## YIl x

where a = relative volatility y = mole fraction of light component or key in vapor phase

This relationship is usually rearranged into

* 1 + (a - l)x and used to calculate vapor-phase compositions in equilibrium with a particular liquid-phase composition (see Chap. 1),

Refer to Chap. 3 for a more detailed discussion of this nomenclature and its usage.

### 5.1 Existing Systems 5.1.1 Simple distillation

In simple distillation, the vapor leaving the still passes into a total condenser, and the liquid leaving the condenser passes into a product receiver. No reflux is returned to the still. The first vapor which leaves the still is richer in the lighter compo nent than the liquid originally present because the still acts as a single theoretical separation stage. As the process continues, the material remaining in the still becomes increasingly depleted in the lighter component, so the vapor leaving the still progressively contains larger amounts of the "heavy" component. Thus, the "product" in the receiver gets diluted with material which continuously becomes heavier.

Lord Rayleigh (15) first analyzed such a system mathematically. With no reflux returning to the still, the rate at which the more-volatile component leaves the still is equal to the rate of change of composition in the still.

where dV = vapor rate, moles/h W = total moles in still

Differentiating Eq. (5.8),

Rearranging

Integrating this equation gives

0 0