SOLUTION: a laboratory needs to make a 21-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 10%
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Question 1094740: a laboratory needs to make a 21-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 10% to get the desired concentration? Found 2 solutions by josmiceli, greenestamps:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = liters of pure acid needed
Let = liters of 10% solution needed
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(1)
(2)
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(2)
(2)
Subtract (1) from (2)
(2)
(1)
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and
(1)
(1)
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7 liters of pure acid are needed
14 liters of 10% solution are needed
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check:
(2)
(2)
(2)
(2)
(2)
OK
(1) Look to see how far (or close) the percentage of the mixture is to the percentages of the two ingredients:
The percentage of the mixture, 40%, is "twice as close" to 10% as it is to 100%. That means there must be twice as much of the 10% ingredient as the 100% ingredient. So 2/3 of the mixture must be the 10% acid solution, and 1/3 must be the pure (100%) acid.
2/3 of the 21 liters is 14 liters; so you need 14 liters of the 10% acid solution and 7 liters of pure acid.
If you want to use the slow traditional algebraic solution method...
let x = liters of 10% acid solution
then 21-x = liters of pure (100%) acid
The total mixture is 21 liters; the amount of acid is 10% of the x, plus 100% of the (21-x). You want the amount of acid to be 40% of the total mixture, so
liters of the 10% acid solution: x = 14
liters of pure (100%) acid: 21-x = 7
