The Phase Rule. Duhems Theorem

An isolated system consisting of liquid and vapor phases in intimate contact eventually reaches a final state wherein no tendency exists for change to occur within the system. The temperature, pressure, and phase compositions reach final values which thereafter remain fixed. The system is in equilibrium. Nevertheless, at the microscopic level, conditions are not static. The molecules comprising a phase at a given instant are not the same molecules that later occupy the same phase. Molecules with sufficiently high velocities near the interface overcome surface forces and pass into the other phase. However, the average rate of passage of molecules is the same in both directions, and no net interphase transfer of material occurs. 

The three most common measures of composition are mass fraction, mole fraction, and molar concentration. Mass or mole fraction is defined as the ratio of the mass or number of moles of a particular chemical species in a mixture or solution to the total mass or number of moles of the mixture or solution  

Molar concentration is defined as the ratio of the mole fraction of a particular chemical species in a mixture or solution to its molar volume  

This quantity has units of moles of / per unit volume. For flow processes convenience suggests its expression as a ratio of rates. Multiplying and dividing by molar flow rate ri gives  

The molar mass of a mixture or solution is, by definition, the mole-fraction-weighted sum of the molar masses of all species present  

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