The Adsorption of Vapors by Alumina. - Industrial & Engineering

Removal of sulfur dioxide from stack gases by a modified Claus process. Robert T. Struck , Metro D. Kulik , and Everett Gorin. Environmental Science ...
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I N D UXTRIAL A N D ENGINEERING CHElMIXTRY

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Results in this case give a composition very close to the theoretical for magnetite (Fe304, or FeO Fez03). I n general, the results also indicate that the preliminary treatment with copper sulfate and cyanide solutions to remove metallic iron and the precipitated copper has no appreciable effect upon the iron present in the sample as either ferric or ferrous oxide. Consistent and reasonable results have been obtained with the method in nearly all analyses, some of the results of analysis of samples of hematite ore in varying stages of reduction by carbon monoxide gas being given in Table v. I n amounts above about 1 per cent, the presence of ferrous sulfide causes high results for both metallic and ferrous iron. Copper sulfate solution tends to dissolve the ferrous sulfide slowly, so that part of the sulfide iron is titrated as metallic iron. This dissolving action of the copper sulfate is not complete, and part of the ferrous sulfide remains to be dissolved by the acid. In this solution hydrogen sulfide is

Vol. 17, No. 1

evolved, which reduces part of the ferric iron in solution. I n samples containing around 1.0 per cent sulfur or less, however, nearly all the sulfide iron will analyze as metallic iron and the ferrous iron will not be appreciably in error. . TABLEV Sample 1

Total iron Per cent 70.4

Metallic iron Per cent 1.4

Ferrous iron Per cent 28.0 27.9 35.3 3.5.2 37.3 37.5 9.9

2

72.1

9.7

3

72.6

10.0

4

75.1

33.7

5

66.2

5.9

12.7 12.9

6

so.0

39.8

8.0

9.8

The Adsorption of Vapors b y Alumina' By I,. A. Munrb and F. M. G. Johnson MCGILLUNIVERSITY, MONTREAL, CANADA

Air was aspirated a t a The adsorption of vapors by alumina has been investiconstant rate through a purson2that alumina, pregated by a dynamic method. ifying train, then through pared by heating the The adsorptive power of the alumina depends on its state the liquid with which it was hydroxide in an open vessel of hydration. The curves show that the adsorption may to be saturated, and finally over a smoky flame, was a be divided into three classes, one of which denotes catathrough a tube containing very efficient drying agent. lytic decomposition of the vapor. the adsorbent, all a t room Dover and Marden,3as well Alumina is a very good adsorbent for all the vapors intemperature (20' C.). The as Marden and E l l i ~ t t , ~ vestigated. It can be used for the recovery of gasoline, course of the adsorpti'on was have investigated the dryether, benzene, the alcohols, sulfur dioxide, and ammonia followed by weighing the ing power of alumina pregas. It is not, however, suitable for the recovery of such a l u m i n a and saturating pared in this way. They vapors as acetone, ethyl acetate, amyl acetate, various liquid a t intervals. The found that the aluminawas a alkyl halides, and acetyl chloride and bromide. gain in weight of the alumore efficient drying agent mina and the loss in weight than calcium c h l o r i d e , quicklime, or sulfuric acid. Phosphorus pentoxide was the of the liquid are expressed as cubic centimeters of vapor only desiccant of greater efficiency. Fisher, Faust, and a t standard temperature and pressure. Curves are obWaldenb used alumina in organic combustions, and ob- tained by plotting the volume of vapor supplied per gram tained the theoretical amount of hydrogen within 0.33 per of adsorbent against the volume of vapor adsorbed per cent. McIntosh, working in this laboratory, found on at- gram of adsorbent. These curves give a comparison of tempting to dry ammonia gas by alumina that the gas was the relative number of molecules of the different vapors adsorbed by it. I t therefore seemed probable that alumina adsorbed from air-vapor mixtures saturated at room temperawould be an adsorbent for other gases. Silica gel has already ture (20"C.). They also show the efficiency of the adsorbent been found to be a good adsorbent.6 The similarity of for each vapor under these conditions. These curves also alumina and silica gels suggested that the former would also give information as to the nature of the adsorption. be efficient in this respect. Preparation of Alumina This paper describes briefly the results obtained in a preI n the first experiments the alumina was prepared by heatliminary investigation on the adsorption of vapors by alumina, ing the pure hydroxide in an open vessel over a smoky flame. about thirty vapors having been studied. This method was soon discarded for a more definite one. General Procedure A U tube was filled with a known weight of the hydroxide in In an industrial application of alumina as an adsorbent, it the form of a fine powder. Small plugs of asbestos were used is probable that the process would involve adsorption from a to retain the alumina. The tube was placed in a bath of current of vapor-air mixture. For this reason a dynamic potassium and sodium nitrates a t 400" C. for 2 hours, while a t the same time dry air was drawn through the alumina. The method was chosen. resulting loss in weight gives the amount of water driven 1 Received May 28, 1924. off-i.e., the extent of dehydration. This is expressed as 2 J . A%. Chem. doc., 34,911 (1912). per cent of the initial weight. (Column 3, Table I) a I b i d . , 39, 1609 (1917). 4 THISJOURNAL, 7, 320 (1915). The total water content of the hydroxide was determined 8 I b i d . , 14, 1138 (1922). by blasting for several hours in a platinum crucible a t 8 McGavic and Patrick, J . A m . Chem. SOL, 42, 946 (1920); Miller, the highest temperature of the blast lamp. According to Chem. Mel. Eng., 28, 1155 (1920).

