Mole Concept Examples: Easy Chemistry Problems and Solutions

The mole concept is one of the most important topics in chemistry. It helps us connect the tiny particles that make up matter with measurable quantities such as mass, moles, and the number of particles.

Many chemistry problems involve converting between moles, mass, particles, atoms, molecules, ions, and formula units.

The good news is that most mole concept problems can be solved using a few simple formulas.

In this guide, you will find several mole concept examples with step-by-step solutions. The examples start with basic calculations and gradually move to more challenging problems.

If you want a broader introduction before working through these examples, read this complete guide to the mole concept.

Important Mole Concept Formulas

Before solving the examples, remember these important formulas.

1. Moles from Mass

n = m ÷ M

Where:

• n = number of moles
• m = mass in grams
• M = molar mass in g/mol

For more detailed examples, see how to convert grams to moles.

2. Mass from Moles

m = n × M

You can learn more about this conversion in how to convert moles to grams.

3. Moles from Particles

n = N ÷ N_A

4. Particles from Moles

N = n × N_A

Here:

N_A = 6.022 × 10²³ particles/mol

For a detailed explanation of this value, see What Is Avogadro's Number?

5. Mole-to-Mole Conversion

For chemical reactions:

Moles of desired substance = Moles of given substance × (Coefficient of desired substance ÷ Coefficient of given substance)

See Mole to Mole Conversion for more step-by-step practice.

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Example 1: Calculate Moles from Mass

Question

How many moles are present in 18 g of water (H₂O)?

Step 1: Find the Molar Mass

The molar mass of H₂O is:

H₂O = (2 × 1.008) + 16.00

= 18.016 g/mol

For a simple school-level calculation, we can use approximately 18 g/mol.

Step 2: Use the Formula

n = m ÷ M

Step 3: Calculate

n = 18 g ÷ 18 g/mol

n = 1 mol

Answer

18 g of H₂O contains approximately 1 mole of water.

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Example 2: Calculate Moles from 44 g of CO₂

Question

How many moles are present in 44 g of carbon dioxide?

Step 1: Calculate Molar Mass

CO₂ contains:

• 1 carbon atom = 12.01 g/mol
• 2 oxygen atoms = 2 × 16.00 g/mol

Therefore:

M = 12.01 + (2 × 16.00)

M = 44.01 g/mol

Step 2: Use the Formula

n = m ÷ M

Calculation

n = 44 g ÷ 44.01 g/mol

n ≈ 1 mol

Answer

44 g of CO₂ contains approximately 1 mole of CO₂.

For more information about calculating molar mass, see What Is Molar Mass?

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Example 3: Calculate Mass from Moles

Question

What is the mass of 2 moles of NaCl?

Step 1: Find the Molar Mass

NaCl contains:

• Na = 22.99 g/mol
• Cl = 35.45 g/mol

Therefore:

M = 22.99 + 35.45

M = 58.44 g/mol

Step 2: Use the Formula

m = n × M

Calculation

m = 2 mol × 58.44 g/mol

m = 116.88 g

Answer

2 moles of NaCl have a mass of 116.88 g.

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Example 4: Convert Moles to Molecules

Question

How many molecules are present in 2 moles of water?

Formula

N = n × N_A

Calculation

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Answer

2 moles of H₂O contain 1.2044 × 10²⁴ water molecules.

For more practice, see how to convert moles to particles.

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Example 5: Convert Molecules to Moles

Question

How many moles are present in 3.011 × 10²³ CO₂ molecules?

Formula

n = N ÷ N_A

Calculation

n = (3.011 × 10²³) ÷ (6.022 × 10²³)

n = 0.5 mol

Answer

3.011 × 10²³ CO₂ molecules = 0.5 mole of CO₂.

For additional practice, see how to convert particles to moles.

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Example 6: Calculate the Number of Atoms in a Mole

Question

How many carbon atoms are present in 2 moles of carbon?

