Question

Consider a gas in equilibrium with a surface. The surface can adsorb the gas molecules onto any of M independent, distinguishable sites (distinguishable because the binding sites are localized to specific parts of the surface). The molecular partition function for an adsorbed molecule is q(T) ≡ exp[−β A_surface].

a) Assume that the adsorbed molecules are independent and use the canonical ensemble for N adsorbed molecules to compute the chemical potential for the molecules on the surface. Remember to include the number of ways to adsorb the molecules onto the surface. Also remember that the molecules themselves are indistinguishable.

b) Use our results for an ideal gas to compute the chemical potential in the gas.

c) If the gas and surface phases are in equilibrium, how does the fractional coverage, N/M, depend on the pressure in the gas. Your expression is known as the Langmuir adsorption isotherm.

Answer 1