I

T WAS found by John-

I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y

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Walker,' a 3-hour ignition is sufficient for the complete dehydration of alumina. All samples were blasted for a t least 10 hours, however, for it was found that sometimes the sample had not reached constant weight after 3 hours' ignition. The water content of the hydroxide used was found to be 32.80 per cent. If one considers the composition of the hydroxide to be represented by the formula Al(OH)S, the theoretical amount of water is 34.6 per cent. If such a compound does exist, the discrepancy may be due t o a loss of water by it. Effect of Water C o n t e n t of Gel on Adsorptive Power

Dover and Marden3 give a table showing the adsorption of water vapor by alumina in different states of hydration. They consider that variation in the amount of water in the alumina has no effect on the amount of vapor adsorbed. Gel-

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20 40 60 80 100 120 140 160 Amount of vapor supplied in cc. per gram of adsorbent

FIG.I-ADSORPTION CURVESFOR

ETHER,USING ALUMINAIN

DIFFERENT HYDRATION, 1, ( a ) Alumina prepared by smoky flame ( 6 ) Alumina dehydrated 29.6 per cent-i. e. adsorbent contains 4.5 per cent water (c) Alumina dehydrated 27.6 per cent-i. e. adsorbent contains 7.2 per cent water 2, Alumina dehydrated 20.0 per cent-i. e. adsorbent contains 16.0 per cent water 3, Alumina dehydrated 18.0 per cent-i. e. adsorbent contains 18.1 per cent water 4, Alumina dehydrated 14.1 per cent-i. e. adsorbent contains 21.8 per cent water STATES OF

Curve

Curve Curve Curve

\

dard, working in this laboratory on the adsorption of ammonia gas by alumina, drew the same conclusions. This has been tested by measuring the adsorption of ethervaporbysamples of alumina having different amounts of combined water. The saturation values are given in Column 7 of Table I. Fig. 1 shows the, curves obtained. The broken line in all the curves is the line of complete adsorption. The curves follow this line when the alumina is 100 per cent efficient. TABLE I-EFFECT OF

a'ATER

CONTENT

ON SORBED

Per Initial Dehy- Weight cent weight dration of adwater Sam- of gel Per sorbent in add e Grams cent Grams sorbent Flame 10.93 8:jl 29.6 4:5 6.13 28.2 5.65 7.87 6.4 27.0 6.07 7.2 8.39 20.0 5.67 16.0 7.09 7.54 18.0 6.18 18.1 7.09 14.1 6.09 21.8

AMOUNTOF

ETHERVAPOR AD-

Amount

Weight adsorbed adin cc./ sorbed gram Grams adsorbent 1.5214 42.1 42.7 0.8645 0.7569 40.5 0,8600 42.9 0.5014 26.8 18.0 0.3678 0.3380 16.8

U . S. Dep!. A g r . , Circ 101, l(1912).

