DISTRIBUTION LATY, ADSORPTION, AND REACTION
1091
(8) I ~ I R S OBS.,: Thesis, University of Jerusalem, 1939. BOBTELSKY, lI.,ASD KIRSOS,B . : Compt. rend. 208, 1577 (1939). (9) I~OLTHOFF! I . 11.:Die Jlassnnalyse, 1-01, 11, p . 356. J. Springer, Berlin (1931). (10) ROBERTSOS,A . C . : J. rlm. Chem. S O C .47, 1299 (1925); 48, 2072 (1926); 49,1630 (1927). BOHSSOS.IT,L., ASD ROBERTSOS, .I.C . : J. Am. Chem. SOC. 46, 2512 (1923). (11) WEISS, J . : J. Phys. Chem. 41, 1107 (1937).
D I S T R I B U T I O S LLIW,,1DSORPTIOS, -4SD CHEMICAL R E h C T I O S . I1 B. P. G’I‘ASI Science C o l l e g e . The I-nzLersify, Patna 6, India Receized M a r c h 2, 1949 ISTRODUCTIOS
I n a previous paper (12) the author has tried t o shon- that if adsorption is regarded as a special case of distribution of a substance between tn-o phases the phenomena of distribution, adsorption, and chemical reaction appear to have a simple correlation. The special feature of the distribution is that the dimensions of the adsorbing phase are regarded as limited. The illustrations in support of this vieu- adduced in that paper have been somen-hat of a qualitative character. I t is proposed t o shon- in this paper that some results of a general nature and some others of a rather strictly quantitative character are in harmony with this vien-. SOME THEORETICAL COSSIDER.iTIOSS REGARDIKG T H E STATE O F ADSORBED MOLECCLES
The adsorption equation of Langmuir (20) and similar equations have been deduced by assuming highly simplified conditions for adsorption. I t is therefore quite e a d y understood that some of the equations have little utility in esplaining the experimentally determined courses of adsorption isotherms. One of the simplified conditions is that the adsorbed molecules be confined t o a homogenous two-dimensional space. Such a condition is probably difficult t o realize x-hen the adsorbent is a solid. There are bound t o be edges, cracks, corners, or boundaries between tn-o or more solid phases, and other factors against the exclusive existence of a homogeneous plane surface. Probably all the theories of adsorption so far regard the adsorbed substance as being present in a more or less homogeneous condition, e.g., a homogeneous gas or a liquid, sometimes Ivith contiauouq pressure or density gradients from point t o point. There are a number of theoretical considerations against these simple vien-s. T o call attention t o a simple point, reference may be made t o the fundamental equation of capillarity (1) :
1092
B. P. GYASI
which gives a relation betn-een the lowering of mechanical pressure from POt o P as the surface tension is lowered from g o t o g at a point having the principal radii of curvature R1, Rz. If u-e consider the Gibbsian picture, the process of adsorption is possible only if a lon-ering of surface tension of the adsorbing material takes place resulting in a decrease of the free energy of the system. The smaller the radii RI ,R2,the larger will be the decrease in free energy due t o adsorption. Hence the more curved surfaces would be particularly favored in the process. For a perfectly formed edge of a crystal or a sharp crack we may put R1 equal t o 0. For perfectly formed corners R1 and R? each may be put equal to 0. The release in free energy due t o release in the mechanical pressure may reach large Yalues for edges and corners even n-hen they are not perfect; a highly preferential accumulation of the adsorbate on them is consequently indicated. Stranski (23) considers perfectly formed crystals of sodium chloride, calculates the electrostatic energies of attachment of ions of the lattice in various positions, and obtains the following values in units of e2,’d, where e = the electronic charge and d = the lattice distance: POSITIOS
Inside edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E n d of inside edge.. . . . . . . . . . . . . . . . . . . . . Inside corner.. . . . . . . . . . . . . . . . . . . . . . . . . . . . ... Surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... E.dge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ESERGl OF AITICHMENT
0.313 0.675 0 . so7 0.132 0.181
