Question

please help me with this

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1. You are trying to make a homemade electrolyte energy drink similar to Gatorade. Gatorade contains 270. mg of sodium chloride and 34.Og of sugars per 591 mL (20.0 oz.) bottle. You have a solution of NaCl that is 5 wt% sodium chloride and the rest water. You have a solution of sucrose (common table sugar) that is 10 wt% sucrose and the rest water. You have as much extra water as needed. What volumes of saline solution, sucrose solution, and water should you combine to make 240mL of liquid at the same salt content, sugar content, and density as Gatorade? Assume: sucrose is the only sugar in this problem and the system is nonreacting. Densities for: Gatorade, 1.030 g/mL 5 wt% NaCl, 1.034 g/mL | 10 wt% sucrose, 1.038 g/mL Note: 1 wt% is equivalent to 0.01 mass fraction (w), i.e. a 1 wt% solution of substance A contains 1 g of A / 100 g total mixture.

Answer 1

Let us assume volume of 5% NaCl soln,volume of sucrose soln,volume of extra water added be VNa,Vs,Vw respectively.

Given:

· Density of 5% NaCl soln=1.034g/mL.

· Density of Gatorade =1.030g/mL

· Density of water added=1.034g/mL

· Density of water=1g/mL

· Amount of NaCl in Gatorade =0.270g in 591mL.

· Amount of sugar in Gatorade=34 g in 591mL

· Total volume of solution =240mL=VNa+Vs+Vw

concentration of NaCl in Gatorade, CNaCl in Gatorade =.270/591 g/mL

concentration of sucrose in Gatorade ,CSucrose in Gatorade=34/591 g/mL

Mass of Nacl soln added to make Gatorade=1.034*VNa.

Mass of sucrose soln added to make Gatorade=1.038*Vs.

Mass of sucrose in Gatorade =0.1*mass of sucrose soln.

                                                                =0.1*1.038*Vs

Mass of NaCl in 5 %solution =0.05*mass of nacl solution

                                                              =0.05*1.034*VNa            -(1)

Amount of Nacl in 240 ml Gatorade =concentration of NaCl in Gatorade*volume of solution.

=.270/591*240                 -(2)

Amount ofsucrose in 240 ml Gatorade =concentration of sucrose in Gatorade*volume of solution.

Equating eq(1) and (2)  

=0.05*1.034*VNa=.270/591*240              

VNa=2.12078 mL

Similarly for sucrose

0.1*1.038*Vs=34/591*240

Vs=133.0164 mL.

Also density of solution is =mass of solution/volume of solution.

1.034 VNa+1.038&Vs+Vw VNa+Vs+Vw = 1.03

=1.034*VNa+1.038*Vs+Vw=1.03*240

1.034*VNa+1.038*Vs+Vw=247.2

Vw=106.936mL