Aqueous twophase extraction is used to purify a recombinant

Aqueous two-phase extraction is used to purify a recombinant HIV-beta-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 100 kg mixture of 20% w/w PEG in water, and 150 kg of a mixture of 20% w/w PEG of a and 25% w/w salt in water. Also on hand is 200 kg of an aqueous stock solution of 50% w/w PEG, 200 kg of an aqueous stock solution of 40% w/w salt, and an unlimited supply of extra water If all of both leftover mixtures must be used, how much of each stock solution and additional water is required?

Solution

Solution) We need to make a 450kg of solution which contains19.75% w/w PEG and 17% w/w potassium phosphate salt.

It means that 450 kg of solution must contain 19.7 x 4.5 = 88.65kg PEG (19.75% w/w) and 17.7 x 4.5 = 79.65kg salt (17.7% w/w). so, we need to make a 450kg solution containing 88.65kg PEG and 79.65kg salt mixed in 281kg of water.

And we are provided with 100kg of left over 1 having 20 % w/w PEG which means 20kg of PEG in 80kg of water. And we have 150kg of leftover 2 having 20% w/w/ PEG and 25% salt which means 30kg of PEG and 37.5kg of salt in 82.5kg water.

And we have two stock solution; stock 1 have 200kg of solution containing 50% of PEG and stock 2 have 200kg of solution containing 40% of salt.

If we use both the left overs, then we have 100kg (20kg of PEG + 80kg water) and 150kg (30kg PEG + 37.5kg salt + 82.5kg water) mixed together resulting in 250kg solution (50kg PEG + 37.5kg salt + 162.5kg water).

This way we require 200kg more solution which contains (88.65-50 = 38.65kg PEG and 79.65-37.5 = 42.25kg salt).

Now, take this required amount from the stock 1 and stock 2.

Calculate how much of stock 1 contains 38.65kg PEG and how much of stock 2 contains 42.15kg of salt.

From stock 1; 200kg solution contains 100kg PEG (50% w/w) or 2kg solution contains 1kg PEG.

Hence 38.65 kg PEG will require = 38.65 x 2 = 77.3kg solution of stock 1

From stock 2; 200kg solution contains 80kg salt (40% w/w) or 2.5kg solution contains 1kg salt.

Hence 42.15kg salt will require = 42.15 x 2.5 = 105.375kg of stock 2.

So, the total amount taken so far is; 100kg left over 1 + 150kg left over 2 + 77.3kg stock 1 and 105.375kg stock 2 = 432.675 kg

Make up this solution up to 450 kg by adding 17.325kg water.

This way we add 100kg left over 1, 150kg left over 2, 77.3kg stock 1, 105.375 kg stock 2 and 17.325kg of water.