# Question ba500

Jul 26, 2016

"% v/v" = 20%

#### Explanation:

The problem provides you with the volume of solute, which in your case is ethanol, $\text{CH"_3"CH"_2"OH}$, and the volume of solvent, which in your case is water, so right from the start you know that you're looking for the solution's volume by volume percent concentration, $\text{% v/v}$.

The solution's volume by volume percent concentration tells you how many cubic centimeters of solute you get for every ${\text{100 cm}}^{3}$ of solution. The first thing to do here will be to figure out the total volume of the solution.

${V}_{\text{total" = V_"solute" + V_"solvent}}$

${V}_{\text{total" = "40 cm"^3 + "160 cm"^3 = "200 cm}}^{3}$
Now, you know that you have ${\text{40 cm}}^{3}$ of ethanol in ${\text{200 cm}}^{3}$ of solution, which means that ${\text{100 cm}}^{3}$ of solution will contain
100 color(red)(cancel(color(black)("cm"^3color(white)(a)"solution"))) * ("40 cm"^3color(white)(a)"CH"_3"CH"_2"OH")/(200color(red)(cancel(color(black)("cm"^3color(white)(a)"solution")))) = "20 cm"^3color(white)(a)"CH"_3"CH"_2"OH"
So, if ${\text{100 cm}}^{3}$ of solution contain ${\text{20 cm}}^{3}$ of ethanol, it follows that the solution's volume by volume percent concentration is
"% v/v" = color(green)(|bar(ul(color(white)(a/a)color(black)("20% CH"_3"CH"_2"OH")color(white)(a/a)|)))#