# Question e1868

Sep 18, 2017

Mix 468.75 mL 0.5% solution with 281.25 mL 0.1% solution.

#### Explanation:

Well, practically, if you are in a lab, the simplest thing to do would be to dilute the 50% solution! But, I assume that they really want you to simply mix the two given solutions together to make the math more interesting.

This is similar to a regular molarity or molality mixing problem. Two volumes of two concentrations equal one volume of another concentration, as long as the dimensions are the same. Two equations in two unknowns – no problem.

$X + Y = 750$ This is the ratio of the two volumes. We can substitute one for the other to use in the next equation. Y = 750 – X

$0.5 \times X + 0.1 \times Y = 0.35 \times 750$
$0.5 \times X + 0.1 \times \left(750 - X\right) = 262.5$ ; 0.5 xx X – 0.1 xx X + 75 = 262.5

$0.4 \times X = 187.5$ ; $X = 468.75$ ; Y = 750 – 468.75 = 281.25#

CHECK:
$0.5 \times X + 0.1 \times Y = 0.35 \times 750$ ; $0.5 \times 468.75 + 0.1 \times 281.25 = 262.5$
$234.373 + 28.125 = 262.5$ ; $262.5 = 262.5$ CORRECT!