# Question 651e9

Dec 11, 2015

${V}_{{C}_{3} {H}_{8} O} = \text{330 mL}$

#### Explanation:

A solution's percent concentration by volume is defined as the volume of the solute, which in your case is isopropyl alcohol, $\text{C"_3"H"_8"O}$, divided by the total volume of the solution, and multiplied by $100$.

$\textcolor{b l u e}{\text{% v/v" = "volume of solute"/"volume of solution} \times 100}$

In your case, rubbing alcohol is said to contain $\text{70. %v/v}$ isopropyl alcohol. What that means is that every $\text{100 mL}$ of rubbing alcohol will contain $\text{70. mL}$ of isopropyl alcohol.

You're interested in finding out how much isopropyl alcohol you get in $\text{473 mL}$ of rubbin alcohol, so you can say that

473 color(red)(cancel(color(black)("mL rubbing alcohol"))) * ("70. mL C"_3"H"_8"O")/(100color(red)(cancel(color(black)("mL rubbing alcohol")))) = "331.1 mL C"_3"H"_8"O"#

You need to round this off to two sig figs, the number of sig figs you have for the percent concentration by volume

${V}_{{C}_{3} {H}_{8} O} = \textcolor{g r e e n}{\text{330 mL}}$