T H E ADSORPTION O F GASES BY SOLIDS W I T H SPECIAL R E F E R E S C E TO T H E ADSORPTION O F CARBON DIOXIDE BY CHARCOAL BY
n. H .
LOWRY AKD P.
s. OLMSTEAD
Introduction Although many attempts' have been made to develop a theory of adsorption of gases by solids which will allow quantitative prediction of the effect of changes in temperature and pressure on the quantity of gas adsorbed by a given adsorbent, none of the theories, with the possible exception of that of Polanyi, may be said to be satisfactory. This is due to the fact that the mathematical relationships resulting from the various theories have all contained constants which cannot be directly determined; as a result there now exist many empirical equations which fit almost equally well the dataobtained either at constant temperature, or at constant pressure, or with constant amount adsorbed. Polanyi's theory, on the other hand, assumes that the force of attraction of the solid adsorbent for the gas molecules decreases with increasing adsorption in a way which is characteristic of the adsorbent, but which is independent of temperature and can be determined from a single isotherm. The amount of gas adsorbed at any other temperature or pressure can then be calculated if the way in which the volume and intermolecular attraction of the gas change with temperature and pressure is known. Although these relationships are given in an equation of state, it is very difficult to apply to experimental data the theory of adsorption as developed originally by Polangi and later by Berenyi. The following references include only papers since 1910 in which a theory of adsorption is developed and presented mathematically in a form which allows application to experimental data: a. I . F. Homfra Z.physik. Chem.,74, 129 (1910). b. G. C. Schmiit; Z. physik. Chem., 74, 704 (1910); 77, 646 (1911); 78, 667 ( 1 9 1 2 ) ; 83 674 ( 1 9 1 4 ) . c. S.Irirrhenius: hIeddel. fr. K . Vet. ,\kad. Sobelinst (z),SI. 7, (191I ) . d. A. 51. Williams: Trans. Faraday Soc., 10, 167 (1914); Proc. Roy. Soc. Edin., 38,23 (1918); Proc.Roy. Soc.,96A,287(1919). e. 4.Eucken: Verh. deutsch. physik. Ges. 16, 345 (1914); Z. Elektrochemie, 28, 7,257 (1922). f . 31, Polanyi: Verh. deutsch. physik. Ges., 16, 1 0 1 2 (1914);18, 5 5 (1916); Z. Elektrochemie,26, 370 (1920); 28,1 1 0 (1922). g. I. Langmuir: Phys. Rev., ( z ) , 6 , 79 (1915); 8, 149 (1916); J. Am. Chem. Sac., 40, 1361 (1918);see also D. Reichinstein: Z. physik. Chem., 107, 119 (1923). h. L. Berenyi: Z. physik. Chem., 94, 628 (1920); 105, j j (1923); Z. angew. Chem., 35, 237 (1922). i. D . C . Henry: Phil. Mag.,44,689 (1922). j . R. Lorene and.4. Lande: Z. anorg. Chem., 125,47 (1922). k. B. lliin: 2. physik. Chem., 107, 145 (1923); 116, 431 (1925); J. Russ. Phvs. Chem. Soc. 56, z (1924); Phil. Mag.,48, 193, (r$z1),'50,1144(1925);Z. PhyGk, 33, 435 (1925); Physik Z., 26, 497 (1925); 27, 591 (1926); see also H. Cassel: Physik. Z., 26, 862 (1925). 1. W.Tarassoff: Physik. Z., 25,369 (1924). m. AGorbachev: Z.physik.Chem., 117,129 (192jj. n. E. Jaquet: FortschritteChem., 18,437 (1925). o. 4 . hlagnus: Z. anorg. Chem., 158,67 (1926).
