to apply Eq. (61) to calculate Ki at middle pressure.
As mentioned above, the equilibrium ratio K; (or phase equilibrium constant) is an important physical quantity in solving four types of problems about P-T-x-y relation. Besides, for special distillation processes, especially with separating agents, we should pay more attention to another physical quantity, i.e. relative volatility (or separation factor). The magnitude of relative volatility can be used as the index of whether the separation process can occur or which one among all the possible separating agents is the best. For vapor-liquid two phases, relative volatility a, , as a dimensionless physical quantity, is defined as
which holds for either binary or multi-component systems. For the multi-component system, just one heavy key component and one light key component are investigated. In general, in a same distillation column, the heavy components are obtained as the bottom product, whilst the light component as the top product. The heavy and light key components are those which are the most difficult to be separated among the multi-component mixture. In Eq. (62), K: is often relative to the light component, Kl relative to the heavy component. In other words, a,. is always equal or larger than unity. For special distillation processes, the meaning of relative volatility is:
(1) If at is equal or close to unity, then the separation process isn't worthwhile to be carried out. Otherwise, the investment on equipment and operation may be unimaginable. It is generally required that a, > 1.20 at least.
(2) The larger a, is, the more easily the separation process will be carried out. So, for special distillation processes with separating agents, we prefer to select the separating agent which has the largest a .. Of course, under this condition, other factors such as price, toxics, chemical stability and so on, should be considered.
From the definition of au and Eqs. (35) and (61), it is deduced that
at the low pressure, and
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