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NITROGEN ISOTHERM AND SOLID SURFACE AREA      87

            versally accepted standard method for measurement of surface area is the
            method of Brunauer, Emmett, and  Teller (BET) (Brunauer et al., 1938;
            Adamson, 1967; Gregg and Sing, 1982), in which one determines the adsorp-
            tion isotherm of any of a number of suitable vapor adsorbates (e.g., N 2) on the
            solid (adsorbent) of interest. Suitable adsorbates must be chemically inert to
            the solid, not subject to molecular sieving, and confined to the exterior of the
            solid (i.e., they must exhibit no significant penetration or site specific interac-
            tion with the solid). The BET model [Eq. (4.7)] calculates the monolayer
            capacity (Q m) from the adsorption isotherm; the surface area per adsorbate
            molecule (a m) is estimated from the liquid density as


                                                    23
                                          .
                                     a m = 109 ( M d N)                    (6.1)
                                                 l
            where M is the molecular weight of the adsorbate, d l is the adsorbate liquid
                                                                 3
            density, and N is the Avogadro number. Using d l = 0.808g/cm for liquid N 2 at
                                      2
            77K gives  a m = 16.2  ¥ 10 -20 m per N 2 molecule. The solid samples prior to
            adsorption studies are usually outgassed under vacuum (or under an inert gas)
            at some selected temperature.
              Although N 2  vapor at the liquid N 2 boiling point of 77K is the adsorbate
            most frequently employed for surface-area determination, the method is by
            no means limited to N 2, and a wide variety of other suitable adsorbates (e.g.,
            krypton) produce reasonably consistent results on the same solid. The surface
            area of a solid, considered to be the solid–gas or solid–vacuum interfacial area,
            which is external to the material, is assumed both to preexist and to be un-
            affected by the measurement. Any vapor that may potentially react with or
            penetrate into the solid is not appropriate for surface-area determination. The
            surface area is therefore an intrinsic property of the solid; that is, within the
            precision of the method, it should be independent of the choice of acceptable
            adsorbates (Brunauer et al., 1938). There has been a serious confusion in the
            earlier soil-science literature about the surface areas of soils and clays to which
            we shall attend later.
              We now consider the adsorption data of N 2 vapor at liquid N 2 temperature
            (77K) on selected natural solids given in Table 6.1. The solid samples exam-
            ined were outgassed under a stream of helium at temperature ranging from
            100°C, as for activated carbon, to 150 to 200°C for the rest. Plots of the N 2 -
            vapor uptake (Q) versus N 2 relative pressure (P/P°) for relatively pure silica
            (Alfa Aesar Co.), alumina (calcined, Alcoa Co.), goethite (Ward’s Natural
            Science), Georgia kaolinite (KGa-2), K-saturated Arizona montmorillonite
            (K-SAz-1), Ca-saturated Arizona montmorillonite (Ca-SAz-1), and activated
            carbon (CAL grade, Calgon Co.) are shown in Figures 6.1 to 6.3. For the three
            mineral oxides and the two clays, the N 2 isotherms are type II, whereas for
            activated carbon the isotherm is more like type IV, of the Brunauer classifi-
            cation. Among the mineral oxides and clays, certain differences are visible with
            respect to their (concave-downward) curvatures at low P/P° and the related
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