ON T H E ADSORPTIOX O F GASES BY SOLIDS BY ASHUTOSH GANGC‘LI
The intimate connection of adsorption with surface tension was shown long before by Gibbs, subsequently known as Gibbs-Thomson equation. This equation is generally derived from thermodynamical considerations, which also leads to the following extension of the gas laws’ to the surface, TR = RT (1) Where x is the difference of surface-tensions of the pure solvent and solution and R corresponds to the area usually covered by the adsorbed substance. R and T are well-known symbols. Later on Langmuir2 has derived the following interesting relationship between the concentration of the adsorbed substance and the amount adsorbed from purely kinetic theory:
where C is the concentration, k = constant (Langmuir’s constant), 1 = amount adsorbed, being equal to r/R, /3 = another constant. Recently Volmer3 has tried to combine the thermodynamical derivation of Gibbs-Thomson formula with modified equation of state for the surface ~ (-2/3) = R T (3) which is readily obtained from kinetic theory by introducing corrections similar to that of van der Waals. Thus he claims to have arrived at a general formula
which, by neglecting pz reduces to
similar to that of Langmuir if z p is substituted for p. Later on K. C. K a 9 has derived Langmuir’s formula by purely statistical methods and has obtained an interesting formula for the Langmuir constant
where a, R, h, N and T have their usual significance, M is the molecular weight in grams of the adsorbed substance, a is the adsorption potential. Very recently Kar and Ganguli5 have also arrived a t the same Langmuir’s Freundlich: “Capillary and Colloid Chemistry,” 46 (1926). Met. Chem. Eng., 15, 469 (1916); J. Am. Chem SOC.,38, 2221 (1916); 39,1848 (1917). Z.physik. Chem., 115, 253 (1925). * Physik Z.. 26,615 (1925). 6 Physik. Z., (Commummted for publication) 1
3
666
ASIIUTOSH GANGCLI
formula by applying the statistical method of Gibbs. Their value of k is however more general, as ( 2 n ~ ~ e~ -or/RT ~ ) + k = (7) p s p being a constant, and the other symbols having the same meaning as in (6). If we consider the thickness of the adsorption layer to be unimolecular then p in (7) will have’the minimum value h. Thus the value of k becomes
identical with that of S. C. Kar. Now, the adsorption potential cy may be identified with the heat of adsorption. Again, if instead of considering the thickness of the adsorption layer to be multimolecular, we take it as unimolecularJ6then the adsorption potential becomes identical with the maximum value of the potential of Polanyi.’ Incidentally it may be remarked that Lowry and Olmstead* have also suggested that the heat of adsorption = Z:EAX where x = mass adsorbed. E = adsorption potential (as defined by Polanyi) Ax = mass adsorbed; thus for maximum adsorption (which is expected a t the equilibrium stage) the heat of adsorption corresponds to the maximum adsorption potential. The accompanling table taken from the previous paper of Kar and Ganguli5 point out clearly that the heat of adsorption in several cases approximates to Polanyi’s maximum potential as determined by Berenyig from the data of standard authors. TABLE
Gas
Argon Nitrogen Carbon monoxide Carbon dioxide Ammonia Methane Ethylene
I
Heat of Heat of Adsorption Sublimation in Cal. in Cal. 3,636 4,180
Maximum Adsorption Potential in Cal. 4,100 (Homfray)
3,71 j 6,100
6,100
7,200
7,120
7,180 (H), 8,600 (Patrick)
-
4,320
(H), 44.50 (Titoff)
3,686 3,416 7,300
-
-
3,840 (H)
(H), j,.joo (Richardson)
5J3’O 7,100
(HI
