The Determination of Entropies of Adsorption by Gas-Solid Chromatography
Dianne Atkinson and Geoffrey Curthoys University of Newcastle New south Wales, Australla 2308
Gas-solid chromatography provides data from which thermodynamic functions of adsorption a t low surface coverages may be determined. In a previous paper ( I ) it was shown how the heat of adsorption is related to the equilibrium constant for adsorption (a Henry's law constant) and the specific retention volume of the adsorbate. The heat of adsorption gives useful information as to the strength of the adsorbate-adsorbent interaction and further insight into the dynamic nature of this interaction may be gained by a parallel study of the entropy change upon adsorption. Entropies of adsomtion a t various surface coveraees mav be obtained from -~ adsorption isotherms (2-6). The absorption isotherms are measured a t different tem~eratures.the heat of adsor~tion, and free energy of adsorpiion calculated and hence the en: tropy of adsorption determined. Entropies of adsorption also may be found by measuring the heat capacity of the adsorbate-adsorbent system as a function of temperature (7). In this paper it is shown how entropy changes on adsorption may be determined a t low surface coverages from gas-solid chromatography data, based on the standard states for both the non-localized and localized models of adsorption proposed by deBoer and Kruyer (4). In recent years several papers dealing with this field have appeared in the literature (8-11). but further clarification of the relationships involved is warranted. Data for the adsorption of cyclobutane on zeolites N a y and C a y is analyzed. In order that meaningful comparisons may be made with calculated entropy changes, it is necessary to specify standard states for the adsorbate both in the vapor state and the adsorbed state. The standard state for the vapor is universally chosen as the vapor a t 1atm pressure. The standard states for the adsorbed phase, considering both localized and non-localized adsorption, were the subject of debate in the 1950's when entropies of adsorption were calculated initially from adsorotion isotherm data (2-6). It was contended by Everett ,ti1 I h;ut id(:;ili.*cdstandard statin accurate picture-of theadsorption system, especially a t high surface coverages. In particular, the ideal two dimensional gas model for mobile adsorption was considered to he impracticable for cornoarison with real systems. The isotherm data used in these buthors' calculations are impossible to obtain a t sufficientlv low coverages to validate any conclusions hased nn this model as to the mobility of the surface phase. However, the criteria expressed by Everett (6) for the acceptable use of the ideal two-dimensional gas model of non-localized adsorption are satisfied in the gas-solid chromatographic method in which adsorbate concentrations are so low that the system is operating in the linear region of Henry's law isotherm. ~~
~
~
.~~~ ~
~~~~~~~~
~~~
~
Non-Localized Adsorption Model The enuilibrium constant for the process: gas (3d, p atm) + gas(2d,
where p is the equilibrium pressure uf the thrcr dimensional pUia the standard pressure, I' is the ndsurhiite conccn&at&. and P i s the standard adsorbate concentration based on the choice of the standard surface state. The standard surface state for non-localized adsorotion. . . as proposed by deBoer and Kruyer (4) is the ideal two dimensional eas in which the adsorbedmolecules are the same distance apart as in the three-dimensional gas phase; that is, cm a t 0°C and 1atm pressure. From the two di3.34 X mensional ideal gas law, the area per mole of adsorbate is directly proportional to the temperature and inversely proportib"al the two dimensiona&ressure, arid so the standard area per mole of adsorbate a t any temperature is given by :as,
~
T .273
AsU= A%( -
.
A?= 2.4577. T 10Rem2molF1
(3)
(4)
where T is the average temperature of the study. T h e reciprocal of Astfis the standard surface concentration,
F"4.069 X 10-9/T mol (5) ~ by eqn. (2) is now The equilihrium constant, K r , p ,defined transformed into P.T K P . ~=. ~ (6) p .4.069 X By definition of P and the ideal gas law this expands to
where the other equilibrium constant, K,,,,, is defined by Km.,c,~ = n,/A (9) in which A is the surface area of the adsorbent in cm2. In the previous paper (1) it was shown that the specific retention volume of the adsorbate (i.e. the retention volume per , gram of adsorbent) a t the column temperature, V g ( ~ ,is) equal to this equilibrium constant, i.e., Vg(~.i= K n , c . ~ (10) Some of the previous authors (8-10) have overlooked this necessary involvement ofg, the weight of the adsorbent, in this definition. The standard free energy change is related to the equilihrium constant in terms of pressure,
is expressed as
802 1 Journal of Chemical Education
~~~
where Azt is the area covered by a mole of two dimensional gas a t O°C and 1atm pressure (= N.rz). Hence
r mol cm-3
or, so that K , may be dimensionless, as
~
and
The specific retention volume reduced to O°C, V g ( m Iis defined by
V,ww
273 .T,
=
Adsorption of Cyclobutane on Zeolites pretreated at 400°C, in temoerature ranae 493°-5230 K. Heat of
(14)'
Adsorption kJmol-'
-AS? Entropy of Adsorption, JK-' mol-' Non-localized Model Localized Model (stat. mech.) (apt.) (stat. mech.) (expl.)
and
Adsorbent
The plot of In Vg(273)against l/Tc is a straight line over the temperature range involved, the slope of which is directly vrooortional to the standard enthaluv . . . . change, and the intercept
