$9\mathrm{.}14$ Figure $9\mathrm{.}58$a shows a fow of the top trays of a conventionally arranged fractionator. It has been

suggested that a richer distillate might be obtained by the scheme shown in Fig. $9\mathrm{.}58b,$ because of

the richer reflux to tray $1.$ All trays are theoretical. The condenser is a total condenser, delivering

liquid at the bubble point in both cases. For both arrangements, $\frac{L_0}{D}=\frac{L_0}{L_R}=1\mathrm{.}0.$

$($a$)$ For a binary mixture which in cvery respect follows the McCabe$-$Thiele simplifying

assumptions, sketch fully labeled $Hxy$ and $xy$ diagrams for the scheme of Fig. $9\mathrm{.}58b.$ Mark on the

$Hy$ diagram the location of every stream on Fig. $9\mathrm{.}58b$ and the required difference points. Show

construction lines and tie lines.

$($b$)$ Prove that for all otherwise similar circumstances the scheme of Fig. $9\mathrm{.}58b$ in fact delivers a

leaner distillate than that of Fig. $9\mathrm{.}58$a$.$

Figure $9\mathrm{.}58$ Arrangements for Prob. $9\mathrm{.}14.$