AN IMPROVED METHOD FOR THE DETERMINATION OF 1SOTHER.MALS BY THE RETENTIVITY TECHNIQUE L. J. BURRAGE King’s College, London, England Received October 18, 1991 INTRODUCTION
In a previous publication (1) a new method for the determination of sorption isothermals of vapors on charcoal was described; the present paper records a development of this method whereby the accuracy is greatly increased and the technique simplified. No experimental details are given, as these were described fully in the previous papers (1, 2). This method consisted in the conversion of the approximate isothermals obtained under the retentivity test conditions into true isothermals. Briefly, this was achieved by carrying out a number of determinations employing columns of charcoal of different lengths and plotting the logarithm of the weight of vapor retained against the logarithm of the volume of charcoal for a constant volume of air passed, and then extrapolating the weight figures to 1 cc. to get rid of the “pressure-length effect.” The tangents drawn to the retentivity curve obtained from these extrapolated data gave rise to the true isothermal, At the time of publication it was realized that this method would not apply to an isothermal of the water type on or above that portion where the quantity of substance sorbed increases rapidly for a small increase of pressure, and an attempt was made to make it hold good under all conditions. As this technique seemed to allow of an extremely detailed examination being made of the structure of the isothermal, an experiment was carried out on a single column of charcoal of about 10 CC. volume, charged with water vapor, the flow of air being interrupted a t very frequent intervals. By this means it was hoped to anchor the retentivity curve exactly over its entire range, and then by drawing an extremely large number of tangents, the detailed isothermal structure would be obtained. The result of this experiment was characterized by one very striking fact; the retentivity curve was found to consist of a series of straight lines intersecting one another a t definite points (e.g., figure 1, which represents the retentivity curve of a water isothermal on Charcoal K 2 a t 15°C. Charcoal K2 was a peat charcoal activated with phosphoric acid; apparent density = 0.312). The resultant isothermal (figure 2, dotted lines) does not 33
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L. J. BURRAGE
consist of a series of rounded loops as had been obtained heretofore; the breaks are all sharply rectangular. It was found that with isothermals on silica gel, as had been previously discovered in the case of charcoal, there are no breaks below 0.1 mm., the isothermal consisting of a smooth curve (3). This rectangular structure makes it possible for an improved method for the determination of adsorption isothermals to be put forward which will hold good under all conditions using but a single column of charcoal. If one charges the charcoal column a t a vapor pressure which is intermediate between two horizontal portions of the isothermal, then on desorption a linear section will result on the retentivity curve, and a t a definite quantity value this line will be intersected by another. Now the straight 1,t.t.
200
FIQ.1
lines correspond to constant pressures over the quantity ranges indicated and will give rise to two horizontal sections on the isothermal. Only the second of these corresponds to a true step, however, for the first is inherent in the experimental procedure, since it is caused by the formation of the gradient inside the column. Reference to a previous publication (1) will show clearly how this occurs. Owing to this gradient the average quantity of vapor in the column expressed as milligrams per gram is smaller than corresponds to the pressure over the end of the column. The error which this gradient introduces in the quantity value steadily diminishes until a t a very small quantity figure it is zero, the average quantity in the column and the quantity corresponding to the pressure over the end of the column being identical.
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DETERMINATION OF ISOTHERMALS
The improved technique is essentially as follows: (a) The pressure is calculated from the slope of the linear sections of the retentivity curve, the difference in the quantity values giving the amount of substance which has been carried away in a certain volume of air (the difference of the corresponding volume figures). (b) The quantity values are calculated thus: The amount of substance held at zero pressure is subtracted from the quantity figures for all retentivity curve breaks. These are “corrected” quantity values. The ratio of the corrected saturation figure to the corrected quantity figure at the first retentivity break is calculated. The corrected quantity values for each break are then multiplied by this ratio and the amount held at zero pressure added, whereby the true quantity for each break is obt’ained, resulting in a true isothermal. TABLE 1 (1)
(2)
542.8 488.0 390.3 284.5 186.1 80.4 35.7 29.0 26.3 23.6
519.2 464.4 366.7 260.9 162.5 56.8 12.1 5.4 2.7 0.0
(3)
(4)
-
-
519.2 410.1 291.8 181.7 63.5 13.5 6.0 3.0 0.0
542.8 433.7 315.4 205.3 87.1 37.1 29.6 26.6 23.6
A criticism may be advanced in the case where the initial charging pressure coincided with that at which a step occurred, in which case it would appear that the linear section on the retentivity curve due to the formation of the gradient and that due to the first step would be continuous, thus preventing a calculation of the true isothermal. It has been shown, however, by sorbing from an air stream charged to a definite pressure with vapor, that one must charge at a distinctly higher pressure value to pass along the horizontal portion of a step. This being so it is perfectly valid to use this new method, since the sorption point will not pass along the horizontal step but will remain on the vertical portion joining this step with the one below. In table 1the method of operation is shown in full. The vertical columns have the following significance: (1) quantity values at the retentivity curve breaks; (2) the corrected quantity figures; (3) the figures in the previous column multiplied by the ratio of the corrected saturation figure to the corrected quantity figure at the first retentivity break; (4)the latter
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L. J. BURRAGE
+
column the amount held at zero pressure, all figures being expressed as milligrams per gram. The quantity held a t zero pressure is 23.6 mg. per gram. The isothermal in figure 2 has been converted to a true isothermal (continuous lines) in this manner, the individual points being omitted. The
TABLE 2 PRESSURE OF BREAK
QUANTITY RANGE OF STEP
DIFFERENCE
mnL.
