Shen and Smith [Ind. Eng. Chem. Fundam., 7, 100–105 (1968)] measured equilibrium-adsorption isotherms at four temperatures for benzene vapor on silica gel having the following properties: S_g = 832 m²/g, V_p = 0.43 cm³/g, ρ_p = 1.13 g/cm³, and average d_p = 22 A. The adsorption data are:

(a) For each temperature, obtain a best fit of the data to 

(1) Linear, 

(2) Freundlich, and 

(3) Langmuir isotherms. Which isotherm(s), if any, fit(s) the data reasonably well? 

(b) Do the data represent less than a monolayer of adsorption? 

(c) From the data, estimate the heat of adsorption. How does it compare to the heat of vaporization (condensation) of benzene?

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Partial Pressure of Benzene, atm 5.0 x 10 1.0 × 10-³ 2.0 × 10-3 5.0 x 10-3 1.0 x 10 2.0 × 10-² 70°C 14.0 22.0 34.0 68.0 88.0 Moles Adsorbed/g Gel x 105 90°C 6.7 11.2 18.0 33.0 51.0 78.0 110°C 2.6 4.5 7.8 17.0 27.0 42.0 130°C 1.13 2.0 3.9 8.6 16.0 26.0