A distillation column is separating \(100 \mathrm{~mol} / \mathrm{s}\) of a \(30 \mathrm{~mol} \%\) acetone, \(70 \mathrm{~mol} \%\) methanol mixture at atmospheric pressure. The feed enters as a saturated liquid. The column has a total condenser and a partial reboiler. We desire a distillate with an acetone content of \(72 \mathrm{~mol} \%\), and a bottoms product with \(99.9 \mathrm{~mol} \%\) methanol. A reflux ratio of 1.25 the minimum will be used. Calculate the number of ideal stages required and the optimum feed location. VLE for this system is described by the modified Raoult's law, with the NRTL equation for calculation of liquid-phase activity coefficients, and the Antoine equation for estimation of the vapor pressures.

The Antoine constants for acetone (1) and methanol (2) are ( \(P_{i}\) in \(\mathrm{kPa}, T\) in \(\left.{ }^{\circ} \mathrm{C}\right): A_{1}=14.3916, B_{1}=2795.92, C_{1}=230.0 ; A_{2}=16.5938, B_{2}=3644.30, C_{2}=239.76\). The NRTL constants are \(b_{12}=184.70 \mathrm{cal} / \mathrm{mol}, b_{21}=222.64 \mathrm{cal} / \mathrm{mol}, \alpha=0.3084\) (Smith et al., 1996).