end of a 12-month of comdete solution of the standaids. Assuming one ton of period. " As indicated previously, the 150-20b and 48-65 mesh prodlime requirement of the soil was ucts, respectively, as the standfound to be 5500 pounds of ards, the quantities of each of calcium carbonate per 2,000,000 the other separates required for Pulverized limestone products, carying in their pounds of soil. It was derided equal neutralizing effects a t the percentage contents of the carious particle sizes, to add e n o u g h high-calcium times mentioned are given in require evaluation in terms of their relative limestone to the soil to satisfy Table 111. effectiveness at the end of given periods of time half this lime requirement by METHOD OF DETERMININQ RATES after being applied to acid soils. Assuming the time of complete solution of OF SOLUTION OF LIMESTONE t h e s t a n d a r d (48-65 mesh) there are no interfering factors, the diameters of SEPARATES which, it was assumed, would all particle sizes should be reduced by solution to just be completely dissolved at It was decided to test the the same extent in unit time. This being the case, the end of 12 months. This rates of solution of the various it should be possible to evaluate a n y particle size would have required 2750 pounds separates of two limestones, and or composite of particle sizes in terms of some of the 48-65 mesh separate, exof mixtures of them, under acid cept for the fact that the highsoil conditions. A Mahoning standard particle size. It would then remain to calcium stone contained some silt loam soil, having a lime redetermine the rate of reduction of the diameter of impurities and had a total neuq u i r e m e n t ( m o d if i e d Jones the standard particle in the soil in question. It tralizing power of only 93 per method') of 5500 pounds of calwas found that the theoretical evaluations are cent. Correcting for this lack cium carbonate per 2,000,000 nearly valid in the soil f o r finely pulverized of purity, it was necessary to pounds of soil and a pH of 4.65, add 2958 pounds of this sepawas selected for this purpose. separates, but not f o r the coarser separates. rate. The other separates were A large quantity of this soil was Apparently the limiting factor in the latfer case applied according to the ratios thoroughly mixed to insure uniis diffusion. given in the second column of formity. A series of cypress Table 111. They were applied, frames having forty-eight units, therefore, in such amounts as t o each with areas of 625 sauare inches and depths of 14 inches, were placed in a location produce the same effect as the 45-65 mesh separate a t the excavated for that purpose. The varying limestone treat- exact time when this latter separate had just dissolved. Representative plots have been chosen for consideration. ments were thoroughly mixed with 200-pound portions of the prepared soil, and each treated portion was placed in one The plots selected, in duplicate, were those numbered 21-30 and 44-45. Plots 21-30, in pairs, were treated with 4-6, 8-10, of the forty-eight units. 14-20, 28-35, and 48-65 mesh separates of high-calcium TABLE11. THEORETICAL EFFICIENCIES OF PULVERIZED stone, respectively. Plots 44-45 received 48-65 mesh doloLIMESTONE PRODUCT, IN COMPARISON WITH STAXDARD mitic stone. SEPARATES, AT EXACT TIMEOF COMPLETE SOLUTIOX Barley and clover were grown in rotation on these plots OF THESESTANDARD SEPAR.4TES for the purpose of securing a crop measure of the efficiency of DIRKILVED SEPARATERATINGS the several limestone treatments. By reason of the fact that 150-200 48-65 150-201) 48-65 SCREEN SCREEN mesh mesh mesh mesh there was no opportunity for surface run-off, water accumu.MESH ANALYSIS= standard standard standard standard lated in these frames in the winter and, on freezing, covered % % % % % 4.. 7. 3-4 3.90 12.8 0.18 0.50 the area with ice to the injury of the crops. The yields were 17.8 6.7 4-6 9.90 0.66 1.76 so erratic as to be useless. This did not interfere with that 11.40 24.6 6-8 2.80 9.5 1.0s
V
A
8-10 10-14 14-20 20-28 28-35 35-48 48-65' 65-100 100-150 150-2OOa Through 200
11.40 7.50 7.00 4.00 4.10 3.40 1.94 1.94 1.40 1.14 30,98
12.8 17.8 24.6 33.2 44.4 57.8 73.0 87.5 97.5 100.0 100.0
33.2 44.4 57.8 73.0 87.5 97.5 100.0 100.0 100.0 100.0 100.0
1.46 1.33 1.72 1.32 1.82 1.96 1.41 1.69 1.36 1.14 30.98
__
3.78 3.33 4.04
2.92 3.58 3.31 1.94 1.94 1.40 1.14 30.98
__
Percentage efficiencies 48.11 63.42 a This is a sample of pulverized limestone such as is being offered for sale in many localities. T h e analysis would ordinarily be reported as follows: 64 per cent through 10-mesh, 37 per cent through 50-mesh, and 33 per cent through 100-mesh Screens.
