Shen and Smith [Ind. Eng. Chem. Fundam., 7, 100-105 (1968)] measured equilibrium-adsorption isotherms at four different temperatures for pure benzene vapor on silica gel, having the following properties: surface area = 832 m²/g, pore volume = 0.43 cm³/g, particle density = 1.13 g/cm³, and average pore diameter = 22 A.

The adsorption data are as follows:

(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 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 this value compare to the heat of vaporization (condensation) ofbenzene?

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Moles Adsorbed/g Gel x 105 Partial Pressure of Benzene, atm 70°C 110°C 90°C 130°C 5.0 x 10-4 14.0 6.7 2.6 1.13 1.0 x 10-3 22.0 11.2 4.5 2.0 2.0 x 10-3 34.0 18.0 7.8 3.9 5.0 x 10-3 68.0 33.0 8.6 17.0 1.0 x 10-2 2.0 x 10-2 88.0 27.0 51.0 16.0 78.0 42.0 26.0