# Question c25e3

Oct 10, 2015

400-86/400 *100

Oct 10, 2015

Your solution is 78.5% "v/v" ethanol.

#### Explanation:

A solution's percent concentration by volume is defined as the ratio between the volume of the solute, in your case ethanol, and the total volume of the solution, multiplied by 100.

$\text{%v/v" = "volume of solute"/"volume of solution} \times 100$

In your case, you know that the total volume of the solution is equal to $\text{400 mL}$. Moreover, you know that this solution contains $\text{86 mL}$ of water, which also implies that it must contain

${V}_{\text{solution" = V_"water" + V_"ethanol}}$

${V}_{\text{ethanol" = V_"solution" - V_"water}}$

${V}_{\text{ethanol" = "400 mL" - "86 mL" = "314 mL ethanol}}$

The percent concentration by volume of ethanol in this solution is

"%v/v" = (314color(red)(cancel(color(black)("mL"))))/(400color(red)(cancel(color(black)("mL")))) xx 100 = color(green)("78.5%")#

I'll leave the answer rounded to thre sig figs.