Q1(h). BET equation and its terms

Answer in brief

p/[v(p° − p)] = 1/(vm c) + [(c − 1)/(vm c)](p/p°) (Brunauer, Emmett and Teller, 1938: multilayer physical adsorption).

Key points

• p: equilibrium pressure of the adsorbate; p°: saturation vapour pressure of the adsorbate; p/p° = relative pressure.
• v: volume of gas adsorbed at pressure p (at STP) per gram; vm: volume needed to cover the surface with a complete monolayer.
• c: BET constant, c ≈ e^((E₁ − EL)/RT); E₁ = heat of adsorption of the first layer, EL = heat of liquefaction.
• Model: many layers, the first held by E₁, higher layers like a liquid; one layer only ⇒ Langmuir isotherm.
• p/[v(p° − p)] against p/p° is a straight line; slope s, intercept i ⇒ vm = 1/(s + i), c = s/i + 1.