A large value of relative volatility ajk implies that components j and k can be easily separated in a distillation column. Values of ajk close to 1 imply that the separation will be very difficult, requiring a large number of trays and high energy consumption.
For binary systems relative volatility of light to heavy component is simply called a:
where x and y are mol fractions of light component in the liquid and vapor phases respectively. Rearrangement of equation (2.18) leads to the very useful y-x relationship that can be employed when a is constant in a binary system.
Figure 2.14 sketches y versus x lines for various values of a. The larger the relative volatility a, the fatter is the equilibrium curve. For an ideal (Raoulfs law) binary system, a can be expressed very simply as the ratio of the vapor pressures of light and heavy components.
If the temperature dependence of the vapor pressure of both components is the same, a will be independent of temperature. In other words, relative volatility is constant if the vapor pressure lines are parallel in a In P versus 1 /T plot. This is true for many components over a limited temperature range, particularly when the components are chemically similar. Distillation columns are frequently designed assuming constant relative volatility because it greatly simplifies the vapor—liquid equilibrium calculations. Relative volatilities usually decrease somewhat with increasing temperature in most systems.
Relative volatility on x-y diagram
For multicomponent systems, applying the basic definition [equation (2.17)] and rearranging lead to the following explicit relationship between any vapor composition^ and given liquid compositions (x/s) and relative volatilities (ay's).
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