Silica gel behaves in the same way. McGavic and Patrick6 investigated the relation of water content and adsorptive power. They measured the adsorption of sulfur dioxide by gels containing 2.31, 3.51, 4.86, and 7.97 per cent water. The maximum adsorption was obtained with gels containing 4.86 and 9.97 per cent water. Miller6 found that a gel having from 5 to 7 per cent water gave the best results. McGavic and Patrick explain these optimum conditions by supposing that further dehydration increases the diameters of the pores in the gel. The capillary forces are therefore diminished and a smaller amount of the liquid is taken up. On the other hand, the presence of more than 8 per cent of water means the filling of the smaller capillaries by water. This reduces the surface and capillary volume available for the gas, and therefore the amount adsorbed is less. It is possible that the decrease in adsorptive power with increasing water content of the gel is due primarily to the saturation of the residual valence fields by the water. The amount of "active" A I 2 0 3 is thereby decreased and the amount of vapor adsorbed per gram of gel is less. If such is the case, gels differing in water content should give approximately the same curves when the amounts adsorbed and supplied are expressed in cubic centimeters per gram of active A1203 and not as cubic centimeters per gram of adsorbent ( & 0 3 , z HzO). The calculated amounts of active A1203 and the amount of vapor adsorbed per gram of active A1203 are given in the last two columns of Table I. EXAMPLE-sampk of alumina was obtained by heating the hydroxide until it had lost 2.58 grams of water-that is, 29.6 per cent of its initial weight. In this particular case the weight of the adsorbent prepared thus was 6.13 grams, the weight of the hydroxide being. 8.71 a-ams. This samnle of adsorbent took UD 0:8645 gram of-ether Gapor. This weight of ether is equivalerk

::::45 cc. of vapor (0' C., 760 mm.) per gram of adsorbent = 42.7. The total water content of the hydroxide had been found to be 32.8 per cent. The remaining 67.2 per cent we shall consider as being A1208 molecules. Hence we shall say that 32.8 grams of water are associated with 67.2 grams of active A1208. So 29.6 per 67.2 X 29.6 X 8.71 cent of 8.71 grams will be associated with 100 X 32.8 5.28 grams. That is, 5.28 grams of active A1203 have been obtained by removing the water molecules which had satisfied the external fields of these AllOs molecules. Cc. of vapor adsorbed per gram of active A1208 is 22400 X 0.8645= 49.6 74 X 5.28 t o 224;:

ACTIVEA u 0 3 Amount adsorbed cc./ Grams gram 5:28 4.54 4.74 2.91 2.77 2.05

4916

50.5 55.0 52.2 40.2 50.0

It will be seen that samples of alumina which have been dehydrated from 27.6 to 29.6 per cent adsorb the same amount of ether per gram of adsorbent; that is, adsorbents which contain from 4.5 to 7.2 per cent of combined water have the same adsorptive power. If the water present exceeds 7.2 per cent the amount of ether taken up is much smaller and decreases with increasing water content of the adsorbent. That this behavior is not confined to ether is shown by the curves for ethyl iodide. (Fig. 11) Heating the alumina over a smoky flame evidently produces at least 27.6 per cent dehydration, for the curve obtained by using alumina prepared in this manner reaches the same saturation value as the curves for 29.6 and 27.6 per cent dehydration. 7

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20 40 60 80 100 120 140 160 Amount of vapor supplied in cc. per gram of active AlzOa F t G . 2-ADSORPTION C U R V E S FOR ETHER, USING ALUMINA OF DIBFERENT WATERCONTENT AS IN FIG 1. HERRTHE ADSORPTION Is EXPRESSED IN C C . PER GRAMOF ACTIVE A12 .08 CALCULATED FROM THE DEHYDRATION VALUES

Fig. 2 shows the curves for ether expressed in this way. It will be seen that they approximate one curve. The deviations are due, no doubt, to some such effect as McGavic and Patrick suggest. The curve obtained with alumina dehydrated 18 per cent varies so widely from the other curves in both Figs. 1 and 2 that there is probably some error in the determination. I n order that this investigation may be readily compared

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with work on silica gel, the results will be expressed as cubic centimeters of vapor per gram of adsorbent. A few typical examples of adsorption by alumina may be considered in detail. Carbon Dioxide from t h e Air The marked adsorption of carbon dioxide from the air is shown in Fig. 3. A U tube containing freshly prepared alumina was placed in series with vessels containing potas-

