1. **Problem Statement:** Calculate per mole of feed the flow rates of all streams, the relative sizes of the two condenser heat loads, and the relative sizes of the two vaporizer heat loads in the given binary distillation system with intermediate condenser and reboiler. 2. **Key Assumptions and Formulas:** - The system follows McCabe-Thiele assumptions: constant molar overflow, straight and parallel operating lines. - External reflux ratio $R = \frac{L_0}{D} \approx 1.0$. - Feed is liquid at bubble point. - Total condenser and total vaporizer assumptions imply liquid and vapor streams are saturated at bubble and dew points respectively. - Heat loads are proportional to latent heats times molar flow rates. 3. **Define Variables:** - $F$: feed flow rate (moles, set to 1 mole for per mole basis). - $D$: distillate flow rate. - $L_0$: reflux liquid flow rate at top. - $L'$: liquid flow rate in the middle section. - $L$: liquid flow rate in the bottom section. - $G$: vapor flow rate in the bottom section. - $G'$: vapor flow rate in the middle section. - $S$: vapor flow rate from reboiler. 4. **Given:** - $R = \frac{L_0}{D} = 1 \Rightarrow L_0 = D$. - Total feed $F = 1$ mole. - Since $D + B = F = 1$, and assuming no losses, $B = 1 - D$. 5. **Flow Rates:** - From reflux ratio, $L_0 = D$. - Distillate $D$ and bottoms $B$ sum to 1 mole. - Vapor and liquid flows in column sections relate by mass balances: - Top section: $G = L_0 + D = 2D$. - Middle section: $G' = L' + D'$ (to be determined from feed and internal balances). - Bottom section: $S = L + B$. 6. **Heat Loads:** - Condenser heat loads $Q_C$ and $Q_E$ proportional to condensation of vapor streams $G$ and $G'$. - Reboiler heat loads $Q_B$ and $Q_S$ proportional to vaporization of liquid streams $L$ and $L'$. - Relative sizes found by ratios of molar flow rates times latent heat (assumed constant). 7. **Calculations:** - Since $R=1$, $L_0 = D$. - Assume $D = d$, then $L_0 = d$, $F=1$, $B=1-d$. - Vapor flow at top $G = L_0 + D = 2d$. - Intermediate condenser and reboiler flows $L', G'$ and $L, G$ determined by internal balances and feed location. 8. **Summary:** - Flow rates per mole feed: - $D = d$ - $L_0 = d$ - $B = 1 - d$ - $G = 2d$ - $L', G', L, G, S$ depend on feed stage and internal balances. - Relative condenser heat loads proportional to $G$ and $G'$. - Relative reboiler heat loads proportional to $L$ and $L'$. **Final answer:** Per mole of feed, the distillate and reflux flows are equal ($D = L_0$), vapor flow at the top is twice the distillate ($G = 2D$), bottoms flow is $1-D$, and intermediate flows depend on feed stage. The condenser heat loads are proportional to vapor flows condensed ($Q_C \propto G$, $Q_E \propto G'$), and reboiler heat loads proportional to liquid vaporized ($Q_B \propto L$, $Q_S \propto L'$). Exact numerical values require feed composition and stage data.