Density Examples in Chemistry

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Density.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Chemistry.

Concept Recap

The mass of a substance per unit volume, measuring how tightly packed the particles are within a material.

Density answers 'how heavy is this for its size?' A small lead ball is heavier than a large foam ball — lead is denser.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Density asks what the sample is, what property is being used, and whether a new substance is formed.

Common stuck point: Students often know a formula related to density but skip the recognition step: Am I classifying matter or using properties, state, particle behavior, or mixture evidence to describe a sample? That leads to a correct-looking substitution attached to the wrong chemical model.

Sense of Study hint: Ask: Am I classifying matter or using properties, state, particle behavior, or mixture evidence to describe a sample?

Worked Examples

Example 1

easy
A block of aluminum has a mass of 135135 g and a volume of 50.0 cm350.0\,\text{cm}^3. Calculate its density.

Answer

ρ=2.70 g/cm3\rho = 2.70\,\text{g/cm}^3

First step

1
Use the density formula ρ=mV\rho = \frac{m}{V}.

Full solution

  1. 2
    Substitute the given values: ρ=135 g50.0 cm3\rho = \frac{135\,\text{g}}{50.0\,\text{cm}^3}.
  2. 3
    Evaluate the quotient to get ρ=2.70 g/cm3\rho = 2.70\,\text{g/cm}^3.
Density is an intensive property — it does not depend on the amount of substance. Every sample of pure aluminum has the same density, making it useful for identification.

Example 2

medium
A piece of metal has a mass of 78.078.0 g. When placed in a graduated cylinder containing 25.0 mL25.0\,\text{mL} of water, the water level rises to 35.0 mL35.0\,\text{mL}. Calculate the density and identify the metal if possible. (Iron = 7.87 g/cm37.87\,\text{g/cm}^3, Copper = 8.96 g/cm38.96\,\text{g/cm}^3, Zinc = 7.13 g/cm37.13\,\text{g/cm}^3)

Example 3

medium
A 27.0 g aluminum cylinder has a length of 2.0 cm and a radius of 1.0 cm. Find density. (Use V=πr2hV = \pi r^2 h, π≈3.14\pi \approx 3.14)

Example 4

medium
A gas occupies 5.00 L and has mass 8.95 g. Find its density in g/L. Does it likely float or sink in air (air density ~1.20 g/L)?

Example 5

hard
A 30% (by mass) NaCl solution has density 1.20 g/mL. What mass of NaCl is in 500 mL of this solution?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Will an object with density 0.85 g/cm30.85\,\text{g/cm}^3 float or sink in water (ρ=1.00 g/cm3\rho = 1.00\,\text{g/cm}^3)?

Example 2

hard
A solid cube has a side length of 3.0 cm3.0 \text{ cm} and a mass of 81 g81 \text{ g}. Calculate its density. If the cube is cut in half, what is the density of each piece? Explain.

Example 3

easy
A block has mass 60 g and volume 20 cm³. Find its density.

Example 4

easy
A sample has mass 50 g and volume 10 cm³. Find its density.

Example 5

easy
Water has density 1 g/cm³. What is the mass of 250 cm³ of water?

Example 6

easy
A liquid has density 2 g/mL. Find the volume of 80 g of it.

Example 7

easy
If a metal cube has mass 100 g and volume 25 cm³, what is its density?

Example 8

easy
Object A has density 8 g/cm³; object B has density 2 g/cm³. Which is denser?

Example 9

easy
Will an object with density 0.8 g/cm³ float or sink in water (density 1 g/cm³)?

Example 10

easy
Cutting a gold bar in half changes its mass and volume. Does its density change?

Example 11

medium
A rock displaces 15 mL of water in a graduated cylinder and has mass 45 g. Find its density.

Example 12

medium
A cube measures 2 cm on each side and has mass 64 g. Find its density.

Example 13

medium
Two metals: aluminum (2.7 g/cm³) and iron (7.9 g/cm³). Equal volumes of each are taken. Which has more mass and why?

