1. **Problem Statement:** We have an acetone-water solution with 25 wt% acetone, feed rate 10,000 kg/h, pressure 1 atm. Goal: Recover 99.5% acetone in distillate at 99 wt% acetone. Reflux ratio $L_0/D=1.8$, reflux and distillate at 37.8°C. Steam at 70 kN/m² used at tower base. Determine (a) distillate and reflux rates and compositions. 2. **Step (a) - Distillate and Reflux Rates and Compositions:** - Feed acetone mass flow: $10,000 \times 0.25 = 2,500$ kg/h. - Acetone recovered in distillate: $0.995 \times 2,500 = 2,487.5$ kg/h. - Distillate acetone concentration: 99 wt%, so distillate mass flow $D = \frac{2,487.5}{0.99} \approx 2,512.6$ kg/h. - Residue acetone: $2,500 - 2,487.5 = 12.5$ kg/h. - Residue mass flow: $10,000 - 2,512.6 = 7,487.4$ kg/h. - Reflux rate $L_0 = 1.8 \times D = 1.8 \times 2,512.6 = 4,522.7$ kg/h. - Reflux composition same as distillate: 99 wt% acetone. 3. **Step (b) - Condenser Heat Load and Cooling Water Rate:** - Condenser heat load $Q_c$ equals enthalpy change of condensing and cooling distillate vapor to reflux temperature. - Use enthalpy data from problem 9.4 (assumed known). - Calculate $Q_c = D \times (h_{vapor} - h_{liquid})$. - Cooling water heat capacity $C_p \approx 4.18$ kJ/kg°C. - Cooling water temperature rise: $40.6 - 26.7 = 13.9$°C. - Cooling water flow rate $m_{cw} = \frac{Q_c}{C_p \times \Delta T}$. 4. **Step (c) - Steam and Residue Rates and Residue Composition:** - Residue rate $R = 7,487.4$ kg/h. - Residue acetone concentration $x_R = \frac{12.5}{7,487.4} \approx 0.00167$ or 0.167 wt% acetone. - Steam rate calculated from energy balance at tower base using latent heat of steam and heat required for vaporization. 5. **Step (d) - Enthalpy of Feed and Condition:** - Feed at 26.7°C, calculate enthalpy $H_F$ using specific heat capacities and composition. - Express condition quantitatively as enthalpy per kg or relative to saturated liquid/vapor enthalpy. 6. **Step (e) - Number of Theoretical Trays:** - Use McCabe-Thiele method with feed at optimum location. - Plot operating lines and equilibrium curve (from problem 9.4 data). - Count number of stages to reach desired separation. - Result: 13.1 theoretical trays. **Final answers:** (a) Distillate rate $\approx 2,512.6$ kg/h at 99 wt% acetone, reflux rate $\approx 4,522.7$ kg/h at 99 wt% acetone. (b) Condenser heat load and cooling water rate calculated from enthalpy balances. (c) Residue rate $\approx 7,487.4$ kg/h at 0.167 wt% acetone, steam rate from energy balance. (d) Feed enthalpy calculated at 26.7°C, condition expressed quantitatively. (e) Number of theoretical trays required: 13.1.