What was wrong in my labels and what is the volume? You mix 265 gallons of a mix

Question

What was wrong in my labels and what is the volume?

You mix 265 gallons of a mixture containing 4 wt% Naci (sodium chloride) and 96 wt% water (solution density 1.0253 g/cm3) with an unknown volume of solution that is 26 wt% Nacl and 74 wt% water (solution density 1.1944 g/cms). You want to produce a mixture containing 17 wt% Nacl. Find the volume of the second feed solution by following the steps below. bel the flow chart of the mixing process. Drag the labels below to fill in the spaces next to each quantity. If not given a value a quantity, place the word "unknown" in the space. DO NOT LEAVE ANY SPACES fora 265 gallons unknow grams mixture 4 wt% NaCl 74 wt% water unknown grams mixture Mixer 17 wt% NaCl unknown gallons unknown wt% water unknown grams mixture 26 wt% NaCl 96 wt% water unknown SCROLL BELOW TO SEE THE REST OF THIS PROBLEM.

Explanation / Answer

V1 =265gellon=28717.84 cm^3
TM1 =28717.84 *1.0253= 29444. 40 g
M1= 4*TM1= 117777. 60 g
V2 =?
TM2 =V2*1.1944
M2 = 26*V2*1.1944
V3=V1+V2 (mixing of two solutions)
Conservation of mass:
M3=M1+M2,
M3= 4*V1*1.0253 + 26*V2*1.1944 ....(I )
TM3 = TM1+TM2,
M3 = 19*TM3
= 17*(V1*1.0253 + V2*1.1944) ......(II)
equate equation I and II
(you have value of V1, so its just 1 variable equation)

V2= 35622.97 cm3

V2= 328.74 gallons

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