Avogadro's Number Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Avogadro's Number.

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 defined number of particles in exactly one mole of any substance: $6.022 \times 10^{23}$ .

A mind-bogglingly large number — but it's exactly the right size to make atomic counting practical.

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: Avogadro's Number starts with the given amount, names the substance, and chooses the conversion factor that cancels the old unit.

Common stuck point: Students often know a formula related to avogadro's number but skip the recognition step: Am I using a mole bridge, molar mass, formula ratio, or balanced-equation ratio to connect measured amounts? That leads to a correct-looking substitution attached to the wrong chemical model.

Sense of Study hint: Ask: Am I using a mole bridge, molar mass, formula ratio, or balanced-equation ratio to connect measured amounts?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Moles Mistakes

Worked Examples

Example 1

easy

How many molecules are in

2.5

mol of

\text{CO}_2

Answer

1.51 \times 10^{24} molecules

First step

Convert moles to particles with Avogadro's number:

N = n \times N_A

Full solution

2
Substitute the values: $N = 2.5 \times 6.022 \times 10^{23}$ .
3
Multiply to get $N = 1.506 \times 10^{24}$ molecules, which rounds to $1.51 \times 10^{24}$ molecules.

Avogadro's number (

N_A = 6.022 \times 10^{23}\,\text{mol}^{-1}

) converts between moles and individual particles. It works for atoms, molecules, ions, or any countable entity.

Example 2

medium

How many individual oxygen atoms are in

1.5

mol of

\text{H}_2\text{O}

Example 3

medium

How many molecules are in 2.5 moles of water (

\text{H}_2\text{O}

)? How many individual atoms is that?

Example 4

medium

How many formula units are in 0.1 mol of

\text{Na}_2\text{SO}_4

Example 5

hard

How many total ions are in 0.1 mol of

\text{Mg}_3(\text{PO}_4)_2

Practice Problems

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

Example 1

easy

How many atoms are in

0.50

mol of iron (Fe)?

Example 2

medium

How many chloride ions are in

0.200

mol of

\text{CaCl}_2

Example 3

easy

What is the numerical value of Avogadro's number?

Example 4

easy

How many particles are in 1 mole of sugar?

Example 5

easy

How many particles are in 3 moles of a substance?

Example 6

easy

How many atoms are in 1 mole of

O_2

molecules?

Example 7

easy

Convert

6.022 \times 10^{23}

atoms to moles.

Example 8

easy

Does Avogadro's number apply to ions like

Na^+

Example 9

easy

How many particles are in 0.25 mol of argon?

Example 10

easy

How many molecules are in 5 moles of

H_2

Example 11

medium

How many atoms are in 0.5 mol of

CO_2

Example 12

medium

A sample has

1.8066 \times 10^{24}

molecules. How many moles is that?

Example 13

medium

How many hydrogen atoms are in 2 moles of

H_2O

Example 14

medium

How many moles of

O_2

contain

3.011 \times 10^{24}

oxygen atoms?

Example 15

medium

Which has more atoms: 1 mol

H_2

or 0.4 mol

CH_4

Example 16

medium

How many formula units are in 1.5 mol of

NaCl

Example 17

medium

How many sodium ions are in 2 mol of

Na_2SO_4

Example 18

medium

How many atoms are in 0.5 mol of

NH_3

(count all atoms)?

Example 19

medium

How many moles of atoms are in

1.2044 \times 10^{24}

atoms?

Example 20

challenge

A balloon holds

1.2044 \times 10^{24}

atoms of helium. What is its mass if

He

4\text{ g/mol}

Example 21

challenge

N_A

were instead defined as

3.0 \times 10^{23}

, how many of these 'new moles' equal

6.0 \times 10^{23}

particles?

Example 22

challenge

How many total ions are in 0.5 mol of

Al_2(SO_4)_3

(count all ions)?

Example 23

easy

How many molecules are in 0.5 mol of

\text{N}_2

Example 24

easy

How many atoms are in 1 mol of helium?

Example 25

easy

Convert

3.011 \times 10^{23}

atoms to moles.

Example 26

easy

How many particles are in 4 mol of any substance?

Example 27

easy

Convert

1.204 \times 10^{24}

atoms to moles.

Example 28

easy

How many ions are in 0.1 mol of

\text{K}^+

Example 29

medium

How many atoms are in 0.25 mol of

\text{CH}_4

(count all atoms)?

Example 30

medium

A sample contains

3.011 \times 10^{24}

molecules. How many moles is that?

Example 31

medium

How many oxygen atoms are in 0.5 mol of

\text{SO}_2

Example 32

medium

How many moles contain

9.033 \times 10^{22}

particles?

Example 33

medium

Which has more atoms: 0.5 mol of

\text{H}_2

or 0.5 mol of He?

Example 34

medium

How many chloride ions are in 0.25 mol

\text{AlCl}_3

Example 35

medium

How many moles of water contain

3.011 \times 10^{23}

molecules?

Example 36

hard

A 9 g sample of water has how many molecules? (

M_{H_2O}=18

)

Example 37

hard

A sample of

\text{CO}_2

has

1.2044 \times 10^{24}

molecules. What mass does it have? (

M_{CO_2}=44

)

Example 38

hard

How many electrons are in 0.5 mol of

\text{H}_2\text{O}

? Each molecule has 10 electrons.

Example 39

hard

A sample contains

1.806 \times 10^{22}

atoms of carbon. How many grams is that? (

M_C=12

)

Example 40

hard

What mass of gold (

M=197

) contains

3.011 \times 10^{22}

atoms?

Example 41

challenge

A diamond contains 0.05 mol of carbon atoms. How many carbon-carbon bonds are present, assuming each C atom forms 4 bonds and each bond is shared by 2 atoms?

Example 42

challenge

If 1 mole of pennies were stacked, the column would be roughly

9.6 \times 10^{19}

km tall. Estimate how many years light (300,000 km/s) would take to travel that distance. (1 year

\approx 3.15 \times 10^7

← Back to Avogadro's Number Formula Explained Common Mistakes Practice Mode

Related Concepts

Mole Molar Mass

Background Knowledge

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

mole