Two fundamentally different limestones were used in these tests. One was a high-calcium stone obtained from the Colgan Limestone Products Company of Columbus, Ohio. The other was a dolomitic stone secured from the National Lime and Stone Company of Carey, Ohio. The chemical analyses of these stones are given in Table TV. 1
J . Assoc. Oficaal Agr. Chem., 1, 43-4 (1915)
TABLE111. THEORETICAL QUANTITIES O F EACHSEP.4RATJ3 REQUIRED TO PRODUCE SAMEEFFECT AS ONE TONOF STANDARD SEPARATES AT EXACT TIMESOF COMPLETE SOLUTION OF THESE ST.4NDARD SEPARATES QUlUTITY PER ACRE4
3-4 4-6 6-8 8-10 10-14 14-20 20-28 a Two
TABLEIv.
ANALYSES OF
VARIETYOF STONE
ACRE^ 48-65 mesh standard Pounds 2280 2050 2000 2000 2000 2000
Q U ~ X T I T YPER
150-200 48-65 mesh meah standard standard Pounds Pounds 42,600 15,600 11,200 29,800 8.100 21,000 6:ono 15,600 4;500 11,200 8,100 3,460 2,740 6,000 million pounds of sod
SCREEN MESH
SCREEN MESH 28-35 35-48 48-6.5
65-io0 100-150 150-200
150-200 mesh standard Pounds 4500 3460 2740 2280 2050 2000
LIMESTONES USED
CALCIUM
%
IN
MAGNESIUM
%
High-calcium 36.00 00.64 High-magnesium 21.20 11.84 Total neutraliming power in terms of calcium carbonate.
TESTS T. N. P.0
% 93 108
I N D u s T R I A L A N D 'E N G I N E E R I N G
1000
cH E M I sTR Y
Vol. 24, No. 9
REMAININQ IN SOILAT VARIOUB TIME phase of the experiment having to do with the reaction TABLEVII. LIMESTONE ISTERVALS AFTER APPLICATION OF EQUIVALENT QUANTITIESO between the limestone and the soil. OF SEVERAL SEPARATES The plots were sampled at various intervals during a period -CaCOa PER 2,000,000 POUNDS SOILof 4 years. Each sample from each plot consisted of a comPLOTTREATMEXTS End End End Screen Pera of 12 of End 24 of 36 of 48 posite of five borings, r i t h a 11/4-inchaugur, to R depth of 62/3 mesh acre months months months months inches. Twice during this 4-year period the soil was rePounds Pound8 Pounds Pound8 Pounds 4-6 16,242 11,700b 12,650 moved from each compartment, thoroughly mixed, and 10,740 10,000 8-10 8,536 7,740 5,700 4,030 3,520 replaced in its compartment. 14-20 5,073 4,120 3,440 1,400 760 TREATMENTS OF REPRESENTATIVE PLOTS TABLEV. LIMESTONE SCREEN MESH
PLOT
TREATMENT P E R ACRE^ Pounds
21-22 23-24 25-26 27-28 29-30 44-45
4-6 8-10 14-2 0 28-35 48-65 48-65
16,242 8,536 5,073 3,373 2,958 2,556b
28-35 48-65 48-650
562 301 173 114 100
100
Data were secured from analyses, all made a t the end of the 4-year period, of samples chosen at the various intervals mentioned above. The lime requirement determinations were made by the Jones method. The pH determinations were run electrometrically, using the quinhydrone electrode. The residual carbonates were determined by decomposition in vacuo and absorption of the evolved carbon dioxide in barium hydroxide solution.
With but few exceptions the decreases in soil acidity, whether measured by lime requirement or by pH determinations, were of the same relative order in any series of limestone treatments. The lime requirement data, being somewhat more consistent, are given in Table VI. IN LIMEREQUIREMENT OF SOILDVE TO TABLEVI. DECREASE TREATMENTS WITH VARIOUSLIMESTONE SEPARATES
4-6 8-10 14-20 28-35 48-65 48-651 a
End
Per acre0 Pounds
16,242 8,536 5,073 3,373 2,958 2,556
PER
2,000,000P O U N D E SOIL-
End
1,000 00 1.240
160 00 200
00 00 00
of t...___ h e w nartirlra o
of 12
of 24
months Pounds
months Pounds
End of 36 months Pounds
months Pounds
End
1200 990 1305 1810 2210 1170
1485 1870 2240 2405 2285 1855
2255 2430 2945 2370 2235 2265
2575 2685 2815 2090 1945 2045
of 48
Quantities theoretically necessary t o produce same effects a t exact time
TABLEVIII. RELATIVE EFFICIENCIES OF VARIOUSLIMESTONE SEPARATES PLOT TREATMENTS Screen mesh
4-6 8-10 14-20 28-35 48-65 48-656
-RELATIVE EFRECTIYENESSEnd End End End of 12 of 24 of 36 of 48 months months months months
Per acrea Pounds
16,242 8,535 5,073 3,373 2,958 2.556
%
%
%
%
52 44 57 80 98 51
65
99 106 129 104 98 99
113 118 123 92 85
106 100 81
90
a Quantities theoreticallv necessary to produce same effects a t exact
time of complete solution b Dolomitic limestone.
