# Five mL of ethanol has a mass of 3.9 g, and 5.0 mL of benzene has a mass of 4.4 g. Which liquid is denser?

Jan 10, 2016

Benzene.

#### Explanation:

As you know, density is defined as mass per unit of volume.

$\textcolor{b l u e}{\text{density" = "mass"/"unit of volume}}$

So, what you it mean for one substance to be denser than another substance?

Well, the denser substance would have to have a bigger mass in the same volume. In your case, you know that $\text{5 mL}$ of ethanol have a mass of $\text{3.9 g}$, but that $\text{5 mL}$ of benzene have a mass of $\text{4.4 g}$.

This tells you that benzene is denser than ethanol, since you'd get a bigger mass of benzene in the same volume.

Now, you can compare the densities of the two substances by making sure that you're using the same unit of volume for both substances. In this case, volume is given to you in milliliters, which means that the unit of volume will be $\text{1 mL}$.

So, what would the mass of $\text{1 mL}$ of ethanol be?

1 color(red)(cancel(color(black)("mL"))) * "3.9 g"/(5.0color(red)(cancel(color(black)("mL")))) = "0.78 g"

The density of ethanol, ${\rho}_{e}$, will thus be $\text{0.78 g/mL}$, meaning that every milliliter of ethanol has a mass of $\text{0.78 g}$.

Likewise, the mass of $\text{1 mL}$ of benzene will be

1 color(red)(cancel(color(black)("mL"))) * "4.4 g"/(5.0color(red)(cancel(color(black)("mL")))) = "8.8 g"

The density of benzene, ${\rho}_{b}$, will be equal to $\text{0.88 g/mL}$, meaning that every milliliter of benzene has a mass of $\text{0.88 g}$.

Since

${\rho}_{b} > {\rho}_{e}$

you can say once again conclude that benzene is slightly denser than ethanol.