The ratio of energies of attachment in the first three re-entrant positions is almost as 1:2:3. The external positions also differ considerably, by about 30 per cent between surface and edge and 60 per cent betn-een edge and corner. Taylor, Eyring, and Sherman (25) show that there is a quantum-mechanical justification for the special attachment of atoms at corners of previously formed lattices and in linear arrays during the formation of crystals. It is therefore very likely that in the adsorption of extraneous materials also certain positions may be favored much more than others and there may be special concentration of the adsorbate along edges or corners of particles of the adsorbing body. If the ratio3 of energies of attachment obtained by Stranslii are applicable t o adsorption also, a rough qualitative variation in the heats of adsorption may be predicted for different amounts of adsorption. Assuming the mean measured heat of adsorption as 10,000 cal. per mole under ordinary conditions of experiment, a quite frequent value, one should expect a variation from a lower limit of about 5000 cnl. t o an upper limit of about 15,000 cal. T’ariations of this order are common (18, 18). Further, the smallest variation in Stranski’s figures is of about 30 per cent in the transition from the external surface t o the external edge; it corresponds to about 3000 cal. per mole, which is yet much higher than the value of RT at the usual temperatures. Barrer (2) has treated the subject of sorption by zeolites statistically and cal-
DISTRIBGTIOS L.%K, .IDSORPTIOS, A S D REACTIOX
1093
culated the partition functions for different types of motion the molecules may take up in the sorbed state with respect t o the lattice of the zeolite. He employs these partition functions for calculating the accompanying entropy changes. K h e n similar units are employed and reasonable values for the constants appearing are >ubstituted, it is found that the entropy change accompanying desorption i- not far from the entropy change accompanying evaporation. Barrer therefore concluded that the motion of' the adsorbed molecules may he restricted and about of the same kind as in the liquid state; it is considered that the translational motion of the molecules n-ithin the lattice may be almost absent. Such a consideration militates against the proved mobility of the adsorbed molecules and the large rates of adsorption usually observed. Further, the constant 0 in the Langmuir equation
enters into the calculation for the entropy change in desorption. I t is not always that in actual measurements b comes out t o be a constant. Thus, the author (13) found that in all the cases studied by him b was variable, the largest divergence being in the case of carbon tetrachloride. It is significant that, particularly for carbon tetrachloride, the difference between the observed and calculated entropy changes of Barrer was great, although he was using a different adsorbent. On the basis of his calculations Barrer has also shon-n that there is a simple relation between the isosteric heat of adsorption Q and the energy required t o enable a -orbed molecule t o escape into the vapor phase, x. When the sorbed molecule po-sesses all the three degrees of translational motion and is completely free to rotate, Q = - x. For every degree of translational or rotational freedom converted into a degree of vibrational freedom, - x must be increased by R 2 t o give the corresponding value of Q. If the molecules can exist in all states possible, the maximum and minimum values of Q should show a difference of ( - x 3 R T ) x or 3 R T . The term in the bracket corresponds t o the state of the molecule ryith six degrees of freedom and free rotation. At ordinary temperatures we -1iould expect a difference of about 2000 cal. in the measured estreme value< of the isosteric heat if different types of motion exist at different stages of adsorption. Such variations are frequent (14). The existence of adsorbed molecules in different states of motion is therefore a possibility which cannot be ruled out according t o this method of approach. I n other words, there is justification for considering adsorbed molecules to form linear or two-dimensional arrays or t o be confined to definite points on the adsorbing surface.