mg./gram
mg./gram
11.53 8.60 7.35 6.61 5.80 4.58 2.35 1.55 0.25
542.8-433.7 433.7-315.4 315.4-205.3 205.3- 87.1 87.1- 37.1 37.1- 29.6 29.6- 26.6 26.6- 23.6
-
-
109.1 118.3 110.1 118.2 50.0 7.5 3.0 3.0
NUMBER OF EXPERI. H l N T A L POINTS
10 8 6 9 8 6 5 4 3
figures for the pressure and quantity range of each step and the number of experimental points on that step are given in table 2. EXPERIMENTAL
Desorption experiments in a n air stream charged with vapor at definite pressures To verify the rectangular structure of adsorption isothermals and also t o justify this new procedure, desorption experiments were carried out using an air stream charged to definite pressures with vapor, the points
DETERMINATION OF ISOTHERMALS
37
obtained being checked against the isothermals obtained by the improved retentivity method. Such experiments have been carried out with water and carbon tetrachloride on charcoal and on silica gel.
*I
FIQ.3
Fra. 4
The crosses represent such desorption points and the circles mark the ends of the steps (the individual points being omitted) in the isothermals derived by the modified retentivity technique. The results shown in figure 3, representing water isothermals on coconut charcoals at 15°C. (Fl, steam activated; apparent density 0.534: D1, steam activated (4))
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give definite evidence of this rectangular structure when dealing with the desorption points alone (crosses). In figure 4 are shown isothermals of carbon tetrachloride and water on silica gel. In every case there is close agreement between the desorption points and the isothermals derived by the improved technique. Figures are quoted in table 3 which show the variation in quantity values obtained by the two methods. TABLE 3 QUANTITY ADSORBENT
ADSORBATE
Charcoal D1
Silica gel
Silica gel
TEMPERATURE
PRESSURE
25°C.
cc14
Desorption points
Improved
retentivity method
mm.
mg./gram
mg./gram
11.3 11 .o 10.6 10.3 9.8 9.1 8.4 8.1 7.0
295.1 295,l 277.6 276.8 276.8 270.0 262.4 262.4 232.9
295.1 295.1 275.7 275.7 275.7 260,3 260.3 260.3 230.8
25°C.
8.4 0.9 0.15 0.10
175.8 92.9 48.3 43.0
182 .O 89.0 48.3 43.0
20.5"C.
6.70 6.10 5.60 4.60
175.0 159.5 147.2 130.3
175.0 159.8 146.7 130.4
DISCUSSION
It has been found (1) that the agreement is good between isothermals obtained by the static technique (air absent) and by the retentivity method, the chief difference being the speed of attainment of equilibrium. In the case of desorption isothermals, using the static technique, the vapor has to diffuse away and this is hindered markedly by the presence of foreign molecules (such as carbon dioxide) on the surface, whereas, in the presence of air, the vapor molecules are removed continuously by the moving stream, together with foreign molecules, the latter method, therefore, causing a quicker cleaning-up and thus a more rapid attainment of equilibrium. In the case of water desorption isothermals, when desorbing to constant pressure, it is necessary to lower the vapor pressure below that a t which a
DETERMINATION OF ISOTHERMALS
39
step occurs before the water comprising that step can be removed, hence the pressure at which a step occurs is lower than it would be if all disturbing factors were absent. I n the present technique this cannot occur, as one is actually dealing with the quantity adsorbed in an infinitely small layer a t the end of the charcoal column, and the pressure over this falls with sudden jumps from one step to another, hence there is no tendency for false equilibria to occur, the pressure drop being sufficiently large to allow all the water sorbed on that step to escape. This aspect will be treated more fully in a future publication on water hysteresis. The results which have been obtained fully justify this improved technique which is considered to be distinctly in advance of other methods in accuracy and has the additional advantage of being rapid, while giving the exact form of the isothermal over its whole range. SUMMARY
An improved technique for the determination of isothermals has been described. The derived isothermals have been found to consist of a series of rectangular steps. Comparison has been made with points obtained by desorbing to constant pressure. The author desires to thank Prof. A. J. Allmand for the interest he has taken in this work. REFERENCES (1) BURRAGE: J. Phys. Chem. 34, 2202 (1930). (2) ALLMAND AND BURRAGE: J. SOC.Chem. Ind. 47,3721' (1928). (3) ALLMAND, BURRAGE, AND CHAPLIN: Trans. Faraday SOC. 28,218 (1932). (4) ALLMAND AND BURRAQE: Proc. Roy. SOC.London 130, 610 (1931).
