A. L. MYERSAND S.SIRCAR
3412
A Thermodynamic Consistency Test for Adsorption of apors on Solids
.L. Myers* and S. Sircar School of Chemical Engineering, University of Pennsglvania, Philadelphia, Pennsylvania (Rsceived June 28, 1971)
19104
Publkaiwn costs assisted by the National Science Foundation
A thermodynamic consistency test is derived for adsorption of liquids and their vapors on solid adsorbents. The test relates adsorption from any pair of unsaturated vapors to adsorption from their liquid mixture. The test 1s satisfied by experimentaldata for the adsorption of six pairs of vapors on silica gel at 30’.
Adsorption equilibria are usually analyzed in terms of the thermodynamics of adsorption. However, adsorption thermodynamics contain certain variables such as surface tension and surface area that are sometimes ambiguous, particularly under the conditions to be discussed. The following derivation of a thermodynamic consistency test for adsorption of liquids and vapors on solid adsorbents is carried out in the more familiar language of solution therm0dynamics.l This is permissible because the adsorbent, which is assumed to be a crystalline :3olid, has a fixed surface area and pore volume. If the surface area were to change during the experiment, as it might for adsorption on liquid dropiets, then burk solution thermodynamics would fail because it does not allow for changes in the degree of dispersion of the adsorbent. The system is shown schematically in Figure 1. There are two adsorbates (no. 1 and 2) and a solid adsorbent (A) which is nonvolatile. The adsorbent might be silica, gel, activated carbon, zeolite, etc. The gas phase is a mixture of component no. 1 and 2. The condensed phase is the solid adsorbent plus the adsorbed gase:~ Whether the gas is adsorbed in pores or in parallel layers, whether the gas is adsorbed or absorbed is imn1:tterial as long as the process is reversible. The number of molea of each adsorbate in the condensed phase (nl’ and nz‘)is measured by conventional gravimetric or volumetric adsorption experiments. The system is immersed in a temperature bath a t T but the pressrare it3 variable. Under these conditions the Gibbs eyurtlion for the condensed phase is2 nl‘dkI‘
4-/22’dp%’-I- nAdpA
= V’dP
(1)
The prime denotee the condensed phase. The V’dP term may be ignored because AU’ >> A(PV’) for the condensed phase in which V’ is small and the pressure is subatmospheric. At equilibrium PI’ = Pl
(2)
P 2 / = P2
(3)
The Journal of Physical Chemistry, Vol. 76, N o . 83,1972
where p1 and p2 are the values of the chemical potentials in the gas phase. p~ is the chemical potential of the adsorbent. At the low pressure of interest dpi
=
RT d In (Py,)
(4)
for both gases, where yi is the mole fraction of component i in the equilibrium gas phase. Combining eq 1-4 (5) Equation 5 is integrated over a closed path in three steps shown in Figure 2 . Step 1 is the adsorption of pure vapor of component no. 2 for which
and step 3 is the desorption of component no. 1 for which
For step 2 the adsorbent is immersed in a liquid mixture of component no. 1 and 2 which is in equilibrium with its saturated vapor (see Figure 3 ) . There€ore the partial pressure in the gas is equal to the fugacity in the bulk liquid2 P*yi =
(8)
PtaytX(
xiis the mole fraction of component i in the liquid mixture. The activity coefficients in the bulk liquid (y1,yZ) are related according to the isothermal GibbsDuhem equation2 xld In y1
+ xzd In
y2 =
0
(9)
Combination of eq 5 , 8, and 9 gives (1) T. L. Hill, J.Chem. Phys., 18,246 (1950). (2) K. Denbigh, “The Principles of Chemical Equilibrium,” Cambridgeuniversity Press, New York, N. Y., 1966, pp 272,284.
GOW.PTIONOF
3413
Li~yumsAND VAPORSON SOLIDS
A
The quantity i n the riurxierahor is the familiar surface ~ t liquid i o n solutions excess3for ~ ~ ~ s ~ rfrom 121e
^PI'
-
+ nz')x1
(11) (components land 2)
Integration of t:q IO lor step 2 in Figure 1 gives
Adding eo( 6 , 7 , and 12 for the dosed path in Figure 1 we get at T
(13)
Thermodynamic system at condition of sahration.
Figure 3.
