# Question 59469

Feb 1, 2017

$\text{68 g}$

#### Explanation:

The thing to remember about density is that it always tells you the mass of exactly one unit of volume of a given substance.

In this case, the density of mercury is said to be equal to ${\text{13.6 g cm}}^{- 3}$, so one unit of volume is equal to ${\text{1 cm}}^{3}$. This means that the mass of ${\text{1 cm}}^{3}$ of mercury is equal to $\text{13.6 g}$.

$\text{13.6 g cm"^(-3) implies "1 cm"^3 "Hg" stackrel(color(white)(acolor(red)("has a mass of")aaaa))(->) "13.6 g}$

You know that the sample of mercury has a volume of $\text{5.0 mL}$, so use the density of mercury as a conversion factor to find the mass of the sample.

Start by converting the volume of the sample to cubic centimeters

5.0 color(red)(cancel(color(black)("mL"))) * "1 cm"^3/(1color(red)(cancel(color(black)("mL")))) = "5.0 cm"^3#

You will thus have

$5.0 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{cm"^3))) * overbrace("13.6 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the density of Hg")) = color(darkgreen)(ul(color(black)("68 g}}}}$

The answer is rounded to two sig figs.