+
+
ADSORPTIOS O S PHYSICSLLY Ah-D CHEJlICALLY HOhlOGEKEOUS SURFACES
The phenomenon of adsorption would certainly be much better understood if measurements could be made with surfaces having similar physical and chemical properties throughout their estent. Obviously these conditions are difficult to realize with solids. Even an adsorbent composed of perfect crystals of a pure substance would not meet these requirements because there would be planes,
1094
B. P. GPANI
edges. and corners which o d d has e different properties as regards adwrption. -4clean liquid surface ivould be normally free from these disturbing cauqe-. Hence it would be of interest t o examine n-hether adsorption on liquid surface,i 1” amenable t o simpler relations. A%ctualmeasurements of adsorption on liquid surfaces appear limited practically t o those of Oliphant (22) and Bosnorth (3, 4), both of n.honi employed surfaces of liquid mercury. The liquid x a s allon-ed t o fall doim a tube in a fine shoner (0.1 mm.) and the amount of gas or vapor adsorbed n-as measured by noting the decrease in the refractive index of the gas n-ith the help of a Raleigh refractometer. They showed in this Tvay that in the adsorption of carbon dioxide ‘
LOG
p
FIG.1. Adsorption of benzene, heptane, hexane, and pentane on silica gel
and sulfur dioxide on mercury “as long as the adsorbed layer is not saturated n-ith molecules of the component under consideration (n-ith dry gases the monomolecular layer n-as not complete belon- 1 per cent), then the relation hetueen the number of molecules of that given component in the adsorbed layer and the number of the same molecular type in the atmosphere above is of the form: n LY C2i3”(3). I n the nest paper Bosxorth (4) examined the adsorption of formic, acetic. propionic, butyric, and valeric acid vapors on mercury and came t o the cmciusion that ‘,log n plotted against log p . . . shows that the relation betn-een n and p over the range of p for which the film is not tightly packed, i i of the form n a pZj3.’’I n these experiments the amount of adsorption of the rapor. 11as tletermined by a conductivity method sfid the results n-ere checked by surface tension
DISTRIBUTIOS L l K , *\DSORPTIOK, .\SD REACTIOS
1005
measurements. These results may he talien t o confirm rather rigorously equation 3, proposed in the previous paper (12). The adsorbed molecule. ahould be considered t o be distributed in a general \\-a>-on the adsorbing surface. Incidentally, the author has recently re-examined some of his earlier measurements on the adsorption of such indifferent vapors as those of benzene, heptane, hexane, and pentane on silica gel (IC), and finds that the value of 1 I I in the adsorption equation .r nz = ii. C1 is very nearly 2 3 in each case (figure 1). -4 more recent measurement u-ith carbon tetrachloride on silica gel (15) gives the same result. It appears therefore that under appropriate circumstances even solid wrfaces niay act as homogeneous t o a great extent. Compared t o the paucity of data on direct measurement of adsorption by liquid surfaces, the measurements on surface tensions of solutions at different concentrations are more numerous. T e have also some measurements on surface tensions of mercury in contact with different vapors at varying pressures. It is possible to calculate the amount of adsorption of the dissolved substance or the vapor per unit surface of the given liquid by assuming the validity of the Gibbs adsorption equation: '1
If the classical adsorption equation is applicable at the same time From equations i and 1,
- -c. _ _do RT
-
dC
whence by integration - u When C = 0, u = o0 = surface tension of the pure liquid.
.*. UO - u
=
R T . nl;. Cl"'
Taking logarithms on the tn-o sides, log
(UO
-
G)
=
1
IL
log C f log RT.~LI';
The term log RT.nl; being constant at a constant temperature, the value of 1 ' n niay be obtained from isothermal data hy plotting log (G,]- G) against log C and measuring the slope of the resulting curve. .Ilternatively, the ratios of differences hetween successive values of log (G" - G) and log C may lie taken. This is the method adopted in calculating the values of 1 n given in the tables helov . Freundlich (9) has adopted the former procedure in discussing the wrface tension data of Traube (2G), von Szyszkoivshi (24), and Carl Forcsh (8) for normal fatty acids from formic to nonoic, dissolved in miter. He found that the measurements agreed with the equation
1096
B. P. GY-LKI