1602
H . H. LOWRY A S D P. S . OLMSTEAD
This difficulty has led us not only to present briefly in this paper a physicai interpretation of the theory of adsorption and its mathematical development, both of which differ somewhat from those given by Polanyi, but also to show in considerable detail a relatively convenient method of application to the experimental data. Using the procedure outlined in this paper, a test of the theory has been made on the data obtained by Homfray, Titoff, Richardson, Chappuis and S.0. Morgan for the adsorption of carbon dioxide by charcoal. The very satisfactory agreement between experiment and theory gives support to the fundamental assumptions underlying the theory. For convenience in reference we give the following lists of the symbols and their definitions, and of the constants and their numerical values which are used in the following discussions: p&rax. cu. mm.
6 gr. per cc 8, 6‘ x
mg per gr. of carbon
xobs.
Definition o j Symbols “Limiting adsorption volume,” that is, the volume occupied by adsorbed gas which is equal to the effective surface of the adsorbent multiplied by the distance from the surface at which the forces of adsorption are unable to bring about any increase in concentration of the surrounding gas. “Calculated adsorption volume at a particular temperature and pressure,” that is, the volume occupied at any particular temperature and pressure by that part of the adsorbed gas in which the molecules are as close as or closer than they are in the liquid state at that temperature. (o. approaches qmaxas the temperature approaches o°K. Differential of volume in the adsorbed gas. Subscript denoting the level separating densities less than that of the liquid at a particular temperature from those higher than that of the liquid. Density in any dq. Alinimum density in the surrounding gas atmosphere. Average density of the adsorbed gas within q s for the temperature and pressure at which x was measured. Mass of adsorbed gas. Observed value of x at a particular temperature and pressure. Calculated value of x for a particular temperature and pressure. That part of x&s which corresponds to x,. Mass of adsorbed gas compressed into a small volume A y of density 6.
1603
ADSORPTION OF GASES BY SOLIDS
"Adsorption potential," that is, the energy required to compress a gram molecule of the gas atmosphere to the density 6 at which some Ax exists on the surface of the adsorbent. Energy necessary to compress a gram molecule from A€ Va. to V = I . Subscript denoting a variable level. 1 V gram molecular Volume. volume P atmospheres Pressure. T OK Temperature. T, "K Critical temperature. R calories per Gas Constant. degree K Constants from van der Waals' equation. a, b Constant appearing in relationship of a to T. CY Value of b for T' = co at temperature T. (b,) T Value of b for P = 00 at temperature T. (bo) T e Base of natural logarithms.
e
calories per gram molecule of adsorbed gas
Table of Constants2
R
= 1.9876cal. per degree Kelvin = 0.0036618GMV log, = 2.3026 loglo 0°C = 273.09"K GMT' = 22416 cc. J = 4,184. 10' ergs. per cal. I atmo. = 1.01320 1 0 6 dgne/cm2
atmos,'deg
.
Physical Interpretation of the Theory The fundamental assumption underlying the theory of adsorption is that there is a force of attraction between dissimilar molecules. That such a force exists between similar molecules is the conclusion reached in considering such phenomena as: the heat of vaporization; van der Waals' constant a ; surface tension; etc. I t seems, therefore, quite reasonable to assume that a similar force exists between molecules of different types even if they are in different states of aggregation. That it is exhibited by different molecules in the same state of aggregation follows directly from van der Waals' theory of mixtures. If it is assumed that the force between the molecules takes the form of an intermolecular potential gradient, it is possible to develop a theory of adsorption similar to that of Eucken(Ie). This has been found sufficient for the explanation of adsorption at small gas pressures and for gases a t temperatures above their critical temperatures. At these pressures and temperatures real and ideal gases are much alike and the results to be expected for an ideal gas The values of these constants are those given by van Laar in "Zustandsgleichung," (1924)
1604
H . H. LOWRY AliD P . S. OLMSTEAD
