Question

1) A chemist has 2.5 liters of a solution that is 70% acid. How much WATER should be
added to obtain a 50% acid solution?

Answer 1

A 2.5-L solution with a 70% concentration of acid contains

0.70 (2.5 L) = 1.75 L

of acid.

Suppose you add x L of water, which contributes no additional acid. Then the new volume is (2.5 + x) L, but the amount of acid in the solution stays the same. If the new concentration is 50%, then

1.75 / (2.5 + x) = 0.50

Solve for x :

1.75 = 0.50 (2.5 + x)

1.75 = 1.25 + 0.50x

0.50 = 0.50x

x = 1