Problem 2: Aqueous two-phase extraction is used to purify a recombinant HIV--gal

Question

Problem 2:

Aqueous two-phase extraction is used to purify a recombinant HIV--galactosidase fusion peptide produced in Escherichia coli. For optimum separation, 450 kg of a mixture of 19.7% w/w polyethylene glycol (PEG) and 17.7% w/w potassium phosphate salt in water is needed. Left over from previous pilot-plant trials is 200 kg of a mixture of 20% w/w PEG in water, and 200 kg of a mixture of 20% w/w PEG and 25% w/w salt in water. Also on hand is 100 kg of an aqueous stock solution of 50% w/w PEG in water, 100 kg of an aqueous stock solution of 40% w/w salt in water, and an unlimited supply of extra water.
If all of both stock solution mixtures must be used, how much of each of the leftover mixtures and additional water are required?  

Explanation / Answer

450 kg mixture = 19.7% w/w PEG (88.65 kg PEG) + 17.7% w/w salt (79.65 kg salt) + 62.6 % water (281.7 kg water)

1. Left over

200 kg = 20 % PEG (40 kg) + 80% water

2. Left over

200 kg = 20% PEG (40 kg) + 25 % salt (50 kg) + 55% water

3. stock solution

100 kg = 50 % PEG (50kg) + 50% water

4. stock solution

100kg = 40% salt (40 kg) + 60% water

Take 200 kg left over no.2 which has 40 kg PEG and 50 kg salt. Then take remaining 100 kg PEG stock solution and 100 kg salt solution.

We need only 48.65 kg PEG from 100 kg stock so add extra 1.35 kg water to it which makes 101.35 kg.

Also we need 29.65 kg salt from 100 kg stock so add extra 10.35 kg water to it which makes 110.35 kg

So 200 kg + 101.35 kg PEG+ 110.35 kg salt = 411.7 kg

450 - 411.7 = 38.3 kg water

Add 38.3 kg water to make up to 450 kg.

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