# A mass of mercury occupies 0.95 L. What volume would an equal mass of ethanol occupy? The density of mercury is 13.546 g/mL and the density of ethanol is .789 g/mL?

Feb 1, 2016

$\text{16 L}$

#### Explanation:

For a given substance, its density tells you the mass occupied by one unit of volume of that substance.

In essence, density is a measure of how well the molecules of a substance are packed in a unit of volume. In your case, the densities of the two substances are expressed in grams per milliliter, which means that a unit of volume will be $\text{1 mL}$.

So, mercury has a density of $\text{13.546 g/mL}$, which means that $\text{1 mL}$ of mercury will have a mass of $\text{13.546 g}$. On the other hand, $\text{1 mL}$ of ethanol will have a mass of $\text{0.789 g}$.

Your strategy here will be to use the density of mercury to find the mass that occupies $\text{0.95 L}$, then use the density of ethanol to find the volume that would have an equal mass.

So, you will have - don't forget to convert the volume from liters to milliliters

 0.95 color(red)(cancel(color(black)("L"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * overbrace("13.546 g"/(1color(red)(cancel(color(black)("mL")))))^(color(purple)("density of mercury")) = "12,868.7 g"

The volume of ethanol that will have an equal mass is

$\text{12,868.7" color(red)(cancel(color(black)("g"))) * overbrace("1 mL"/(0.789color(red)(cancel(color(black)("g")))))^(color(purple)("density of ethanol")) = "16,310.1 mL}$

Rounded to two sig figs and expressed in liters, the answer will be

"16,310.1"color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = color(green)("16 L")