A milk mixture was prepared by dissolving of 400g of skimmed milk powder into a 10L milk solution.

The milk solution was then added to the filtration tank. The flow rate was observed over the time it took to has 2L of the solution left in the concentrate. Sample of permeate were collected until 8L total of permeate was obtained.

Water was added to the feed tank containing protein concentrate. The volume of water added to the feed tank was calculated. The addition of water results in the lactose concentration being 1/20^th of original concertation.

How much water is required to perform the diafiltration step show your calculation steps and explain.

extra info

Protein: 36.1g Carbohydrate: 52.9g (all carbohydrates are lactose)

Lactose moles= 342.3g/mol

Concentration milk powder 400/10= 40g/L

Lactose concentration formula: C_f =C₀e^Vw/v

Vw- volume of water

C₀= original concentration

C_f= final concentration

Vw=2(Ln(-C_f/C₀))