Vol. 17, No. 1

Acetic Acid Glacial acetic acid is adsorbed completely until the alumina has taken up 15 per cent of its weight. The adsorption continues until the weight of the adsorbent has increased 25 per cent. It will be seen from the curve (Fig. 4) that the efficiency of the alumina as an adsorbent for acetic acid decreases very rapidly after it has adsorbed 15 per cent of

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FIQ.3-ADSORPTION OF C A R B O N DIOXIDEF R O M AIR Curve 1, Alumina tube in series with containers of KOH, HaSO4, P n O c i. e., air adsorbed. Curve 2, KOH bulbs removed. CO: adsorbed

sium hydroxide, sulfuric acid, and phosphorus pentoxide, respectively. Curve 1 shows the adsorption of pure air. The potassium hydroxide bulb was then removed and the weight of the alumina was found to increase (Curve 2). This shows the adsorption of carbon dioxide. Water

An examination of the curves for all the vapors studied will show that water (Figs. 4 and 5 ) exceeds all other vapors in the magnitude of adsorption. It is adsorbed with 100 per cent efficiency until the alumina has taken up 18 per cent of its own weight. The curve then falls away gradually from the total adsorption line, until finally, when saturation is reached, it has adsorbed an amount equal to 23 per cent of its weight. Acetone The curve for acetone (Fig. 4) shows a great similarity to the curve for water. Adsorption continued until the alumina

100 200 300 400 Amount of vapor supplied in mg. per gram of adsorbent FIQ.&-CURVE (1) GASOLINE;(2) BENZENE; (3) WATER

had become a paste. This might be due to the presence of a trace of water as an impurity in the acetone. The water would be “sorbed” by the alumina and the acetone would dissolve in this water. When the experiment was stopped the alumina had increased 60 per cent in weight.

100 200 300 Amount of vapor supplied in cc. per gram of adsorbent FIG. 4 - c U R V E (1) W A T E R ; (2) ACETONE;(3) ACETIC ACID

its own weight. Beyond this point the amount of vapor unadsorbed, which is represented by the distance between the curve and the total adsorption line, is greatly increased. This fact shows that knowledge of the change in efficiency of the adsorbent would be of importance in any application of adsorption to industry. Gasoline Fig. 5, Curve 1, shows the adsorption of gasoline by alumina. Here the amounts supplied and adsorbed are expressed in milligrams per gram of alumina. Total adsorption is never obtained; t h a t is, the alumina is a t no time 100 per cent efficient. Silica gel acts in the same manner. It will be seen, however, that alumina is a good adsorbent for gasoline vapors, the saturation value being 13.5 grams of gasoline per 100 grams of adsorbent. The specific gravity of the gasoline used was 0.741. The volume of liquid adsorbed is therefore 18.3 cc. per 100 grams of alumina. Gasolines vary so much in their relative constituents that this figure cannot be considered an absolute value.

FIG.

Amount of vapor supplied in cc. per gram of adsorbent ( 1 ) BENZENE; (2) ETHER;(3) ETHYLA W ~ A T B ; (4) AMYLACETATE

6-cURVE

Benzene The curves for water and benzene are aIso given in Fig. 5 in order t h a t the adsorption of gasoline may be compared with that of homogeneous vapors. Benzene, like gmoline, is never completely adsorbed from the vapor-air mixture.

I N D UXTRIAL A N D ENGINEERING CHEMISTRY

January, 1925

The efficiency of the alumina a t the first point on the curve was 91 per cent. The saturated adsorbent contains about 16 per cent benzene, by weight. The adsorption of benzene in cubic centimeters of vapor per gram of adsorbent is shown in Fig. 6.

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20 40 60 80 100 120 Amount of vapor supplied in cc. per gram of adsorbent FIG.7--cURVE (1) PROPYL ALCOHOL;(2) ETHYLALCOHOL;(3) METHYL (5) AMYLALCOHOL ALCOHOL:(4) ALLYLALCOI~OL;

91

is 100 per cent efficient until it is within about 40 per cent of saturation. The curves then proceed almost in a straight line, saturation being slowly reached. In the case of sulfur dioxide and ammonia gas the curves follow the complete adsorption line until the gel has become saturated. This is seen in the results of duplicate determinations for the adsorption of pure ammonia gas, given graphically in Fig. 8. The first part of the curves in this class-i. e., where the adsorbent is 100 per cent efficient-probably represents what Langmuir calls “primary adsorption.” The second part of the curve-i. e., the gradual falling-away to zero efficiencyno doubt represents “secondary adsorption,” capillary condensation, and diffusion into the alumina. In those cases in which the break in the curve is very sharp, it is probable that these latter phenomena are absent. Such curves point to surface condensation alone. When the entering gas is diluted with air the break is not so sharp. (Fig. 8) This is probably 8.