df 48-65
mesh material.
The actual efficiency of the 48-65 mesh separate, on the basis of satisfying one-half the lime requirement, was 80 per cent a t the end of the first yearly interval. If we again give the 4 8 6 5 mesh separate a rating of 100 the relative percentage efficiencies of the other separates on the basis of applying them in equal amounts are as given in Table IX. This table also gives the theoretical efficiencies, or the fractional decomposition values, of these separates for a diameter reduction equal to the diameter of the 48-65 mesh separate. TABLEIX. RELATIVE EFFICIENCIES OF LIMESTONE SEPARATES
of complete solution of 48-65 mesh material.
SCREEN MESH
b Dolomitic limestone.
The standard of comparison was the 48-65 mesh, highcalcium material. It was assumed this material would go into complete solution in 12 months. However, the data in Table VI indicate that part of this material remained undissolved a t the end of this 12-month period. There remained in the soil enough carbonate to overcome any loss by leaching and to bring about a maximum decrease in soil acidity a t somewhere near the end of 24 months. Further evidence on this point is shown in Table VI1 in which are given the residual carbonates for these same plots at the end of the four yearly periods. Apparently all but 200 pounds (acre basis) of the 48-65 mesh material had dissolved in the soil by the end of 12 months. The theory of application assumes, however, that the rate of solution will be proportional to the limestone surface exposed. On this basis, if the diameter reduction continued a t its average rate for the first 12 months, the 200-pound residue would have been entirely dissolved at the end of 20.3 months. At this time the effectiveness of all separates as applied should have been the same.
Dolomitic limestone,
KO data on the soil a t the end of this theoretical period of 20.3 months are available. Consequently, the data secured at the end of the 24-month period must be considered. Recalculating the data of Table VI on the basis of 100 per cent effectiveness of the 48-65 mesh, high-calcium separate a t the end of this 24-month period, the relative efficiencies of the other separates in the amounts applied are as shown in Table VIII.
RATESOF SOLUTION OF LIMESTONE SEPARATES I N SOIL
PLOT TREATMENTS c C a C O a
1,600 200 1,890
a Quantities theoretically necessary t o produce same effects a t exact time APPLICATIOX of c o m d e t e solution of 48-65 mesh material. RATIO b Th'e evidence indicates t h a t this quantity should have been larger than it is. Accuracy in sampling t h e soil was difficult b y reason of t h e large size
a Quantities theoretically necessary t o produce same effects a t exact time of complete solution of 48-65 mesh material. b Dolomitic limestone, corrected for high neutralizing power b u t not for slow r a t e of solution
Screen mesh
3,373 2,858 2,556
THEORETICAL EFPICIENCIES
% 4-6 6-8 8-10 10-14 14-20 20-28 28-35 35-4s 48-65 a
17.8 24.8 33.2 44.0 57.8 73.0 87.5 97.5 100.0
OBBERVED EFFICIENCIES E n d of 24 months
End of 12 months
% 9.9 12.5'3 15.1 24.0" 33.9 53.0" 71.6 94.0' 100.0
% 11.9 19.9' 27.7 41.5' 56.5 75.'O 92.5 98.5" 100.0
Values b y interpolation.
P~ACTICAL APPLICATIONS In terms of field practice, the data indicate that, if it were desired to produce the same effects on the soil reaction by the end of a 12-month period, it would take practically ten times as much of the 4-6 mesh material as of the 48-65 mesh material. Similarly, if the same effects were desired at the end of a 24-month period, approximately eight times as much of the 4-6 mesh material would be required as of the 48-65 mesh material. .4ccording to the theory on which the work was based, the ratio between these two separates, for identical effects at the time of complete solution of the 48-65 mesh material, was 5.6 of the former to 1 of the latter.
