114. A batch reactor produces 25g/L of product. The fermentation time is 4 days and 1 day extra is
required as downtime for cleaning, sterilization and setting up the reactor. If total number of working
days is taken at 300 days/year. Then to produce 1 ton/year of product the reactor size has to be
approximately
1. 6.67 L
2. 66.7 L
3. 667 L
4. 6667 L

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Given Data:

• Product yield per batch = 25 g/L

• Fermentation time per batch = 4 days

• Downtime per batch = 1 day

• Total time per batch = 4 + 1 = 5 days/batch

• Working days per year = 300 days

• Total number of batches per year = 300 / 5 = 60 batches/year

• Target annual production = 1 ton/year = 1000 kg = 1,000,000 g

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Step-by-Step Calculation:

1. Let the reactor volume be V (in liters)

Then, product produced per batch = 25 g/L × V = 25V g

2. Product produced per year = 25V × 60 = 1500V g

Set this equal to the desired annual production:

1500V = 1,000,000
=> V = 1,000,000 / 1500
=> V ≈ 666.67 L

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Final Answer:

3. 667 L