are obtained. I n general, however, theory and experiment do not check a t high gas pressures nor at temperatures below the critical, indicating that in order to include real gases a t all temperatures and pressures in a complete theory of adsorption the equation of state must be considered. To do this it is possible to follow the outline given by Polanyi“ and BerenyiIh. They have considered a solid adsorbent existing in an atmosphere of gas. For this system the fundamental assumption may be interpreted to mean that there is a force of attraction between the adsorbent and the atmosphere of gas which surrounds it. This force, which may be assumed to be dependent on the kind and separation of the mutually acting molecules and independent of the temperature over the temperature ranges usually considered in adsorption (i.e., 80 to ~ o o ” K )is, exhibited in the gas atmosphere by changes in density. If the temperature is sufficiently below the critical temperature of the gas, the concentration of molecules may be as great as, or greater than, it is in the liquid, or the solid, state at that temperature. Because of this, the “limiting adsorption volume,” p,,, may be defined as the maximum volume which may be occupied by adsorbed gas in which the gas molecules are as close as or closer than they would be in a liquid at that temperature. I t is convenient to determine this volume from experimental data obtained at some temperature well below the critical temperature and at some pressure of surrounding gas below, but very near the saturation pressure, since near the saturation pressure and well below the critical temperature a very small amount of energy is necessary to cause liquefaction. Since neither the surface of the adsorbent nor the distance through which the forces of adsorption act can be accurately measured, the limiting adsorption volume must be determined by some means such as indicated. For any particular temperature and pressure, that part of qmnxwithin which the molecules are as close as, or closer than, in a liquid at that temperature will be called the “calculated adsorption volume,” and will be designated by pe. At very low temperatures one may well assume that the adsorbed gas is almost entirely within the volume ossince within this volume the density will greatly exceed the density in the surrounding atmosphere. However, since p8decreases very markedly with increase in temperature and since most measurements of adsorptlon have been made at relatively high temperaturps, it is necessary to consider not only pa,but the whole region pmnx The statements made in the preceding paragraph may be best understood by considering the distribution of density within the limiting adsorption volume. This may be shown by three typical cases, as in Fig. I , in which 6 is plotted as a function of q. Curve I is an example of a gas adsorbed at a pressure near saturation and at a temperature well below its critical temperature. I t indicates the densities through the adsorbed volume when the at3 For temperatures above the critical temperature, tpa must be given a slighly different interpretation, because the molecules can no longer exkt in the liquid state. In such cases it is sufficient to consider that part of wax,within whlch the molecules are as dense or denser than the density corresponding to the extrapolated saturation pressure a t thoEe temperatures.
1605
ADSORPTION OF GASES BY SOLIDS
tractive forces are sufficient to keep all adsorbed molecules as close together as they are in a liquid, i.e. when all the adsorbed gas lies within pa. Curve 3 shows the distribution in densities when it is never possible to have the molecules as close together as they are in a liquid. This represents the distribution at temperatures well above the critical temperature. The more general type of curve, such as is ordinarily obtained with carbon dioxide, is characteristic of the intermediate range of temperatures and is represented by Curve 2 , in which, although pais less than one-half pma, by far the greater part of the adsorbed gas lies within cps. It is obvious that the quantity of gas adsorbed may be obtained by integrating (6 - 6,)dcp between the limitso and Prnaxt or
FIQ.I Typical 6-9 Curves Pmax
(Pa
x
=J(6 - 6), 0
dp
+ J ( 6 - 6,) (Pa
Pmaa
d (= ~
J 6 d -~
krnax.
(1)
0
or, since under most experimental conditions, 6, is small and may be neglected, Ymax
x =
(2)
0
At high temperatures or high pressures it is sometimes necessary to retain 6max.
In order to determine the energy which must be expended in compressing the gas taken from the surrounding atmosphere to the density distribution it has in the adsorption volume, use must be made of the equation of state. This equation is an expression of the way in which the density may be expected to vary with temperature and pressure. Mathematically the total energy necessary for the compression is given by the following expression :
1606
n. H.
LOWRY AND P.
s.
