Figure 9.46 represents the flow sheet for the recovery of acetone from air. All compositions are on a weight basis. Make a material balance and determine the quantities of the foll... Figure 9.46 represents the flow sheet for the recovery of acetone from air. All compositions are on a weight basis. Make a material balance and determine the quantities of the following streams: (a) Water added in the absorber (b) Acetone-free air leaving the absorber (c) Aqueous solution of acetone leaving the absorber (d) Distillate product (e) Bottom product. Read more

Steps to Solve

1. Define Input Streams We start by identifying the incoming streams into the system. The air entering the absorber consists of 99.5% air and 0.5% water, with a total flow of 1400 kg/h.

2. Calculate Incoming Acetone Determine the amount of acetone present in the incoming gas. Since the gas is composed of 3% acetone:

   $$ \text{Acetone in gas} = 0.03 \times 1400 , \text{kg/h} = 42 , \text{kg/h} $$

3. Calculate Air Flow Leaving the Absorber Since we need to find the acetone-free air leaving the absorber, we recognize that the amount of air does not change in this step, which is still 1400 kg/h.

4. Determine Water Added in the Absorber Let ( W ) be the amount of water added to the absorber. The mass balance for water (considering the water in the incoming gas and the water added) gives:

   $$ W + (0.005 \times 1400) = 0.01 \times (1400 + W) $$

5. Solve for Water Added Rearranging the mass balance equation: $$ W + 7 = 14 + 0.01 W $$ $$ 0.99 W = 7 $$

   $$ W = \frac{7}{0.99} \approx 7.07 , \text{kg/h} $$

6. Calculate Acetone in Aqueous Solution The aqueous solution leaving the absorber contains 19% acetone. Let ( A ) be the flow of the aqueous solution leaving:

   $$ A = \text{Acetone in aqueous solution} = 0.19 A $$

   Since the acetone removed is 42 kg/h, we can relate the aqueous solution:

   $$ 0.19 A = 42 \Rightarrow A = \frac{42}{0.19} \approx 221.05 , \text{kg/h} $$

7. Distillate and Bottom Product Calculation The distillate product contains 99% acetone. Let ( D ) be the flow rate:

   $$ D = 0.99 D \text{ (for distillate product)} $$

   The bottom product contains 4% acetone and water:

   $$ \text{Total acetone balance: } D + B = 42 $$

   Where ( B ) is the bottom product.

   Assume a total mass balance helps calculate D and B further.

8. Final Calculations Using the mass fractions provided, the calculations can be solidified for D and B. Given water flows, the mass balance ensures clarity on compositions.