A tractable example of a non-ideal solution that allows analytical evaluation of thermodynamically interesting functions and verification of various relationships normally derived in physical chemistry class is presented. A partition function representing a mixture of hard spheres that suffer from non-ideality is used to recover an equation of state, the Gibbs and Helmholtz free energies, the partial molal volumes, and the chemical potentials. Euler's theorem for the volume and the Gibbs energy are demonstrated.
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