We are testing a new packing for separation of benzene and toluene. The column is packed with \(3.5 \mathrm{~m}\) of packing and has a total condenser and a partial reboiler. Operation is at \(760.0 \mathrm{~mm} \mathrm{Hg}\), where Perry et al. (1963, p. 13-3) report that \(\alpha\) varies from 2.61 for pure benzene to 2.315 for pure toluene, and Doherty and Malone (2001, p. 39) report the range as 2.40 to 2.27 . At total reflux, we measure a benzene mole fraction of 0.987 in the condenser and 0.008 in the reboiler liquid. Find HETP:

a. Using \(\alpha=2.27\).

b. Using \(\alpha=2.61\).

c. Using a geometric average \(\alpha\) based on all four values.

Use either the Fenske equation or a McCabe-Thiele diagram.