OLMSTEAD
J VdP, (34 6, and K is a proportionality factor correcting Ax to gram molecules. In this expression e, which has been called the “asdorption potential,” represents the energy required to compress a gram molecule of the gas atmosphere to the density 6 a t which some small mass Ax exists on the surface of the adsorbent. This energy is a result of the attractive force of the adsorbent for the surrounding gas. Some equation of state must be assumed before the value of this integral can be obtained. Physically the process of adsorption, as outlined by this theory, may be pictured as consisting of the filling of a number of small volumes Acp, with gas at a pressure large enough to compress the gas to a density 6,. Since a potential where, c =
6, e2 = S V d P ,
(4) 6, exists at the ith cell and the potential where the density is 6, is 0,it follows that after (i - I) cells are filled a difference of potential el - o remains to draw molecules into the ith cell. Equation (4) is an expression for the potential which by assumption depends only on the kind and separation of the mutually acting molecules. This makes the quantity a function of volume only, or E = f(cp). The additional assumption has been made that for gases which are not associated (that is, do not form double molecules), this distribution of potential is independent of temperature.
Development of the Theory As a result of the discussion in the last section, the relationship between the adsorption potential, e, and volume, cp, of gas adsorbed is seen to be an important one. By the use of an equation of state this e - q relation may be determined for a given adsorbent and gas from the observed values of the amount of adsorbed gas, the pressure of the external gas atmosphere and the temperature of the system. Since the relationship between e and 0 is assumed to be independent of temperature, it is theoretically possible to obtain a complete curve at any temperature. However, if measurements are limited to pressures below one atmosphere, the complete curve is not obtained at high temperatures because the amount of gas adsorbed is relatively small, i.e., p is small; at low temperatures, the e - p curve can generally be determined only for large values of p, because a large amount of gas is adsorbed before the pressures can be read accurately (i.e.>pressures less than I mm). In equation (4) the relationship between the quantity e and others which may be
ADSORPTIOS OF GASES BY SOLIDS
1607
measured is shown. Each value of p must be obtained at a point corresponding to a particular value of E . This is given by the upper limit of the integral in the expression
which, of course, is similar to equation (2a). Of the factors in equations (4) and ij), P,Y,6,' and 6, are related by an equation of state. In general, x, cannot be calculated until some knowledge of the relationship between 6, and (eI is obtained. For a particular temperature T and external gas pressure P, 6, may be secured as a function of ti from equation ( 4 ) . On the other hand, pi must be determined from observed values of x and from some estimate of the way in which 6 varies with p. This leads to approximations from which a provisional e - p curve may be obtained. At temperatures well below the critical temperature, most of the adsorbed gas has a density equal to or greater than that of the liquid. For a first approximation, the minimum density of the liquid at the ternperature of the experiment may be substituted for the average density of the adsorbed gas. Using this and the observed values of x, \ d u e s of p may be obtained by the equation, xobs. = p 8 6' (6) where 6' is thc average density of the adsorbed gas within the volume ps for the temperaturr and pressure at which x was meanurcd. Values of e a t corresponding densities (6,) may be computed from equation ( 4 ) . From a temporary E - w curve obtained in this way and a 6 - e curve obtained from equation ( 4 ) and the PI' data, it is possible to use simultaneous values of 6 and p to calculate x and xs. If x,,~ is identical with &ha for all values, the temporary e - p curve may be considered final. If disagreements occur, certain corrections may be made. The average density corrected for the calculated x5 is given by the equation s, = Ips6 ' .
(7)
.I corrected value of x, may be obtained by the relationship: xcorr,= x, . &bs __.
(8)
XcaI
The value of s,,,, may then be used in equation (6) with the corrected value of 6' to determine p5. The e - q curve determined by this calculation is a second approximation. Generally not more than two corrections are necessary to obtain the final curve. In order t o find the values of e, by equation (4)> a knowledge of the relationship between P and V is necessary. Values of PT' as a function of P and T are given for a large number of gases in Landolt-B0rnstein.j For the Fee rote 9. Landolt-Bdrnstein: "Physical and Chrrnical Tables,"
(1923).
