The significant structure theory of liquids has been applied to the partially miscible system of the $O_3-O_2$ mixture which exhibits partial miscibility in the temperature range from -195.5 ℃ to -179.9 ℃.
The thermodynamic condition for phase separation is the following equation:
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The partition function of the binary liquid mixture are constructed in a manner that random mixing is assumed and the whole form of the partition function of the mixture is like the one-fluid form and the parameters appearing in this theory are used like the equation originally proposed by van der Waals.
We calculated the coexistence curve of the $O_3-O_2$ varing the molefractions to find the temperature at which two liquids are separated.
The agreement between the theory and experiment is quite satisfactory.