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A laboratory technician needs to make a 48-liter batch of a 40% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 20% to get the desired concentration



Answer :

Answer:

The technician need to combine 12-liter of pure acid and 36-liter of 20% acid to make a 48-liter of a 40% acid solution.

Step-by-step explanation:

To find the volume of each batch of acid, we can create a system of equations.

Let:

  • [tex]x[/tex] = volume of the pure acid (100%)
  • [tex]y[/tex] = volume of the 20% acid

Given:

(a) the solution volume = 48-liter

This means the total volume of the 100% acid and the 20% acid equals to 48-liter:

[tex]x+y=48\ ...\ [1][/tex]

(b) the acid volume = 40% × 48-liter

This means the total acid of the 100% acid and the 20% acid equals to 40% × 48-liter:

[tex]100\%\times x+20\%\times y=40\%\times48[/tex]

[tex]x+0.2y=19.2\ ...\ [2][/tex]

By combining [1] & [2]:

    [tex]x+y=48[/tex]

[tex]x+0.2y=19.2[/tex]

---------------------- (-)

     [tex]0.8y=28.8[/tex]

          [tex]y=36[/tex]

By substituting [tex]y=36[/tex] into [1]:

[tex]x+y=48[/tex]

[tex]x+36=38[/tex]

[tex]x=12[/tex]

Hence, the technician need to combine 12-liter of pure acid and 36-liter of 20% acid.

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