1608
H. H. LOWRY AND P. S. OLMSTEAD
purpose of this work, these cover a relatively small range of T and P. It is, therefore, necessary to determine, by extrapolation or otherwise, values of PV for other temperatures and pressures. Van der Waals’ equation,6which is often used for this extrapolation, is not of sufficient accuracy in all cases. For certain gases, van Laar’ has shown that, for a wide range of pressures and temperatures, the following relationship holds:
(& &)
where aT = aTceOL (10) aTc is the value of van der Waals’ a determined from the critical data, a is a constant, and
I +
(bu) T = van der Waals’ b a t temperature T, (ba)T - (bo)T
where (ba)Tis the value of b a t V = rn and (bo)T = b = T’ a t infinite compression. From equation (4) one may obtain,
6, 6,
=
SVdP =
[PV]
6, 6, -JPdV
6, 6, 6, Substituting the value of P from equation ( 9 ) , this becomes
Then since
6 The use of van der Waals’ equation a t constant temperature where the constants a and b can he directly determined from PV data as recommended by Berenyi (Ref. ~ hfor ) a test of the Polanyi theory of adsorption, is not satisfactory since the values of a and b are dependent on the pressures used in determining the values of PV. The particular values of these constants used by Berenyi are not given in his paper. This makes it almost impossible to check his calculations for comparison with other data. Van Laar: “Zustandsgleichqng von Gasen ufi3 Flussigkeiten,” (1924).
’
1609
ADSORPTIOS O F GASES BY SOLIDS
arcomplete solution of equation ( 1 2 ) is: e, = R T
(bJ T
V - (bo)T
-
2aT __log9 RTV
--
When equation ( I 5 ) is applied to observed data a number of simplifications may be made. Almost all measurements are made a t pressures less than one atmosphere and a relatively small error will be introduced by neglecting ' for 6 = 6,. Introducing the proper aT, (bo)T and (b,)T with respect to 1 constants the value of t i is then given by r
-
L
From this equation two others which are of interest in special cases may be obtained. If aT = a and (b,)T = (b,)T = b, the equation of state reduces to the usual van der Waals' equation and equation ( 1 6 ) becomes
( I 6.k)
which is similar to those obtained by Berenyi and Polanyi.8 If the equation of an ideal gas is assumed, a = b = o and this equation may be written
From equation ( 1 6 ) and e - 6 distribution may be obtained for any 6,. In practice, the distribution for 6, which gives V = is obtained first. That for any other 6, is obtained by a change in e which is independent of 6: Ae = 4 . 5 7 6 7 T log Va, (18) Berenyi: 2. physik Chem., 94, 632 (1920); Polanyi: Verh. deutsch. physik. Ges., 18, 64 (1916).
For carbon dioxide Y is related t o 6, by the equation M - -\' - ~994599
224166,
(17)
where M is the molecular weight. The numerical factor on the left side is determined from van Laar's modified van der Waals' equation for P = I , and R T = I that is, for T = 273.09"K. I t represents a correction to be applied to the gram molecular volume a t 0°C. and 760 mm. Hg pressure to make it conform with the volumes used in the equation of state. This factor differs with different gases.
1610
H. H. LOWRY A N D P. S . OLMSTEAD
These E - 6 curves are used with the preliminary e - cp curve in determining the calculated value of 5. This leads finally to a e - p curve which represents points determined from observations at a large number of temperatures and pressures. The Heat of Adsorption In equation (3) an expression was given for the total work involved in compressing the adsorbed gas from the density at which it exists in the gas atmosphere to the density distribution on the adsorbed volume. If this is divided by the mass of adsorbed gas, the work done in compressing one gram molecule of the gas is obtained. x
ZeAx
--
- work done per gram molecule.
