how many liters is 70% alcohol solution must be added to 50 L of 40% alcohol solution to produce a 50% alcohol solution

Question

how many liters is 70% alcohol solution must be added to 50 L of 40% alcohol solution to produce a 50% alcohol solution

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niczorrrr 1 year 2021-09-03T15:02:33+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-09-03T15:04:23+00:00

    Answer:

    50%

    Step-by-step explanation:

    This question is solved by C1V1 + C2V2 ÷ V1 + V2 = final concentration

    Let x = volume of 70% solution

     

    let’s express the concentrations as decimals, so 70% = 0.7, 50% = 0.5, and 40% = 0.4

     

    then 0.7X + 50L.4 ÷ X + 50L = 0.5

     

    this equation becomes 0.5(X + 50) = 0.7X + 20

    which yields 0.5X + 25 = 0.7X +20

    combining, we get 5 = 0.2X, and 25 = X

     

    when we mix the two volumes, we get 50L x 40% + 25L x 70%,

    which yields 20L of 100% alcohol, and 17.5L of 100% alcohol, for a total of 37.5L of alcohol in 75L of solution

     

    which is a final concentration of 50%

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