Assignment
A bulk gas is in contact with a "sticky" surface which has A sites available for molecular adsorption. Each gas molecule lowers its energy by an amount ε if stuck to one of the A surface sites. (Note ε > 0 so the net energy change is - ε .) Each site can only contain at most 1 molecule and please DO NOT assume that the surface molecular density is small. (You cannot use the diluteness assumption.) The chemical potential of the gas is µ and the temperature of this system is T.
1) You may assume the chemical potential and temperature of the surfaceadsorbed phase equals the bulk chemical potential µ and T. What does this rely on? (Hint : Think about adsorption-desorption timescales.)
2) Calculate the grand potential ?(T,A,µ) for the surface. Show that kT e-?/kT can be expressed as a summation over N (N=0∑ ..... ) and show that this sum is dominated by a particular value of N.
3) Express the surface density of molecules (the fraction of sites occupied by molecules) as a function of ε, µ and T.