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Boleslaw Ludwik Dunks' The Kosciuszko Foundation New York City
Surfme Area of Activated Charcoal by Langmuir Adsorption Isotherm
The study of the Langmuir adsorption isotherm of acetic acid by activated charcoal, offered in a basic physical chemistry course, involves plotting the relevant dat,a and finding the corresponding constants. The purpose of this paper is to suggest an interpretation of the experimental data to make the exercise more meaningful for the student. This is the estimation of the specific adsorption area of charcoal. For the adsorption of acid from its aqueous solution, the Langmuir isotherm can he expressed as:
+ bC
C/X = a
(1)
conccntratim ol xcctic acid solution, in inoles/liter, which is in dynamic oquilibrium with acctic acid adsorbed on the charcoal, X = number of moles of acetic acid adsorbed by one gram of charcoal, when the solution in contact with it has the equilibrium concentration C; the units of X are moles/g, where g = gram of dry charcoal, a = constant; its units are the same as those of C/X, b = constant; its units are g/male. C
activit,y of 0.1, is iudependeut of molecular weight but related to the absolute activity. Hence it may be assumcd that molecules of such acids, on the charcoal surface, would be oriented vertically in closely packed
=
Figure 1 shows a plot of X with respect to C, for room temperature, with "Norit A" charcoal used as an adsorbent. The experimental techniques were similar to those outlined in various physical chemistry laboratory manuals (1). Figure 2 shows a plot of C / X values with rcsprxt to C. The straight line, drawn according to the linear rcgression method, fits the data. Hence it can be inferred that the acetic acid molecules, within t,he indicated concentration range, form a monomolecular layer on the surface of charcoal. The constants a and b of the Langmuir isotherm represent the intercept and the slope respectively, of the line drawn in Figure 2. The isotherm implies that as the values of C become larger, the contribution of the constant a to the value of C / X becomes negligibly small. Thus: lim C/X
=
bC
(2)
Cancellation of C terms, and taking the recriprocal of equation (2), gives
am x = x,,,
=
~/b
(3)
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" l ~ - ' r n o l e ~ / lC i,~~
3
Figure 1. Number of moles of acetic acid adsorbed by one gram of "Norit A oaivoted charcoal with respect to the equilibrium concentrotion of aqueous acetic acid solution, at-room temperature.
monomolecular lay$rs. . The cross-section of the acids is known to be 21 A* (5). The foregoing information, and the experimentally determined constant b of the Langrnuir isotherm, permits then an estimation of the specific area, S: S = (l/b) x N x 21 x 10- meters)' (4) where N stands for the Avogadro number. Example: The reciprocal of thcslopc of the plot in Figure 2 is l/b
=
AC/A(C/X) = 5.33 X 10-Smolo/g
Hence : x 6.023 x 1023 (molecules/male) x 21 X (mP/molecule) = 6.74 x 10' m2/g
S = 5.33 X lo-' (molmlg)
-.
C X 4 --
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lkter
110
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90 -
70 -
The X,,, denotes the maximum capacity, in moles of acetic acid, which can be held by one gram of charcoal as a monomolecular layer. According to Hansen and Craig ($), the adsorption by nonporous carbons of various aliphatic normal monocarboxylic acids from their aqueous solutions, up to an Present address, U. S. Naval Radiological Defense Labor* tory, San Francisco 24, California.
2
1
Figure 2.
2
3
xlo~'maler/lit.r C
The Longmuir isotherm of acetic odd adsorbed on "Norit A,"
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The above result is in close agreement with the mean surface area of 708 m v g of the activated charcoal distributed by the Fisher Scientific Company. Brunauer, Emmett, and Teller (4) derived this number from adsorption studies with nitrogen and other gases, using the molecular cross-sectional areas calculated from the solid state. The value checks also very well with the figures of the American Norit Company, Inc., which reports that the total internal surface of Norti A (according to B.E.T. method, calculated from the benzene adsorption isotherm a t 20°C) usually runs between 600-700 m2/g dry carbon. In addition, the information contained in the work of Hansen and Craig (2) discloses that measurement of the charcoal surface area might offer a potential approach to estimat,e certain dimensions of different substances, providing certain limitations to the activity are observed. Thus the purpose of the experiment might he extended to measure the dimensions of various water-soluble substances, such as oxalic, boric, arsenic, picric, or salicylic acid, to mention but a few. Acetic acid could then be used as a convenient reference material, since it is readily available and easily handled, and its molecular crosssection is known. If thc Langmuir isotherm holds, the
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equation for finding the dimension, I), of nnot.her suhstance, using acetic acid as reference, is:
where ba and bD are the relevant constants (in g/mole) of the Langmuir isotherm, determined under identical experimental conditions, for the acetic acid and anot,her substance, respectively. Literature Cited (1) T,~VINGSTON, ROBERT,"Phy~icoChwnicd Experiments," 3rd ed., The Macmillan Co., New York, 1957, pp. 257-9; I)ANIEI.S, FARRINGTON, ET AL., "Experimental Physical Chemistry," 5th cd., McGraw-Hill Book Co., New York, 1956. OD. 226-7: and STEINBACA.0'M'o F.. AND ICING.
211 (1954). (3) RUTGER~, A. G., "Physical Chemistry," Interscience PubWALTER J.. lishers, Inc., New York, 1954, p. 27; MOORE,
"Physical Chemistry," 2nd cd., Prentice-Hall, Inc., EngleSAMUEL, wood Clifls, N. J., 1955, p. 510; and GLASSTONE, "Tho Elements of Phgsicd Chemistry," D. Van h'ostrand Co., Ine., New Yark, 1946, p. 556. (4) BRIINAUER, S., ET AL., J . Am. Chern. Sor., 60, 309 (1938).
