# Question a9226

Feb 16, 2017

$\text{19 g}$

#### Explanation:

The density of a substance tells you the mass of exactly one unit of volume of that substance. Simply put, the density of a substance provides you with a conversion factor that can be used to go from mass to volume or vice versa.

In this case, the liquid is said to have a density of ${\text{0.775 g mL}}^{- 1}$, which means that you get $\text{0.775 g}$ for every $\text{1 mL}$ of this liquid.

color(darkorange)("0.775 g")color(white)(.) color(blue)("mL"^(-1)) -> color(darkorange)("0.775 g") color(white)(.) "for every" color(white)(.) color(blue)("1 mL") color(white)(.)"of liquid"#

Now, you know that your sample has a volume of ${\text{25 cm}}^{3}$. Keep in mind that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{\text{1 mL" = "1 cm}}^{3}}}}$

You can thus use the density of the liquid as a conversion factor to find the mass of the sample

$25 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{cm"^3))) * (1color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("cm"^3)))) * "0.775 g"/(1color(red)(cancel(color(black)("mL")))) = color(darkgreen)(ul(color(black)("19 g}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the volume of the sample.
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