Example 14

medium
A liquid has density 1.2 g/mL. What is the mass of 500 mL of this liquid?

Example 15

medium
An irregular metal piece has mass 270 g and, by displacement, a volume of 100 cm³. Could it be aluminum (density 2.7 g/cm³)? Show your reasoning.

Example 16

medium
Why can a large wooden log float while a small iron nail sinks, even though the log is heavier?

Example 17

medium
A gas has density 1.25 g/L. What is the mass of 8 L of this gas?

Example 18

medium
A student measures density in g/mL but reports volume in liters by mistake. If true density is 2 g/mL and they use 3 L as 3 mL, what mass do they wrongly compute, and what is the correct mass?

Example 19

medium
A rectangular bar measures 5 cm by 2 cm by 1 cm and has mass 70 g. Find its density.

Example 20

challenge
A 100 g alloy is made of 60 g of metal X (density 6 g/cm³) and 40 g of metal Y (density 4 g/cm³), with volumes simply adding. Find the alloy's overall density.

Example 21

challenge
An object weighs 80 g in air. When fully submerged, it displaces 40 cm³ of water (density 1 g/cm³). Determine its density and predict whether it floats.

Example 22

challenge
A hollow steel ball (steel density 7.9 g/cm³) has total volume 100 cm³ and total mass 80 g. Explain how it can float on water and find its average density.

Example 23

easy
A 90 g object has volume 30 cm3^3. Find its density.

Example 24

easy
What is the volume of 150 g of a liquid with density 1.5 g/mL?

Example 25

easy
What is the mass of 50 mL of mercury (density 13.6 g/mL)?

Example 26

easy
Is density an intensive or extensive property?

Example 27

easy
Will oil (density 0.92 g/mL) float on water (1.00 g/mL)?

Example 28

medium
A graduated cylinder shows water rising from 30.0 mL to 47.5 mL when a rock is added. The rock weighs 52.5 g. Find its density.

Example 29

medium
A solution has density 1.20 g/mL. What is the mass of 250 mL of it?

Example 30

medium
Density of an unknown liquid is 0.80 g/mL. What volume holds 200 g?

Example 31

medium
Two cubes of equal volume: lead (11.3 g/cm3^3) and iron (7.87 g/cm3^3). Ratio of lead mass to iron mass?

Example 32

medium
Convert 2.5 g/cm3^3 to kg/m3^3.

Example 33

medium
Why does ice float on water despite both being H2_2O?

Example 34

medium
A 10.0 mL sample of an unknown liquid weighs 7.85 g. Could it be ethanol (d = 0.789 g/mL)?

Example 35

medium
How would you calculate the density of an irregular rock that displaces 12 mL of water and has mass 36 g?

Example 36

hard
A glass beaker has a mass of 50.0 g empty and 312.0 g when filled with 250 mL of liquid X. Find the density of X.

Example 37

hard
A swimming pool measures 10 m ×\times 5 m ×\times 2 m. Mass of water needed to fill it? (d = 1000 kg/m3^3)

Example 38

hard
A balloon contains 5.0 L of helium (d = 0.179 g/L) at room temperature. What mass of helium is inside?

Example 39

hard
A goldsmith claims a ring is pure gold (d = 19.3 g/cm3^3). The ring weighs 9.65 g and displaces 0.65 mL of water. Is it pure gold?

Example 40

hard
A cube of side 5 cm has total mass 175 g and contains a hollow region of volume 25 cm3^3. Find the density of the solid material.

Example 41

challenge
Layer three liquids in a tube: honey (1.42 g/mL), water (1.00 g/mL), oil (0.92 g/mL). List from bottom to top.

Example 42

challenge
A 100 g alloy of metal A (d = 5 g/cm3^3) and metal B (d = 10 g/cm3^3) has total volume 15 cm3^3. Find the mass of metal A. (Assume volumes add.)
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Background Knowledge

These ideas may be useful before you work through the harder examples.

physical property