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**Fugacity-based phase equilibrium criterion for pure component system**

The general criterion of thermodynamic equilibrium has been defined by eqn. 6.38. Applying it to, for example, a vapour (V) and liquid (L) system of a pure component ‘i’ we have:

......(6.91)

**However, for a pure component system: **

**Thus:** ......(6.92)

Thus, using eqn. 6.91 and 6.92 we have:

......(6.93)

The above equation may be generalized for any other types of phases. However, the eqn. 6.93 is rendered more easily applicable if the chemical potential is replaced by fugacity. Thus integrating eqn. 6.86 between vapour and liquid states of a pure component:

......(6.94 & 6.95)

Now applying eqn. 6.93 to 6.95 it follows

**Or:**

......(6.96)

In eqn. 6.86 indicates the value for either saturated liquid or saturated vapor, this is because the coexisting phases of saturated liquid and saturated vapor are in equilibrium. Since under such condition the pressure is we can write:

Thus, employing eqn. 6.86 again, it follows:

......(6.97)

Both eqns. 6.93, 6.96 and 6.97 represent equivalent criterion of vapor/liquid equilibrium for pure species.

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