One hundred moles of feed, containing 50 percent A (more volatile component), are batch distilled to produce 60 moles of distillate at one atmosphere system pressure. Equilibrium data of this binary mixture can be generated using relative volatility value of 2.16. Calculate composition of the distillate collected and residue remained.
Solution:
For our case, D is 60, and W is F minus D or 40 moles. Batch distillation is not a steady state
process as the batch is constantly changing in composition and volume. The Raleigh equation is used to solve the
pot composition as follows: log of F over W is equal to integral of the
function one over (y minus x) between the limits of xW and xF. When y can be estimated using relative
volatility, alpha, then this integral results into a non-linear equation given
as: log of F over W is equal to one over (alpha minus one) times (log of xF
over xW minus alpha times log of ((one minus xF) over
(one minus xF)).
Plugging in the values, F, W, xF and alpha (using
trial and error technique), one can find xW to be 0.328. Amount vaporized is F time xF
minus W times xW, The distillate composition is found to be
0.615.