Question

Consider a simple model of dimerization. Two molecules are present on a cubic three-dimensional lattice with number of lattice sites V. When molecules sit next to each other, there is a net favorable energy of -?. The system is maintained at a constant temperature T. Neglect edge effects in the lattice, i.e., assume periodic boundary conditions. (a) How many microstates are there in total, and how many have the two particles as neighbors? (b) What is the canonical partition function? (c) What is the absolute probability of a single microstate that has the two particles as neighbors? (d) What is the total probability of seeing a dimer, in any microstate? Express your answer using the concentration of particles, c = 2/V, instead of V.

          Consider a simple model of dimerization. Two molecules are present on a cubic three-dimensional lattice with number of lattice sites V. When molecules sit next to each other, there is a net favorable energy of -?. The system is maintained at a constant temperature T. Neglect edge effects in the lattice, i.e., assume periodic boundary conditions.
(a) How many microstates are there in total, and how many have the two particles as neighbors?
(b) What is the canonical partition function?
(c) What is the absolute probability of a single microstate that has the two particles as neighbors?
(d) What is the total probability of seeing a dimer, in any microstate? Express your answer using the concentration of particles, c = 2/V, instead of V.

Consider a simple model of dimerization. Two molecules are present on a cubic three-dimensional lattice with number of lattice sites V. When molecules sit next to each other, there is a net favorable energy of -?. The system is maintained at a constant temperature T. Neglect edge effects in the lattice, i.e., assume periodic boundary conditions.
(a) How many microstates are there in total, and how many have the two particles as neighbors?
(b) What is the canonical partition function?
(c) What is the absolute probability of a single microstate that has the two particles as neighbors?
(d) What is the total probability of seeing a dimer, in any microstate? Express your answer using the concentration of particles, c = 2/V, instead of V.

Added by Sandra H.

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