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The law of equipartition of energy (one of the principal results of statistical mechanics): the average energy associated with every degree of freedom is

Chemical potential of a dilute solution, the chemical energy is expressed in terms of free energy:

The free energy is composted of water free energy, solute energy, and a mixing entropy term due to possibility of rearranging the solute molecules:


To calculate the mixing entropy (configurational entropy), we first examine the number of ways of distributing the water and solute molecules. Using the lattice model, we have:

Chemical potential of a dilute solution determine the entropy is obtained from Boltzmann entropy formula:

Chemical potential of a dilute solution total free energy:

Chemical potential within a dilute solution:

In general, the chemical energy is related to the logarithmic function of solute concentration:

