# Question 53186

Jul 18, 2017

$100$ $\text{mL alcohol}$

#### Explanation:

I'll assume the percentage is that by volume.

We're asked to find the amount of alcohol that needs to be added to $400$ $\text{mL}$ of a 15% solution to yield a 32% solution.

What we can first do is determine the amount of water present, because this quantity doesn't change (only alcohol is added):

"water" = overbrace((0.85))^(100%-15% = 85% "water")(400color(white)(l)"mL") = 340 $\text{mL}$

We want to make a 32% by volume solution of alcohol, so we can realize that $340$ $\text{mL H"_2"O}$ is

100%-overbrace(32%)^"desired alcohol percentage"=68%

of the solution. Using this, the total volume of the new solution is

"total volume" = (340color(white)(l)"mL")/(0.68) = color(red)(500 color(red)("mL"

The original volume is $400$ $\text{mL}$, so the amount of alcohol needed to be added is

"alcohol added" = color(red)(500 color(red)("mL" $- 400$ $\text{mL}$ = color(blue)(100 color(blue)("mL"#