Question

The company operates 1000 gallon batch fermentors that operate daily. The media used in the fermentation contains 5% glucose (g/100 mL) and 10 g/L NaCl. We have three liquid streams available in the plant: (1) pure water, (2) a 10 M solution of NaCl, (3) a 20 % solution of glucose. Please calculate the flow rates (lbs/day) of each solution that are needed to meet our fermentation demands.

Answer 1

1000 gallon = 3785 liter daily

second stream = 10 M solution = 10 mole /liter = 584 g/liter ( 1 mole = 58.4 g NaCl) this stream has to be converted to

10 g/ Liter by adding pure water. this mean we will have to add 57.4 liter of pure water 584 g/ (57.4L+1L)=10 g/L

third stream 20 % solution of gulucose = 20 g/ 100 mL this stream has to be converrted to 5 % by adding pure water. in this stream we will have to add 300 mL pure water ( 20 g / (100 mL+300 mL) ) = 5 g / 100 mL

total volume of solution = 1 L NaCl +57.4 pure water + 0.1 L gulucose + 0.3 L pure water = 58.8 L (1 L =1000 mL)

we need daily 3785 L solution

all the stream has to be increase by 3785 L/58.8 L = 64.37 times

NaCl = 584 g *64.37 = 37592 g/day = 82.87 lbs /day ( 1 lbs = 453.592 g)

gulucose = 20 g * 64.37 = 1287.4 g/ day = 2.838 lbs/day ( 1 lbs = 453.592 g)

water = 57.4L+0.3 L = 57.7 L = 57700 g /day = 127.2 lbs/day ( 1 L water = 1000 g) ( 1 lbs = 453.592 g)