Geptember, 1932
INDUSTRIAL AND ENGINEERING CHEMISTRY
It is apparent that for the finer separate sizes the observed efficiency values would fit the theoretical somewhere before the 24month period. This is in agreement with the previous conclusion drawn from the residual carbonate data that the standard 48-65 mesh separate would be dissolved in 20.3 months. The observed efficiency values for the coarser separates (10-14 and larger) are relatively low. Diffusion no doubt plays a greater role in the complex process of dissolution as the particle sizes become larger. This possibility is evident when one considers that the distance between the surfaces of the 4-6 mesh limestone particles would be 1.2 cm. if the particles were uniformly distributed through the soil and the rate of application was that used in these experiments.
1001
ACKNOWLEDGMENT This research was financed by The National Agricultural Limestone Products Association, Inc., Columbus, Ohio. The work was begun by L. B. Broughton, now head of the department of chemistry, University of Maryland; it was continued by Herbert F. Kriege, now chief chemist of the France Stone Company, Toledo, Ohio; and it was brought to the present stage by the junior author under the direction of the senior author, a t that time on the faculty of the Ohio State University, Columbus, Ohio. The authors are indebted to Robert M. Salter of the Ohio State University for assistance in formulating the theory on which the investigation was based. RECEIVED April 23, 1932.
High-Speed Agitation under Pressure A. H. MACMILLAN AND NORMAN W. KRASE,Chemistry Department, University of Illinois, Urbana, Ill.
F
OR research purposes, apparatus for establishing intimate contact between gases and liquids, or between
for research purposes a t considerably higher pressures than indicated by Calvert. The apparatus has been thoroughly tested for many weeks after being develoDed for the studs of reactions of carbon dioxide and caibon monoxide with aromatic compounds in the presence of aluminum chloride. Experimental results will shortly be reported.
gases, liquids, and solids, is necessarv in problems inv o l v i n g g a s e s under pressure. This r paper describes such apparatus, readily c o n s t r u c t e d in an ordinary machine shop, and suitable for temperatures to 200" C. and for pressures to 300 atmospheres. These limits can readily be raised if desired. The literature contains some references to a p p a r a t u s previously used for similar purposes. Phillips (4) described a device consisting of cylinders rotating endwise in a thermostat, and Groggins and Hellback (2) improved this in details. In this case the agitation and temperature control no doubt were excellent, but it was impossible t o maintain the reaction mixture under a known or constant gas pressure. Peters and Stanger (3) described a shaking or rocking autoclave, the temperature being electrically controlled and the pressure r e g u l a t e d through a flexible tube connection. This arrangement is also used by manufacturers of laboratory pressure autoclaves where agitation is necessary. The a p paratus described here possesses obvious advantages over previous ones, in that preesure is under exact control a t all times by means of the valve and gage connected to the head and no moving parts such as tubing under pressure are involved. Temperature is also controllable between narrow limits. Stirring conditions are perfectly reproducible and equal to those obtainable in open vessels a t atmospheric pressure. Recently it has been discovered that the essential principle underlying the present device has been described and patented by Calvert ( 1 ) . The present description, however, brings out modifications in design and c o n s t r u c t i o n FIQURE1. VERTICALSECTIOX that make the device more s u i t a b l e TEROUGH APPARATUS I
*
DESCRIPTION OF APPARATUS The illustration shows a vertical section through the apparatus which consists of three separate cylindrical sections. The top section (outside diameter, 9 inches or 22.9 cm.; maximum inside diameter, 4-/leinches or 11.3 em.) is loinches (25.4 cm.) long and closed a t the upper end by a heavy removable head held in place by eight 3/4-in~h (1.9-em.) studs. Guide pins from the cylinder wall to the head permit perfect realignment after each removal of the head. This upper section contains the field and armature of a 0.05-horsepower, 110-volt, 1750-r. p. m., a. c. induction motor. These parts were obtained by dismantling a motor, and removing the shaft and all auxiliary parts. The periphery of the field is turned to fit closely the bore of the chamber and pressed into place against a shoulder as shown. A shaft, "4 inch (1.9 cm.) maximum diameter tapering to 1/4 inch (0.6 cm.) a t the lower end, and 27 inches (68.6 em.) long is turned to fit the armature and pressed in place. The shaft is provided with a ball bearing in the u p per head, and with both a ball bearing and a thrust bearing a t the lower end of the chamber. The distance between bearings is 8 inches (20.3 cm.). These lower bearings are mounted in a short bronze cylinder p r e s s e d i n t o place. Sufficient l u b r i c a n t f o r p r o l o n g e d periods 3f operation can be packed
