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nommies005
18.02.2020 •
Mathematics
Doc has available to have a 20% alcohol solution and a 70% alcohol solution how many liters of each solution should be mixed to make 30 L of a 50% alcohol solution?
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Ответ:
12 L of the 20% solution should be used with 18 L of the 70% alcohol solution
Step-by-step explanation:
assuming that the concentration given is in terms of mass/volume , then doing an mass balance
C₁*V₁ + C₂*V₂ =C₃*V₃
where C= concentration , V= volume , 1,2,3 denotes first , second and final solution respectively.
and since we are mixing the same substance, the total volume V₃ will be the sum of the solutions mixed
V₁ + V₂ = V₃ → V₂=V₃-V₁
thus
C₁*V₁ + C₂*(V₃-V₁) =C₃*V₃
(C₁-C₂)*V₁ + C₂*V₃ = C₃*V₃
(C₁-C₂)*V₁ = (C₃- C₂) *V₃
V₁ = V₃ * (C₃- C₂)/(C₁-C₂)
replacing values
V₁ = V₃ * (C₃- C₂)/(C₁-C₂) = 30 L * (50%-70%)/(20%- 70%) = 12 L
then
V₂=V₃-V₁=30 L - 12 L = 18 L
therefore 12 L of the 20% solution should be used with 18 L of the 70% alcohol solution
Ответ:
The solution is
,
Step-by-step explanation:
Equation:
-Combine like terms:
Add both sides by 2:
-Divide both sides by 26:
So, the answer is
.