This thermodynamic consistency test relates adsorption Erom a pair of unsaturated vapors (the first two integrals) t o adsorption from their liquid mixture (the last integral). However, eq 13 is not applicable to the
10
r" L
c
-,g '1 0.1
1.0
a.
d
s3 0.01 0.1
0.1
IO
1.0 LOGi0n,
n i n rnilllmoler/gm
Figure 4. Adsorption of 1,2-dichloroethane1 benzene, cyclohexane, and n-heptane on silica gel a t 30".
Figure 1. Thermodynaniic system a t subsaturation conditions.
special case where adsorbate .vapor condenses on the solid in the form of liquid droplets, because cooperative forces in the adsorbate are stronger than solid-vapor adsorptive forces and therefore neithcr s o l U t % thermo~~ dynamics nor adsorption thermodynamics applies.
Experimental Section I n order to test eq 13, isotherms of benzene, cyclo~
~
Table I: Integration of Vapor Isotherm for Adsorption on Silica Gel at 30" 6
p n' d P , zumol/g Vapor
tP@,
partial pressure of component 2
Figure 2 . Integration path for thermodynamic consistency tes7 ~
Benzene Cyclohexane n.-Heptane 1,2-Dichloroethane
(3) S. Sircar and A. L.Myers, J . Phys. Ch,em.,74,2828 (1970)
The Journal of Physical Chemistry, Vo2. 76, N o . 93, 1972
A. L. MYERSAND S. SIRCAR
3414 Table 11: Thermodynamic Consistency Test for Pairs of Vapors Adsorbed on Silica Gel a t 30"
s,
pzs n2'
e
---.---.----^pair (1)
(2)
Benzene Benzene Benzene n-Heptane n-Heptane Cyclohexane
Cyclohexane n-Heptane l,%Dichloroethane Cyclohexane l,%Dichloroethane 1,2-Dichloroethane
_I__--.-
'
4.0
i
15.5
15.5
-7.9
'dH6
121'6'
E
$ I
.
.E 2.0 I I
E
asorption
1.0
_..A
0.0 0
20
40
80
60
P in m i l i i m e t m of
I
io0
120
I
140
t ! g
Figure 5 . Adsorption of l,%dichloroethane, benzene, cyclohexane, anc' n-heptane on silica gel a t 30".
C H (1)
--e....
6 6
- 3 0
t
TdP
-14.5 -14.5 -14.5 -7.9 -7.9
7.9
-
3.0
FdP
7.9 7.9 15.5
-s,
mmol/g
P1'
C H CI (2)
2 4 2
-d
lo (yizi)
/Sum/
7.2 7.2 -1.1 0 -8.3 -7.9
=k 0.7
i0.7 i 0.1
=k
0.8 0.7
0.6 0.6 0.1 0 0.7 0.3
Surface excess isotherms for adsorption from liquid pairs on the same gel (Davison PA400, specific surface area based upon capacity a t saturation = 660 mz/g) were also measured a t 30°;4 these are shown in Figure 6. The integrals for the surface excess isotherms are recorded in Table 11. Activity coeflicients in the bulk liquid solutions were obtained from vapor-liquid equilibrium and heat of mixing The consistency test, eq 13, requires that the sum of the integrals in Table I1 be zero. The instrumental error in the integral for the surface excess i s about lo%, estimated using uncertainties of f0.0001 in refractive index (used for measurement of composition) and zt0.01" in temperature. This error is given in Table 11. The measured composition of the solution has an uncertainty of only f1% but this error is magnified by the measurement of small differences in composition due to adsorption. The error in the measurement of vapor adsorption is negligible by comparison. Table I1 shows that the systems studied obey the thermodynamic consistency test within the precision of the experiment, Equation 13 may be used in conjunction with the vapor isotherms to predict, a t a glance, adsorption from liquid mixtures. According to eq 13, component no. 1 is preferentially adsorbed from the liquid (n1° > 0) if nl' > nz at corresponding values of reduced pressure ( P / P ) . The larger the difference (nl' - nz'), the greater the value of rile. Therefore, according t o Figure 5 , we expect dichloroethane to be somewhat more strongly adsorbed from the liquid relative to benzene and strongly adsorbed relative to heptane and cyclohexane. We expect benzene to be strongly adsorbed relative to cyclohexane and heptane The adsorbent
-4 0
0
0.2
0.4
0.6
0.8
1.0
Mole fraction l f component 1
Figure 6. Surfacs excess isotherms of binary liquid mixtures on silica gel a t 30".
