You mix 335 gallons of a mixture containing 4 wt% NaCl (sodium chloride) and 96

Question

You mix 335 gallons of a mixture containing 4 wt% NaCl (sodium chloride) and 96 wt% water (solution density = 1.0253 g/cm, with an unknown volume of solution that is 20 wt% NaCl and 80 wt% water (solution density-1.1453 g/cm3). You wantto produce a m second feed solution by following the steps below. mixture containing 15 wt% Naci Find the volume of the Label the flow chart of the mixing process. Drag the labels below to fill in the spaces next to each quantity. If you are not given a value for a quantity, place the word "unknown" in the space. DO NOT LEAVE ANY SPACES EMPTY 335 gallons unknown grams mixture wt% NaCl wt% water unknown grams mixture 15 wt% NaCl unknown wt% water 96 Mixer unknown gallons unknown grams mixture 20 wt% NaCl 80 wt% water SCROLL BELOW TO SEE THE REST OF THIS PROBLEM. unknown

Explanation / Answer

Solution 1

Grams mixture = density x gallons

= 1.0253 g/cm3 x 335 gallons x 3785.412 cm3/gallons

= 1300196.279 grams

Wt% of water in solution 3 = 1 - 0.15 = 0.85 = 85%

Overall balance

Grams of 1 + grams of 2 = grams of 3

1300196.279 + grams of 2 = grams of 3

NaCl balance

1300196.279 x 0.04 + grams of 2 x 0.20 = grams of 3 x 0.15

Water balance

1300196.279 x 0.96 + grams of 2 x 0.80 = grams of 3 x 0.85

We have 3 equations and 2 unknowns

Solve any 2 equations simultaneously

1300196.279 x 0.04 + grams of 2 x 0.20 = 1300196.279 x 0.15 + grams of 2 x 0.15

52007.85 + grams of 2 x 0.20 = 195029.44 + grams of 2 x 0.15

grams of 2 x 0.20 - grams of 2 x 0.15 = 195029.44 - 52007.85

Grams of 2 x 0.05 = 143021.59

Grams of 2 = 2860431.8

Volume of 2 = Grams of 2 / density

= 2860431.8 g / 1.1453 g/cm3

= 2497539.334 cm3 x 1 gallons/3785.412cm3

Volume of second feed solution = 659.78 gallons

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