(19)
X
This represents the heat of adsorption. When data become available. its value may be compared with experimental results. Application of the Theory to Data on the Adsorption of Carbon Dioxide by Charcoal I n order to show how the relationships obtained may be applied to experimental results on adsorption, several typical calculations will be explained. It is necessary to find the relations existing, at particular temperatures, among c, p, 6, P, and 5 . Since the PV data on carbon dioxide are the most complete, and there is a large amount of data on the adsorption of carbon dioxide by charcoal, this case was chosen for special investigation. T'an L a a F has shown that the P-V data for carbon dioxide may be represented quite accurately by equation (9)." Since this is so, equation (16) may be used in obtaining values of e, for V = I at various levels of 6, for the Seenote ( 7 ) . Values of aT, (hg)T, and (bo)=for C o r have been calculated from Amagat's PV data (Ann. Chim. Phys. (6), 29,68 (1893) ) over the range oo to 198°C. and I to 1000 atmospheres pressure. It was found that the values of aT can be satisfactorily expressed by the equation lo
a~ = oo7285 ,1.2138 - 0.8980 (RT The dependence of 1 bg)T on temperature is given by the equation log (bg)T =
- 3.2232
~
While the values obtained for ( ~ o ) Tlay on a smooth curve when plotted against T, except for the points a t 313.1" & 471.1 , they could not be readil fitted by a simple interpolation formula. In the following table is given a comparison of Tog (bg)Tobtained from equation ( 2 1 ) and from the PV data directly, together with the values of (bo)= obtained from the same data.
273 ' 1 293.1 313. I 333 ' I 353, I 410 I 471. I
-2.5463 -2.5925 -2.6328 -2.6682 -2.6997 -2.7724 -2 8308
-2
-2 -2
-2 -2 -2 -2
5474 5926 6298 6683 7012 7724 8068
I 1468 I 0680 [ I ,1878) I 2208 I 2554 I 3566 11 40581
x
IO-^
1611
ADSORPTION O F GASES BY SOLIDS
temperatures used. These are given in Table I together with the values of RT, a, b,, and bo used in equation (9) for each temperature. Values of ei are omitted for densities greater than the maximum density of the gas and less
TABLE I Calculation of e as a Function of 6 373. I o ti
1193 2312 2607 2737 3243 34x7 3505 3634 4112
2 . j89 2.169
I820
1,952
1,775 1.627 I . 502
450 884
1.394 I . 302
2233 5094
I.220
11112
RT a b, bo
I985 2325 2912
4566 5302 6582
3925 5785 9620
9142
.7199 ,01322
I , 000
.005214
,008245 .ooz836
,001089
.OOII47
I . 366
.00595C . 00 I 868 .oo I 289
than the minimum density of the liquid. Values of e, greater than e. are corrected by the value of the difference in e between the value for the gas a t maximum density and the value for the liquid a t minimum density. This correction should be zero. I n practice the minimum value of e, for maximum density of gas is seldom identical with that for minimum density of the liquid. Thus, at 196.6'C, the value of e, at 6, = 1.25 is taken equal to that a t 6, = .0055. This value of e, is the value of e. at that temperature for V = I . To find the value of e8 a t temperatures above the critical temperature, use is made of the empirical equation originally proposed by van der Waals','* which relates the temperature and pressure at which liquefaction takes place
P
log -5P = 2.89 l2
SeevanLaar: loc.cit..z18ff.
(%-
I)
1612
H. H. LOWRY AXD P. S. OLMSTEAD
70
VOLUME OCCUPIED BY GAS ADSORBED AT POTENTIALS GREUER THAN E.
FIG.3
A D S O R P T I O S OF GASES BY SOLIDS
y
VOLUME OCCUPIED BY GAS ADSORBED AT POTENTIALS GPEAKQ THAN E.
FIG.5
1613
1614
H. H. LOWRY A S D P. S. OLYSTEAD
FIG.6
Cp VOLUME OCCUPIED BY GAS ADWRBED AT POTENTIALS GREATER THAN E.
FIG
161.;
ADSORPTION O F GASES BY SOLIDS
For instance, to calculate the value of
ts for
3j3.1°,
or
72.9= P
0.2921,
and
P
= 249.jj.
Then by successive approximations, using equation (9), vs = 3.323 X IOO, 6, = 0.591, and from the e - 6 curve for this temperature the value of t corresponding to a density of 0.591 is 3505, or es = 3 j o j as shown in Table I. In Table I1 are given the corrections, Ae, obtained from equation ( I S ) , corresponding to the actual pressures used in the experiment. TYith these, corrected values of eS are obtained.
