In order to separate a binary mixture using distillation process, there must be a differences in volatilities of the components. The greater the difference, the easier it is to do so. A measure for this is termed the relative volatility.
We define volatility of component-i as: partial pressure of component-i divide by mole fraction component-i in liquid
For a binary mixture of A and B, therefore:
Volatility of A = pA / xA
Volatility of B = pB / xB
where p is the partial pressure of the component and x is the liquid mole fraction.
Relative volatility is the ratio of volatility of A (MVC) over volatility of B (LVC):
Relative volatility is therefore a measure of separability of A and B.
Since xB = 1 - xA , we have:
Replace with pA = yA PT ; pB = ( 1 - yA ) PT so as to express everything in MVC:
Dropping subscript 'A' for more volatile component, and simplifying: we obtain the equation for relative volatility:
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When a = 1.0, no separation is possible: both component-A and component-B are equally volatile. They will vapourise together when heated. Solving the above equation for a = 1.0, we obtain: y = x.
The larger the value of a above 1.0, the greater the degree of separability, i.e. the easier the separation. Recall that when a system has reached equilibrium, no further separation can take place - the net transfer rate from vapour to liquid is exactly balanced by the transfer rate from liquid to vapour. Therefore, separation by distillation is only feasible within the region bounded by the equilibrium curve and the 45o diagonal line. From the equilibrium curve, we see that the greater the distance between the equilibrium curve and the diagonal line (where y = x), the greater the difference in liquid and vapour compositions and therefore the easier the separation by distillation. This is shown in the Figure below:
Click here for a special case of constant relative volatility.
However, it is important to note that in general, relative volatility of a mixture changes with the mixture composition. Click here for more information.
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