Mixtures of $1-$butanol $+$ water form a heteroazeotrope. A feed of $1-$butanol $+$ water at $F=$

$400\frac{\text{m}\text{o}\text{l}}{\text{m}\text{i}\text{n}},z_{F,\text{w}\text{a}\text{t}\text{e}\text{r}}=0\mathrm{.}4,T_{\text{F}\text{e}\text{e}\text{d}}=293K$ is to be distilled at $1$atm in two columns to provide product

streams with $x_{B,\text{I}\text{,}\text{w}\text{a}\text{t}\text{e}\text{r}}=0\mathrm{.}01$ and $x_{B,II,\text{w}\text{a}\text{t}\text{e}\text{r}}=0\mathrm{.}999.$ The feed enters column I. A decanter is used for

the condensate from the columns and with the butanol$-$rich phase refluxed to Column I and the water$-$rich

phase refluxed to Column II$.$ The boilup in each column will be saturated vapor. The decanter effluents are

at $340K.$ This problem uses the notation from the handwritten colorful handout on heterogeneous

distillation. Column I is to operate at $R_{oI}^{\text{'}}=\frac{L_o}{B_{II}}=1\mathrm{.}5R_{oI,\text{m}\text{i}\text{n}}^{\text{'}}$ and column II is to operate at that

corresponds to the pinch point for $\{$:$(\frac{L_o}{V_1}{)}_{II}).$

a$.$ Sketch the column configuration and determine the flowrates of the bottoms $B_{\text{I}}$ and $B_{II}.$

b$.$ Determine the $q_F$ and the equation for the feed line for column I.

c$.$ Determine the composition of the reflux streams, the degrees of subcooling and $q_{RI}$ and $q_{\text{R}\text{I}\text{I}}.$

d$.$ The pinch condition in Column I is determined by the intersection of the external operating line

with the equilibrium line at the composition of $x_{RI}.$ For the first step of the calculation, rearrange

the external operating line equation for $R_{OI}^{\text{'}}$ in terms of $x_{\text{B}\text{I}\text{I}},y_1$ and $x_{RI}.$ Then use the plot to read

the value of $y_1$ from the equilibrium curve at $x_{RI}$ and calculate $R_{ol,\text{m}\text{i}\text{n}}^{\text{'}}.$

e$.$ Using the specified $R_o^{\text{'}}=1\mathrm{.}5R_{o,\text{m}\text{i}\text{n}}^{\text{'}}$ show your calculations to determine the internal flows in

column I and summarize in tabular form $L_o,V_1,L,V\frac{,}{b}ar(L)\frac{,}{b}ar(V).$

f$.$ For column I, plot the internal stripping line, feed line, and rectifying line. Calculate the

composition at the top of the column using the external operating line and determine the number

of stages needed for column I.

g$.$ For column II$,$ use the plot to determine the pinch value of $(\frac{L_o}{V_1}{)}_{II}.$ From this value determine

the corresponding boilup.

h$.$ Using $1\mathrm{.}3$ times the value of boilup found in part $g,$ determine the internal flows in column II$.$

i$.$ Determine the equations for the internal and external operating lines for column II$.$ Plot the

operating lines and determine the number of stages needed.