Question

You need a 15% alcohol solution. On hand, you have a 180 mL of a 45% alcohol mixture. How much pure

water will you need to add to obtain the desired solution?
You will need
mL of pure water
to obtain
mL of the desired 15% solution.
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Answer 1

Let x be the amount of pure water that you use.

The solution you have contains 0.45 • 180 mL = 81 mL of alcohol.

However much water you use, it won't add any alcohol to the solution, so only its total volume changes. Its new volume would be (180 + x) mL. You want the new solution to have a concentration of 15% so that

(81 mL) / ((180 + x) mL) = 0.15

Solve for x :

81 / (180 + x) = 0.15

81 / 0.15 = 180 + x

540 = 180 + x

x = 360

Then the new solution will have a total volume of 180 mL + 360 mL = 540 mL.

So you need to use 360 mL of pure water to get 540 mL of 15% solution.