Question

Problem 2 Calculate the probability of adsorption of an ideal gas at temperature Ton the surface with Nindependent (and distinguishable) adsorption sites that are either unoccupied with energy 0, or singly occupied with energy e. The chemical potential of the gas is .

Answer 1

Sola Calculatin el curand Canonical Partition function : since gas is ideal gas, hence we can say that the binding sites are "sparsely enough distributed over the surface that they do nal- dimectly interact” and so we can use the relation len Zu: is the single binding site partition sum , Tran Forfitim This, we can write down the grand canonical sum, n20 na 1 no olu pied stute singly ocupied state

Zu= { 1 + 7 PCE-b)]^{; peter Calculation of the curand Canonical Jotential : J = ~ KBT. ln Za >Je- Nen (it ē pleno) JE - NKET in (it ē BLE-4) -(2) Calculatim of The Mean number of adsorbed molecules fece J: Here we need to make use of the thermodynamic Melation between the grand canonical potential , the chemical potential and Jauncle number: (ny z op > Oxy = 2 = --west. min (en64 78len * <m} = NKT Le [pé plesom (ny = NESTP B e B (E-M) N lit e Bleon] + PCEM ? Zn), 2 NC B CEW /tē PCE-A)

ēBLE-4) (n)=N. 1 + ē B CE-41) probability is <ny e B (E-M) N te B (E-M) IP a. - B(E-M Itē BCE-M