# Question 76765

Mar 1, 2017

#### Explanation:

The thing to remember about a solution's volume by volume percent concentration, $\text{% v/v}$, is that it tells you the volume of solute present in $\text{100 mL}$ of solution.

color(blue)(ul(color(black)("% v/v" = "volume of solute"/"100 mL of solution" xx 100%)))

This means that in order for an alcohol solution to have a $\text{40% v/v}$ percent concentration, it must contain $\text{40 mL}$ of alcohol, the solute, for every $\text{100 mL}$ of solution.

This can be calculated by using the above equation

40% = V_"alcohol"/"100 mL" xx 100%#

Rearrange to solve for ${V}_{\text{alcohol}}$

${V}_{\text{alcohol" = (40 color(red)(cancel(color(black)(%))) * color(blue)(cancel(color(black)(100))) "mL")/(color(blue)(cancel(color(black)(100)))color(red)(cancel(color(black)(%)))) = "40 mL}}$

Now, don't forget that you need $\text{40 mL}$ of alcohol for every $\text{100 mL}$ of solution, which implies that the correct answer is A)

$\text{100 mL solution" = "40 mL alcohol" + "60 mL water}$