hexane, n-heptane, and 1,Zdichloroethane vapors adsorbed on silica gel were measured gravimetrically at 30". These isotherms are shown in Figures 4 (low pressure) and 5 (high pressure). The values of the integrals for the vapor isotherms are given in Table I. The Journal of Physical Chemistry, Val. 76, X o . 25, 1978
(4) S. Sircar, Doctoral Dissertation, Universihy of Pennsylvania, 1970. (5) G.Scatchard, S.E. Wood, and J. M. Mochel, J . Phys. Chem., 43, 119 (1939). (6) I. Brown and A. H. Ewald, Aust. J. Res. .Vat. Bur. Stand., 24, 33 (1940). (7) H.S.Myers, Petrol. Rejiner, 36, 178 (1957). (8) J. J. Kipling and D. A. Tester, J. Chem. Soc., 4123 (1952). (9) C. R. Fordyce and D. R. Simonson, Ind. Eng. Chem., 41, 104 (1949). (10) K . Amaya and R. Fujishiro, Bull. Chem. SOC.Jap., 31, 90 (1958).
these qualitative predictions are verified should be neutral with respect to adsorption from liquid shown in Figure 6. res of l ~ ~ ~ and~ heptane ~ ~ because o ~ the ~ isoe ~ mental ~ ~ data e therms cross o w another; preferential adsorption of Acknowledgment. Financial support by t,he Kational beptme a t 1 ow p wssure i s cancelled by preferential Science Foundation is gratefully acknowledged. a ~ ~ s o r ~crf ~ ~~~~~~~~~~~~n~ ~on at high pressure. All of
Analogy between Adsorption from Liquids and Adsorption from Vapors y A, ‘L.Myers* and S. Sircar School of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania (Received M a y 16, 19%)
19104
Publication costs assisted by the National Science Foundation
The relation between adsorption from liquids and adsorption from unsaturated vapors is derived. The surface excess for adsorption from liquids can be calculated from equilibrium data on adsorption of the unsaturated gases. Equations for the surface excess are derived from simple type I and type I1 models of gas adsorption.
Theories of adsoqAion from liquids are made difficult by the chemical heterogeneity and structural irregularity of the solid surface as well as the fact that a t least two cornponcnts are involved in competitive adsorption a t the solid 9urface.l The simplest, case is the interaction of a dense fluid mixture with a solid surface. Lack of specific information about the composition and structure of the surface also complicates theories of adsorption from tingle gases, Several theories that nore the detailed structure of the surface have been proposed, tiit: Lsngmuir,2 Brunauer, Emmett, and Teller (BET) , 8 6teele and E I a l s e ~ ,Frenkel-Halsey~ ill slab theory,&eta:. Although these and other theories are usefgl to a degree for fitting observed data, they contain constants that cannot be independently measured. Thus there is no Fdly adequate theory of adsorption from gases, nor ia there a satisfactory theory of adsorption from IiyJids. Howevcr, the two phenomena are related : adeorptiom from liquids can be fully explained in terms ol adrjorption from their unsaturated vapors. The object of this work is to study the analogy between adsorption from liquids and adsorption from unsaturated vapors.
Equilibria for adsorption from a binary mixture mast obey the foilowing thermodynamic consistency test6
JPP P=O
g d p
p
$‘ nl’ -dP P
I
P=O
+
The first two integrals refer to the pure, unsaturated vapor adsorption isotherms and the last integral refers to the isotherm for adsorption from the liquid mixture. nleis the surface excess of component no. 1; the activity coefficients (y1,y2) and mole fractions (zi,xZ)are those in the equilibrium bulk liquid. Define the integral for adsorption of a pure vapor by
where rpis is called the free energy of immersion of the ith adsorbate. This terminology is appropriate because &* is related to the heat of immersion of the adsorbent in the liquid by a Gibbs-Helmholtz type of equation? With this definition eq b becomes (1) A. C. Zettlemoyer and F. J. Micale, Croat. Chem. Acta, 42, 247 (1970). (2) I. Langmuir, J. Amer. Chem. Soc., 40, 1361 (1918). (3) S. Brunauer, P. H. Emmett, and E. Teller, ibid., 60,309 (1938). (4) W. A. Steele and G . D. Halsey, Jr., J . Chem. Phys., 22,979 (1954). (5) D. M. Young and A. D. Crowell, “Physical Adsorption of Gases,” Butterworths, London, 1962, p 167. (6) A. L. Myers and S. Sircar, J.Phys. Chem., 76,341 2 (1972). (7) 8 . Sircar, J. Novosad, and A. L. Myers, f n d . EWJ.C h m . , Fundam., 11,249 (1972). The Journal of Physical Chemistry, Vol. 78, N o . $3, 1972