TABLE I1 Calculation of el T = 196 6°K. Data of X. Titoff T = 273 P* em Hg
0.03 0 . I8 4.'3 16.86 48.31 69. I O
Yax
At
6s
2934 2234
3384 2684 1460 910 499 359
--
Data of S.0. Xorgan
cal 1824
304 o IOIO 13.2j 3.24j 460 I '33 49 0 7918 -91
= 373, I O K . Data of S. 0. Morgan 3.26 31.85 2567 6072 11.63 8 . 9 2 6 1623 j128 22.35 4.643 1139 4644 751 37.66 4256 2.jj4 54.85 1 . 8 9 0 472 3977 ,,.03 1.34j 220 3725
T
I O I ~ .
o.oj
1520
0 . 3 3 230.3 0.92 82.61 1.94 39.18 3.02 25.23 4.65 16.34 6.07 12.52 7.62 9.974 1.o.58 7.183 73.33 5.701 14.44 5.263 4.431 17.15 23.1j 3.283 27.25 2.789 33.50 2.269 43.33 1.754 51.05 1.489
3977 2953 2396 1991 1752
1516 '372 1248 1070
944 901 806 644 556 443 303 214
5797 4773 4216 381 I 3572 3336 3192 3068 2890 2764 2721
2626 2464 2376 2263 2123 2034
Typical calculations of x and vs are given in Table 111. I n these, use is made of a temporary e - p curve obtained by equation (6) from data taken a t a temperature well below the critical temperature. Values of e and 6 are obtained from Table I. T o find e , , t is corrected by Ae form Table 11. Then, pi is obtained from the e - in curve at the given values of ei. Equation (j) is used to determine the values of xcn, and x,. These are compared with x,bp. and x,,,, obtained by use of equation (8). X corrected value of t,he density is obtained by equation (;) and a new value of paby equation (6).
1616
H. H. LOWRY AND P. S. OLMSTEAD
111
T.4BLE
Calculation of x and ti
Px
T
6i
e
0
4.13
196.6'
. o o j j 450 450
1.25
t
a, - u , __
=
PI -
+At
vl
IO10
145.4
1460 1460
125.6 12j.6
AX
z
mg
.0028
,05544
'p,
19.8
o
1iI.j
xcorr
ps
=
x
170.92
= ljl.4
170.97
6,=-G,,,,
3.26
170.92 12 j.6
- 1.3608
= 1 7 1 . 1 t 1.3608 = 126.0
0
2 j67
73
220
2 787
57
16
.ooo j
,0080
.004 600 .007 710
3167
37.7 33.5 19.2 7.9 4.5 3.'
19.3
.002 j
4.2
.oo j j
,0483 ,023 I
373.1' .OOI
I193 .030 190; .050 2312 .o80 2607 ,010
.IO0 2737
.300 3243 .so0 3417
,591 3505 .700 3634 ,900 4112 1.000 4566 1.032 xca1
3277 3760 4472 4879 5174 5304 5810
14.3 11.3 3.4 1.4
,0085
. I 2 1j
.0200
2.7
.L$
.06 j o .0900
,2260 .1360 ,0910 ,0360
.0400
1.7
1.0
. 2 000
.z000
5984 6072 6201 6679 7'33
1.5 1.3
.2
.A000
,0800
.2
,5455
1.2
.I
,6455
.8
.4
,8000
,1091 ,0646 ,3200
.3
.5
7250
0
.3
,9500 r.0160
,4750 ,3048
xobs
G
2 . 2 4 3 4 2.2516 1.1644 1.1681 .89569 1.3
In Table IV a number of calculations of pshave been summarized. This includes the recalculation of ps after the temporary E - G curve has been replaced by a first approximation. The values of P, are those given for this temperature in Table 11.
