# Density

## Key Questions

They are related by the the density triangle.

#### Explanation:

They are related by the the density triangle. d = $\frac{m}{V}$

m = d×V

V = $\frac{m}{d}$

DENSITY

Density is defined as mass per unit volume.

d = $\frac{m}{V}$

Example:
A brick of salt measuring 10.0 cm x 10.0 cm x 2.00 cm has a mass of 433 g. What is its density?

Step 1: Calculate the volume
V = lwh = 10.0 cm × 10.0 cm × 2.00 cm = 200 cm³

Step 2: Calculate the density

d = $\frac{m}{V}$ = (433 g)/(200 cm³) = 2.16 g/cm³

MASS

d = $\frac{m}{V}$

We can rearrange this to get the expression for the mass.

m = d×V

Example:
If 500 mL of a liquid has a density of 1.11 g/mL, what is its mass?

m = d×V = 500 mL × $\frac{1.11 g}{1 m L}$ = 555 g

VOLUME

d = $\frac{m}{V}$

We can rearrange this to get the expression for the volume.

V = $\frac{m}{d}$

Example:
What is the volume of a bar of gold that has a mass of 14.83 kg. The density of gold is 19.32 g/cm³.

Step 1: Convert kilograms to grams.

14.83 kg × $\frac{1000 g}{1 k g}$ = 14 830 g

Step 2: Calculate the volume.

V = $\frac{m}{d}$ = 14 830 g × (1 cm³)/(19.32 g) = 767.6 cm³

• You can identify an unknown substance by measuring its density and comparing your result to a list of known densities.

Density = mass/volume. Assume that you have to identify an unknown metal. You can determine the mass of the metal on a scale. You can determine the volume by dropping the object into a graduated cylinder containing a known volume of water and measuring the new volume. You divide the mass by the volume and compare the density to a list of known densities.

EXAMPLE

A metal bolt with a mass of 99.7 g is dropped into a graduated cylinder containing 50.0 cm³ of water. The new volume reads
72.1 cm³. Identify the metal.

Solution

V = 72.1 cm³ - 50.0 cm³ = 22.1 cm³

D = m/V = (99.7 g)/(22.1 cm³) = 4.51 g/cm³

Now you compare your density with a list obtained from your instructor or from an on-line source such as

Density is the mass per unit of volume of a substance.

#### Explanation:

Density measures the compactness in molecular arrangement in any substance which determines how heavy or light any substance is.

The density formula is $\text{density}$ = $\text{mass"/"volume}$. Mass units are most commonly grams or kilograms. Volume units are most commonly cubic centimeters (${\text{cm}}^{3}$), cubic meters (${\text{m}}^{3}$), or millileters (mL).

Examples of density include the following:

The density of water at $\text{4"^"o""C}$ can be written as ${\text{1.000g/cm}}^{3}$, $\text{1.000g/mL}$, ${\text{1000Kg/m}}^{3}$, and $\text{1.000kg/L}$.

The density of iron at $\text{0"^"o""C}$ is ${\text{7.874g/cm}}^{3}$ and ${\text{7874kg/m}}^{3}$.

The density of sodium metal at $\text{0"^"o""C}$ is ${\text{0.968g/cm}}^{3}$, and ${\text{968kg/m}}^{3}$.

In order to determine the density of a substance, you need to know its mass and its volume. Then divide its mass by its volume, remembering to divide the units as well.

Example
A ${\text{1.26cm}}^{3}$ sample of the element mercury has a mass of $\text{17.05g}$. What is it's density?

Solution

$\text{density}$ = $\text{mass"/"volume}$ = ${\text{17.05g"/"1.26cm}}^{3}$ =

$\text{13.5g/cm"^3}$

Here is a video example of how to solve a density problem.