It will also be noted that the above table shows a remarkable agreement between the heat of adsorption and heat of sublimation. This agreement if it is true for all cases of adsorption, is certainly of fundamental importance, for it throws a considerable light on the mechanism of adsorption. It has been remarked by several authors that the adsorbed substance is present in a very condensed form on the surface.l0 According to Langmuir* the adsorbed 6Langmulr: loc. cit. 2, Harkins and collaborators: J. Am. Chem SOC., 39, 3j , 3 4 ~ et seq.; also Adam: Proc. Roy. Soc., 9QA, 344, 350 et seq.; also Freundlich: “&apil(1917) lary and Colloid Chemistry,” 314 (1926). Ber. deutsch. physik. Ges., 16, 1012 (1914); 18, 55 (1916), 2. Elektrochemie, 26, 370 (1920). * J. Phys. Chem , 31, 1601 (1927). 2. physik. Chem , 94, 62j (1920). ’OEucken: Ber. deutsch. physik. Ges., 16, 3 5 (1914);Freundlich: “Capillary and eh!.( Soc., 42,946 (1920). Colloid Chemistry,” 3zj (1926);Patrick: J. Am.m
66 7
ADSORPTION O F GASES BY SOLIDS
molecules are held on the surface by the residual valencies of the adsorbent. Since the adsorption potential is equal to the heat of sublimation, i t can be very well supposed that adsorption is essentially a process of condensation on the surface, the adsorbed substance being present as a layer of solid at the interface of the adsorbent forming adsorption compounds, somewhat similar to the solid solution but much more complex in nature. That we are justified in regarding adsorption layer as unimolecular in most cases, and that the heat of adsorption is equal to Polanyi's maximum potential on the one hand and the heat of sublimation on the other is also confirmed by the agreement of the theoretical value of k with that calculated from the experimental data of various standard authors as given in Table 11.
TABLE I1 GS
Temp.
"C
Argon - 78'3 Carbon monoxide ' 0 2ooc
-33.6' ,9
Carbon dioxide
ooc 30'
Sitrogen Ammonia Methane Ethylene
O0
Value of Q used in Cal.
k Calc.
4,100
3.326 X
4,840
3.682 X 104 7.868 X 104 1.689 X IO^
J )
,l
6,100 6,100 4J?l2'
0 '
7,180
5J320 7,100
103
7.745 X 2.484 x 2.048 X
103 106
104
6.645 X 2.384 X
104
IO3
2.002
X
103
105
x
IO2
1.463 X 5.193 x
103 IO(
9.208 X 1.869 X 2.885 X 40.5
6.929 X
Experimenter
6.425 X 15.67 X 1.761 X 1.857 X
9,
3,715
' 0 20'
k Exp.
103 104
104 104
105
Homfray I, 1, 1,
,I
11
I04
102
Richardson Hom fray Titoff Homfray
,,
This agreement (Table 11) gives conclusive evidence in favour of Langmuir's theory. Volmer's methods are defective in the sense that he has combined thermodynamics with kinetic theory. Had he adopted purely thermodynamic methods and used equation (17instead of (3) he would not have arrived a t his so-called general equation (4). Again had he followed the kinetic method throughout, he would have obtained an equation vdp = (R - P)dx instead of his thermodynamical relation2 vdp = Qdn and thus he would have obtained Langmuir's equation. Lastly we may note that the equation of state for adsorbed substance at the surface should be x ( 0 - p ) = RT and not xi2 = RT as has been conclusively shown by the beautiful work of Adttms." The value of P has been I1
LOC.cit. 6; also Frumkin: Z. physik Chem., 116, 490 (1926).
668
ASHUTOSH GANGULI
suggested by him to be equal to double the area of a mole of the adsorbent, similar to the volume correction of van der Waals. If this correction is introduced, a modified Gibbs-Thomson equation
is obtained, y being the surface tension and c the concentration. It may be remarked that for very dilute solution the correction introduced can be neglected for in that case we may regard equation ( I ) to be true. The experimental works of Donnan and Barker12 point that the value of a (observed) is somewhat greater than that of Q (calculated). Again W. C. &IC.Lewis13 and others have been able only to test the order for a. Hence the experimental evidence does not go against the correction suggested above. I have the pleasure of thanking Dr. K. C. Kar for his interest in this work. Physical LabOTabTy, Presidency College, Calcutta. 12
Proc. Roy. SOO.,85-4, j57 (1911). physik. Chem., 73, 129 (1910).
182.