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Allyl Iodide

The curve for allyl iodide is given in Fig. 10. It will be seen that the amount adsorbed is never equal to the amount supplied, but bears a definite relation to it. When the alumina has increased 30.4 per cent in weight, the adsorption ceases abruptly. Other alkyl derivatives have been found to give similar curves. The significance of these curves will be discussed later. As the adsorption proceeded the alumina became discolored. Other Vapors

The curves for the other vapors are given in the succeeding figures. These are self-explanatory and need not be considered in detail. Types of Curves

A general survey of the adsorption curves shows that they may be divided into three classes. TYPEI-The first class includes those that fall away from the complete adsorption line immediately, and continue to do so until saturation is reached. I n this class the efficiency of the alumina is never 100 per cent, and it decreases continuously. The curves for ether, ethyl alcohol, gasoline, amyl acetate, methyl alcohol, benzene, as well as acetyl chloride and acetyl bromide, belong to this type.

I

20 40 60 80 Amount of cas SUDDkd in cc. Der of adsorbent - Itram -GAS FIG.~ - C U R V (1) E SULFUR DIOXIDE 100 PER CENT; (2) AMMONIA 100 PER CBKP; (3) AMMONIA 37.9 PER CENT; (4) AMMONIA 10.6 PER CENT; AIR 89.4 PER CENT

-

TYPE11-This type of curve is found in Figs. 4,7, and 8. This type follows the complete adsorption line for some distance. In the case of water and acetic acid the adsorbent

Amount of vapor supplied in cc. per gram of adsorbent

FIG.9-CURVX (1) ACETYLENE DICHLORIDE(CHCL: CHCL); (2) CHLOROFORM (CHCLI); (3) ETHYLIDENE CHLORIDE(CHaCHCb) ; (4) CARBON TETRACHLORIDE (CCL~)

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20 40 60 80 100 120 140 Amount of vapor supplied in cc. per gram of adsorbent FIG. 1&cURVE (1) ACETYLCRLORIDE; (2) ACETYLBROMIDE;(3) ALLYL BROMIDE;(4) ALLYLIODIDB

due to the adsorption of air. Nitrogen and oxygen are not held very tenaciously and are soon replaced by the gas of higher boiling point. During the temporary adKorption of the air the vapor molecules cannot use these residual valences, so they pass on. This means that the curve falls away from the complete adsorption line sooner than it otherwise would, and saturation is reached by a smooth curve. TYPE111-Figs. 9, 10, 11, and 12 contain examples of the third and most interesting type of adsorption curves. In this class of curve the adsorption is never 100 per cent efficient. The curves proceed in a straight line with a definite slope until saturation is nearly or completely attained. This a t once suggests a chemical reaction. If a molecule is broken and a definite part of it is adsorbed, the ratio of amount adsorbed to amount supplied will be constant, and the curve obtained will be a straight line of a definite slope. Since the rate a t which the vapor was admitted was slow enough to admit of complete adsorption, it is difficult to see any other explanation than that of chemical reaction.

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The curves of Type 111, then, are obtained when decomposition catalysis accompanies adsorption. It is well known that alumina acts as a catalyst in the decomposition of various alkyl halides. Such reactions, however, have previously been noted only a t fairly high temperatures (250' to 400" (2%). Adkins and Nissens used a temperature of 465" C. for the decomposition of ethyl bromide by alumina.

passage through the tube of alumina. If the number of molecules unaffected is relatively large, a curve of Type I is obtained. It cannot be said, however, that curves of Type I represent catalytic action. The initial parts of the curves for methyl acetate and allyl alcohol approximate straight lines, and are included in Type 111. They have not been investigated further.

