3. An ideal monoatomic gas is at an equilibrium with adsorbent surface that has N possible adsorption sites. An adsorbed atom has an energy of 0 relative to its free gaseous state, but there are no interactions between the adsorbed atoms. Use the grand canonical ensemble to calculate the fraction of surface sites that have adsorbed atoms as a function of the gas pressure (p) and temperature (T). (This is called the Langmuir adsorption isotherm.) Follow these steps: a) Calculate the grand canonical partition function for the adsorbed atoms, taking into account the correct degeneracy of each energy state: A state with n adsorbed atoms has energy n0 and there are N!/[n!(Nn)!] configurations with this energy. b) Use to determine the average number of adsorbed atoms , and thus the fraction =/N in terms of the temperature =1/kBT, the chemical potential and 0. c) Since the adsorbed atoms are at equilibrium with the ideal gas made from the same atoms, the chemical potential is just that of an ideal gas at the same p and T. Use the grand canonical partition function of a classical ideal gas derived in lecture to calculate<><>