Mole Examples: 47 Problems with Answers

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

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 fundamental counting unit in chemistry, defined as exactly $6.022 \times 10^{23}$ particles (atoms, molecules, ions, or other entities).

A 'chemist's dozen'—a huge number that makes atom-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: Mole 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 mole 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 Stoichiometry Mistakes

Worked Examples

Example 1

easy

What is a mole and why is it useful in chemistry?

Answer

1 mol = 6.022 \times 10^{23} particles

First step

A mole is a counting unit:

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

particles (Avogadro's number).

Full solution

2
It bridges the atomic scale (individual atoms/molecules) and the macroscopic scale (grams, liters).
3
One mole of any element has a mass in grams equal to its atomic mass in amu.

The mole is the chemist's counting unit, analogous to a 'dozen' but for atoms and molecules. It allows us to relate masses we can measure to numbers of particles.

Example 2

medium

How many moles of water are in

36.0

g of

\text{H}_2\text{O}

? (Molar mass of

\text{H}_2\text{O} = 18.0\,\text{g/mol}

)

Example 3

medium

How many oxygen atoms are in

0.50\,\text{mol}

of glucose (

\text{C}_6\text{H}_{12}\text{O}_6

Example 4

medium

3.0\,\text{g}

of carbon contains how many atoms? (

M = 12

)

Example 5

hard

Compare particle count:

11\,\text{g}

\text{CO}_2

4.0\,\text{g}

\text{He}

. Which has more atoms?

Example 6

hard

200\,\text{mL}

sample of

0.50\,\text{M}

glucose contains how many molecules?

Practice Problems

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

Example 1

easy

How many moles are in

40.0

g of NaOH? (Molar mass =

40.0\,\text{g/mol}

)

Example 2

easy

A sample contains

1.204 \times 10^{24}

molecules of ammonia. How many moles of

\text{NH}_3

is this?

Example 3

easy

How many particles are in exactly 1 mole of any substance?

Example 4

easy

How many atoms are in 2 moles of helium (

He

) atoms?

Example 5

easy

Which weighs more: 1 mole of carbon (

12\text{ g/mol}

) or 1 mole of iron (

56\text{ g/mol}

Example 6

easy

Express

3

moles of water molecules as a number of molecules.

Example 7

easy

How many moles is

1.2044 \times 10^{24}

atoms of neon?

Example 8

easy

Is '1 mole of oxygen' fully specified? Why or why not?

Example 9

easy

How many moles of atoms are in 4 moles of

O_2

molecules?

Example 10

easy

A sample contains

0.5

mol of a substance. How many particles is that?

Example 11

medium

How many moles is

9.033 \times 10^{23}

molecules of

CO_2

Example 12

medium

How many oxygen atoms are in 2 moles of

CO_2

Example 13

medium

Convert

1.5066 \times 10^{24}

atoms of sodium to moles.

Example 14

medium

A flask holds

3.011 \times 10^{23}

molecules of

N_2

. How many nitrogen atoms is that?

Example 15

medium

Order by particle count: 1 mol

He

, 0.5 mol

O_2

, 2 mol

H

atoms.

Example 16

medium

How many total atoms are in 1 mole of

H_2O

Example 17

medium

If 1 mol

Al

weighs

27\text{ g}

, how many atoms are in

54\text{ g}

Al

Example 18

medium

How many moles of

H

atoms are in 3 moles of

NH_3

Example 19

medium

How many molecules are in 0.75 mol of

N_2

Example 20

challenge

A sample has

1.2044 \times 10^{24}

atoms total and is pure

O_2

. How many moles of

O_2

molecules is that?

Example 21

challenge

Two samples have equal particle counts: sample A is

He

, sample B is

CH_4

. If A is

0.5

mol, how many molecules does B have?

Example 22

challenge

How many total atoms are in

0.25

mol of

Ca(OH)_2

Example 23

easy

How many atoms are in

0.25\,\text{mol}

of iron?

Example 24

easy

How many moles are in

3.011 \times 10^{24}

atoms of carbon?

Example 25

easy

How many atoms are in

1.5\,\text{mol}

\text{Ne}

Example 26

easy

1\,\text{mol}

\text{H}_2

the same number of particles as

1\,\text{mol}

\text{He}

Example 27

easy

How many moles of

\text{O}_2

molecules give

3.011 \times 10^{23}

molecules?

Example 28

medium

How many moles of

\text{O}_2

molecules are in

128\,\text{g}

? (

M = 32

)

Example 29

medium

At STP, how many moles of an ideal gas occupy

44.8\,\text{L}

? (

V_m = 22.4\,\text{L/mol}

)

Example 30

medium

How many molecules of water are in a glass containing

54\,\text{g}

of water? (

M = 18

)

Example 31

medium

How many sodium ions are in

0.20\,\text{mol}

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

Example 32

medium

How many moles of

\text{H}

atoms are in

0.5\,\text{mol}

\text{H}_2\text{SO}_4

Example 33

medium

How many moles of

\text{H}_2\text{O}

are in

9.033 \times 10^{22}

molecules?

Example 34

medium

At STP, what volume does

0.25\,\text{mol}

of an ideal gas occupy?

Example 35

hard

How many total atoms are in

0.20\,\text{mol}

\text{(NH}_4)_2\text{SO}_4

Example 36

hard

A sample of

\text{Mg}

contains

1.204 \times 10^{23}

atoms. Find its mass. (

M = 24

)

Example 37

hard

How many chloride ions are released when

0.1\,\text{mol}

\text{CaCl}_2

dissolves fully in water?

Example 38

hard

Are there more atoms in

1\,\text{g}

\text{H}_2

1\,\text{g}

\text{He}

? Justify with mole counts.

Example 39

hard

At STP,

11.2\,\text{L}

of an unknown gas weighs

14\,\text{g}

. Find its molar mass and propose the gas.

Example 40

hard

How many electrons are in

1\,\text{mol}

\text{H}_2\text{O}

Example 41

challenge

A sealed bulb at STP contains

1.12\,\text{L}

of a mixture that is

25\%

\text{N}_2

and

75\%

\text{O}_2

by volume. How many total atoms are in the bulb? (

V_m = 22.4\,\text{L/mol}

)

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Related Concepts

Atom Molecule Avogadro's Number Molar Mass Stoichiometry

Background Knowledge

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

atommolecule