ADSORPTION OF GASES BY SOLIDS
3
h rc)
N
1618
H. H. LOWRY AND P. S . OLMSTEAD
In accordance with the procedure outlined in the preceding paragraphs, cp curves have been determined from the data of Hornfray(la’,Titoff,13 RichardsonJl4 and Chappuis,15 and from more recent data on two widely different types of charcoal (“Columbia Activated” and “Charcoal KO.2”) which were obtained in these laboratories by S. 0. Morgan using a novel method described in a previous article.16 These curves are given together with the observed points in Figs. 2 - 7 . In these figures the solid line has been drawn by the method of running averages. The fact that values of e - cp calculated from the experimental data all fall on a single curve independent of the temperature justifies the assumption that the force of attraction of charcoal for carbon dioxide is not dependent on the temperature over the range considered. In Table V are given the experimental data used in these calculations together with values of x,,~ which have been obtained by use of the e - rp curves. Examination of this table will show that in general there is very good agreement between x,bs and x,,~ The average difference between the observed and calculated values being: Titoff, 4.53%; Richardson, 11.25%; Morgan on “Columbia Activated Charcoal,” 3 . 1 7 7 ~and , on Charcoal KO.2 , 2.48%; Homfray, 5.85%; and Chappuis, 1.29%. In general, the agreement is closest where the experimental accuracy is greatest. The excellent fit obtained for the data of Chappuis is probably due in part to the fact that the measurements were all made at 273.1OK. Furthermore, at least a part of the difference between the values obtained from Morgan’s data on the two charcoals may be attributed to the fact that the data on Charcoal No. 2 were secured on a single sample, and that for “Columbia Activated Charcoal” include independent measurements made on three samples of the charcoal while the calculated values were obtained from the e - rp curve determined from the data of Run No. 37 alone. The average deviations of the different runs on Columbia Activated Charcoal are: No. 21, 4.74Y0; No. 25, 2.59%; and KO.37, 2.18%. I t is interesting to note that the deviation for Charcoal No. 2 and the “Columbia” Charcoal are so nearly identical, in spite of the fact that the adsorptive capacity of the first is only approximately one-tentk that of the second. The agreement obtained in the remaining cases is in the same order as obtained by Berenyi, although by using the method of calculation described in this paper the average differences between experimental and calculated values are not so great as those given in his paper; Le., for Titoff, 4.53% against Berenyi’s 7.16%; Homfray 5.85% vs. 12.47%; and Richardson 1 1 . 2 5 7 ~vs. 15.77~. A part of the better agreement obtained by the method of calculation proposed in this paper is undoubtedly due to the establishment of a better e - p curve. Berenyi used an e - p curve determined from the 273.1°K isotherm and an arbitrary completion of the curve to pmax The calculations made in this paper show, therefore, that the ade
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A. Titoff: z. physik. Chem., 74,662 (1910). L. B. Richardson: J. Am. Chem. SOC.,39,1842 (1917). R.Chappuis: K e d . Ann.,12, 161 (1881). H.H.Lowry and S. 0. Morgan: J. Phys. Chem., 29,I 105(1925).
ADSOFiPTION OF GASES BY SOLIDS
1619
1620
H. H. LOWRY AND P. 6. OLMSTEAD
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H. H. LOWRY B S D P. S. OLMSTEAD
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ADSORPTION OF GASES BY SOLIDS
1626
H . H . LOWRY .4ND P. S. OLMSTEAD
sorption of a gas at any temperature and pressure by a given adsorbent may be quite accurately estimated if the distribution of potential with volume (e - cp) for the gas and adsorbent is first determined. By similar calculations on the adsorption of nitrogen, hydrogen, helium, neon, and argon,-the data having already been obtained by S. 0. Morgan-we hope to be able to establish a relationship between the adsorption of a gas and certain other properties. We wish to take this opportunity to acknowledge the excellent assistance of Mr. S. 0. Morgan in securing the adsorption data and of Misses J. V. Glenn and A. E. Hamilton in making the necessary computations and preparing the figures for this paper. Bell Telephone Lahoratoraes, Incorporate June 10,1927.
’
