where B i is called the insertion parameter, ρ ρ i is the number density of species i , a i is the activity of species i , k B is the Boltzmann constant, and T is temperature, and ψ ψ is the interaction energy of an inserted particle with all other particles in the system. The average is over all possible insertions. This can be understood conceptually as fixing the location of all molecules in the system and then inserting a particle of species i at all locations through the system, averaging over a Boltzmann factor in its interaction energy over all of those locations.