# Question db449

Apr 15, 2017

$\text{1.3% v/v}$

#### Explanation:

For starters, use the density of the solvent to determine the volume of the sample.

500 color(red)(cancel(color(black)("g"))) * "1 mL"/(1.5color(red)(cancel(color(black)("g")))) = "750 mL"

Now, the solution's volume by volume percent concentration, $\text{% v/v}$, will tell you the number of milliliters of solute present for every $\text{100 mL}$ of solution.

In your case, the total volume of the solution will be

overbrace("10 mL")^(color(blue)("the volume of solute")) + overbrace("750 mL")^(color(purple)("the volume of solvent")) = "760 mL"

At this point, you can use the known composition of the solution as a conversion factor to determine how many milliliters of solute would be present in $\text{100 mL}$ of this solution.

Keep in mind that you can do that because solutions have the same composition throughout, i.e. they are homogeneous mixtures.

You will have

100 color(red)(cancel(color(black)("mL solution"))) * "10 mL solute"/(760color(red)(cancel(color(black)("mL solution")))) = "1.3 mL"#

You can thus say that the solution's volume by volume percent concentration is equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% v/v = 1.3%}}}}$

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one significant figure for the volume of the solute and for the mass of the solvent.