20 40 60 80 100 Volume of vapor supplied in cc per gram of adsorbent FIG 11-CURVE (1) METHYL IODIDE; (2) ETHYL IODIDE (ALUMINA DEHYDRATED 27 7 PER CENT); (3) ETHYLIODIDE (ALUMINAD~JHYDRATRD FIG. 12-INITIAL 21 8 PER CENT); (4) BUTYRYL CHLORIDE;(5) ISOBUTYLCHLORIDE

This low-temperature decomposition has been investigated in the case of methyl iodide. Air saturated with the vapor of this compound was aspirated through alumina, then through a worm cooled by carbon dioxide snow and ether, and finally through bromine water or potassium permanganate solution. The decoloration of these reagents showed the presence of an unsaturated linkage in the effluent gas. Fig. 12 shows the initial part of the adsorption curve for methyl iodide as given by three determinations. By taking a distance along the abscissa equivalent to the molecular weight of methyl iodide (142), the ordinate will correspond to the molecular weight of hydrogen iodide (128). Alumina, which was used as an adsorbent in this case, gave a colored solution when shaken up with water. This solution gave an intense blue when tested with starch. TABLE11-SATURATION

VALUES O F VARIOUS VAPORS

VAPOR Acetone ~~~. Acetic acid Acetylene dichloride Acetyl bromide Acetyl chloride Allyl alcohol Allyl iodide Allvl bromide Ammonia Amyl acetate Amyl alcohol Benzene Isobutyl chloride (22' C Butyryl chloride Chloroform Carbon tetrachloride Ether Ethyl acetate Ethyl alcohol Ethylidene chloride ( 2 2 . O Ethyl iodide Gasoline Methyl alcohol Methyl iodide Propyl alcohol Sulfur dioxide Water ~

~~

~

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Grams vapor per 100 grams adsorbent 60. 25.4 24.3 33.2 23.7 14.8 30.4 26.0 ~

2.7

19.0 13.9 15.7 18.2 27.4 25.1 30.8 14.0 15.6 12.9 20.3 32.3 13.3 10.7 42.7 17.8 16.8 23.

Cc. vapor per gram adsorbent 230. 94.4 56.0 60.5 67.6 57.3 40.5 4x.n

ii x

32.8 35.2 45.0 44.0

57.7

46.9 45.0 42.5 39.8 63.0 46.0 46.3

74:i

67.9 66.8 58.7 285.

In the case of ethyl iodide, the curve is displaced somewhat from the theoretical line of complete decomposition. This can be explained by the assumption that a number of molecules are neither adsorbed nor decomposed in their 8

J . A m . Chem. Soc., 46, 130 (1924).

Vol. 17, No. 1

1 .o 1.5 2.0 Grams of vapor supplied PARTS OF ADSORPTION CURVES POR (1) METHYLIODIDE AND (2) ETHYL IODIDE 0.5

The question of the catalytic decomposition of these various vapors by alumina a t room temperature is an interesting one. The authors intend to investigate this later. From this paper, however, it will be seen that in many cases any catalytic activity of the adsorbent can be detected by a consideration of the adsorption curves obtained by a dynamic method. The saturation values for the twenty-seven vapors examined are given in Table 11. These are expressed in grams per 100 grams of adsorbent and as cubic centimeters of vapor per gram of adsorbent; Recovery

Adsorbed vapors, such as gasoline, benzene, ether, alcohols, ammonia, and sulfur dioxide, can be easily recovered by raising the temperature of the alumina a few degrees above the boiling point of the vapor and at the same time passing air through the adsorbent. It has been noted above that alumina adsorbs considerable quantities of these liquids, and it is therefore a good reagent for the recovery of these vapors. Although an excellent adsorbent for acetone, alumina is not suited for the recovery of this solvent. On attempting to remove the acetone by air a t 100" C., the alumina became a russet color. A deep-amber colored liquid came over. This is obviously another case of catalysis. A number of products are formed, probably xylite naphtha, mesityl oxide, mesitylene, etc. I t is obvious that alumina cannot be used for the recovery of those vapors that are decomposed in contact with it. It is found, moreover, that alumina is not a suitable reagent for the recovery of acetyl bromide or acetyl chloride. Ethyl acetate and amyl acetate are also removed from the alumina with difficulty. An apparatus has been constructed by which accurate measurements of adsorption can be made using a dynamic method. The authors are investigating the adsorption of vapors over a wide range of temperature and concentration. Acknowledgment

This investigation was carried out under tenure of a bursary from the Advisory Research Council of Canada, which is hereby gratefully acknowledged.