where ζ ζ L is the partition function of a single adsorbed molecule, N S is the number of adsorption sites (both occupied and unoccupied), and N A is the number of adsorbed molecules which should be less than or equal to N S . The terms in the bracket give the total partition function of the N A adsorbed molecules by taking a product of the individual partition functions (refer to Partition function of subsystems). The 1 / N A ! factor accounts for the overcounting arising due to the indistinguishable nature of the adsorbates. The grand canonical partition function is given by