Multi-stage flash distillation is used to desalinate seawater so it is fit for h

Question

Multi-stage flash distillation is used to desalinate seawater so it is fit for human consumption. A flash distillation tank is composed of small chambers (called "stages"), each at a lower pressure than the previous stage. Salt water enters the first chamber, some fresh water flash evaporates, condenses, and is removed from the distillation tank. The remaining salt water moves to the next chamber, some fresh water flash evaporates, condenses, and is removed from the distillation tank. The remaining salt water moves to the next chamber, and the process repeats until very salty water is expelled as waste. Brine that is 35,000 ppm salt is desalinated through a 5-stage flash distillation process. The pressure in the stages is such that 8.5% by mass of the water entering the stage evaporates and leaves as fresh water. If the desalination plant wants to produce 1800.0 gallons of drinking water per day, how many gallons of brine must the plant take in per day? The density of fresh water is 1.000 g/cm3. The density of brine is 1.025 g/cm3.

Explanation / Answer

1 gallon =3.785 litre

moleculat weight of brine water will be 18.45 (density = weight/molecular weight)

5 stages are required for distillation.

each stage 8.5% evaporates. so 5 stages will evaporate 42.5%

so after 5 step final distilation we will get 57.5% of water.

now molecular weight of brine is different from fresh water.

for 1800 gallon=6813 litre=6813000gram of fresh water.

so after final step 57.5% should be =6813000gm of fresh water

remaining 42.5% addition of mass to the above number will be 2895525gm

if we add 6813000+2895525 = 9708525gm of initial water. but we know that density is 1.025 now on multiplying it with final number .

so 9708525X 1.025 =9951238.12 ml of brine water is required. so 2629 gallon of brine water is required

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