where '(s and I , n are constants of n-hich 1 ) L , about = 0.7, varies little from substance to substance, while s (the relative lowering of surface tension for one mol. solution) varies greatly from substance to substance" (10). Freundlich did not point out that 1 '7z in equation ii is the same as in the classical adsorption equation (equation 1) and did not attempt to understand its significance. Obviously this result also may be taken to confirm equation 3 in a more general, though somen-hat less strictly quantitative, n-ay. Equation 3 requires the value of 1 ' n t o be O.G7 and the agreement is as good as could be expected. EXPERIRIEST.LL D.kT1
I n order to follon- the variation in the value of the index 1 / n closely from concentration to concentration it is necessary that it should be calculated from every pair of consecutive readings separately. -4large number of data comprising those of Bohdan von Szyszkomki (24), T. Iredale (17). H. Cassel ( 5 ) , H. Cassel and TABLE 1 Loute?zng of surface fens?ov o f c r q i i e o u s n - L i i t i j r i c acid (From von hzvszl,owki) Contentration AU
1, n
ii i f / (
concentratzori at 18-19"C
I
I
I
I
0 931 11 621 529 464 0 324 0 367
0 414
398 0 430
0 276 334 0 489
0 184 2i4 0 568
I
0 122 217 0 634
0 Oh2 168 0 750
1
0 055
124 0 SI6
1
0 036 89 0 972
0 024 1
60
F. Salditt ( 7 ) ,H. Cassel and h l . Formstecher ( 6 ) , and Herbert llills (21) have been examined according to the method indicated above. Reference may be made t o the original papers for the units of concentration and lowering of surface tension, go - u = Au, where they have not been mentioned. Only some of the represent at ive data are adduced belon-. von Szyszkowski expresses his concentrations in gram-moles of the solute per liter and takes the surface tension of water a t the temperature of measurement arbitrarily as 1000. Mills expresses his concentrations in gram-moles of the solute per 1000 g. of water. An examination of 1:n in these tables shon-s that there is a variation in the values from unity at the lowest concentrations (or pressures) t o a limiting value of 1/3 ton-ards higher concentrations. I n some cases (tables 4, 5 , and 7) the upper limit of the value of 1I n appears to be 0.7, agreeing with the general value obtained by Freundlich. These observations appear to fit in with the view that at the l o w s t concentrations the adsorption space is three-dimen-
1097
DISTRIBGTIOK LAIV, .iDSORPTlOS, Ah-D REXCTIOX
, 0 0924
Concentration
0 0711 0 0547 C 0421 0 0324 0 0249 0 0102' 0 0147 5Y0 532 488 442 309 353 309 466 0 33211 0 3290 0 3736' 0 3952 0 4602 0 5lb4l 0 5629 0 G122
AU
lln
1 0 0147
Concentration
0 0113 0 0087~0 0067' 0 00521 0 0040~0 00311 0 0021 0 0018 266 226 187 152 117 90 5 69 5 1 50 5 3s 0 61221 0 724jI 0 8060, 1 009 0 98021 1 034 1 1 2472 0 '3bh3'
AU
1 111
I
TABLE 4 Lowering of surface tension of solutions of a m y l alcohol in water at 16.5"C. (From Herbert Mills) 0.273 '0.312 :0.351 0.390 41.5 43.1 44.7 46.3 0.284510.309210.33400.3580
1
~
T-IBLE 5 Lowering of surjure tension of so/i/!zons o j iuleric acid zn water at 16°C. (From Herbert Nills) Concentration. .'0.0072 0.036' 0.0721 0.108 0.144 0.180 0.216~0.252, 0 . 3 6 1 ~Pure acid 1 1 44.2
Au . . . . . . . . . . . ,~ 5.90 17.1 24.7 28.9 32.3 35.2 37.4 30.5 1 4 3 . 8 l / n . , , . . , , . . . . . . ~0.6610~0.5307~0.3874 0.3860'0 ,355310,33340 .3542~0.28761 ~
'r.mr,Ii 6 in contact w i t h i'npor,s o f isnninyl n l m h o l ot rli#erci/i pressiires a! 50°C. (From FI. C'asscl :ind F. Salditt)
Lowering of siirface tension of
iiierwr!/
I
I
p , n i n i . . . . . . . 0.040 ' 0.151 ' 0.470' 0.032 1.90 3.36 5.02 6.71 8.51 10.2 Au, d y n e s . , . ,~ 3 . 2 9.5 16.6 21.8 28.5 35.4 4 0 . 0 :11.S 43.3 51.4 1/11.. . . . . . . 0.819 0.492 0.39s 0.376 , 0.381 1 0.360 0.314 0 . ~ , 1o . 3 1 ~
i
.i
p , mm
1
Au, dynes
1 2 500
l/n
~
0 079 0 697
1
I
~
~
~
~
0 510 1 50 4 61 8 40 13 50 20 10 50 00 75 10 8 900 14 50 ,22 30 ~ 3 630 ~ 2 080 136 50 42 40 48 20 0 31T 1 0 3S3 0 270 0 269 0 264 1 0 277 0 315 1 0 334
'36 10 52 TU
sional but as the concentration increases the dimensions decrease t o tm-o and finally t o one. I n other n-ords, the translatory motion of the adsorbed molecules is free at first but gradually becomes restricted to the two-dimensional surface
1098
B. P. GTASI
and ultimately only to linear motions in it. I n some cases the adsorbed molecules form a tno-dimensional dynamic array even at the lair-est pressures. IIuch higher values of I TL are obtained in some other cases, as appears from tables 8 t o 10. A simple way of understanding those results higher than unity 11 ould he to consider that association takes place among these adsorbed molecule