Formula

N = n × N_A

Calculation

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Answer

2 moles of carbon contain 1.2044 × 10²⁴ carbon atoms.

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Example 7: Calculate the Number of Hydrogen Atoms in Water

Question

How many hydrogen atoms are present in 2 moles of H₂O?

Each H₂O molecule contains 2 hydrogen atoms.

Step 1: Find the Number of Water Molecules

N = n × N_A

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴ H₂O molecules

Step 2: Find the Number of Hydrogen Atoms

Each molecule contains 2 hydrogen atoms.

Number of H atoms = 1.2044 × 10²⁴ × 2

= 2.4088 × 10²⁴

Answer

2 moles of H₂O contain 2.4088 × 10²⁴ hydrogen atoms.

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Example 8: Calculate the Number of Oxygen Atoms in CO₂

Question

How many oxygen atoms are present in 1 mole of CO₂?

Each CO₂ molecule contains 2 oxygen atoms.

Step 1: Find the Number of CO₂ Molecules

N = 1 × 6.022 × 10²³

N = 6.022 × 10²³ molecules

Step 2: Calculate Oxygen Atoms

Number of O atoms = 6.022 × 10²³ × 2

= 1.2044 × 10²⁴

Answer

1 mole of CO₂ contains 1.2044 × 10²⁴ oxygen atoms.

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Example 9: Mole-to-Mole Conversion

Question

According to the equation below, how many moles of water are produced when 3 moles of H₂ react with excess O₂?

2H₂ + O₂ → 2H₂O

Step 1: Identify the Mole Ratio

From the balanced equation:

2 mol H₂ : 2 mol H₂O

Therefore:

1 mol H₂ : 1 mol H₂O

Step 2: Calculate

3 mol H₂ × (2 mol H₂O ÷ 2 mol H₂)

= 3 mol H₂O

Answer

3 moles of H₂ produce 3 moles of H₂O.

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Example 10: Mole-to-Mole Conversion with Different Coefficients

Question

How many moles of NH₃ can be produced from 3 moles of N₂?

The balanced equation is:

N₂ + 3H₂ → 2NH₃

Step 1: Identify the Mole Ratio

From the equation:

1 mol N₂ : 2 mol NH₃

Step 2: Use the Ratio

3 mol N₂ × (2 mol NH₃ ÷ 1 mol N₂)

= 6 mol NH₃

Answer

3 moles of N₂ can produce 6 moles of NH₃, assuming sufficient H₂ is available.

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Example 11: Calculate the Number of Molecules from Mass

Question

How many H₂O molecules are present in 36 g of water?

This is a two-step problem.

Step 1: Convert Mass to Moles

The molar mass of H₂O is approximately 18 g/mol.

n = m ÷ M

n = 36 g ÷ 18 g/mol

n = 2 mol

Step 2: Convert Moles to Molecules

N = n × N_A

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Answer

36 g of H₂O contains 1.2044 × 10²⁴ water molecules.

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Example 12: Calculate Atoms from Mass

Question

How many carbon atoms are present in 12 g of carbon?

Step 1: Convert Grams to Moles

The molar mass of carbon is approximately 12 g/mol.

n = m ÷ M

n = 12 g ÷ 12 g/mol

n = 1 mol

Step 2: Convert Moles to Atoms

N = n × N_A

N = 1 × 6.022 × 10²³

N = 6.022 × 10²³ atoms

Answer

12 g of carbon contains approximately 6.022 × 10²³ carbon atoms.

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Example 13: Calculate Moles of Oxygen Atoms in Water

Question

How many moles of oxygen atoms are present in 3 moles of H₂O?

The formula of water is:

H₂O

Each molecule contains 1 oxygen atom.

Therefore, the mole ratio is:

1 mol H₂O : 1 mol O atoms

So:

3 mol H₂O × (1 mol O ÷ 1 mol H₂O)

= 3 mol O atoms

Answer

3 moles of H₂O contain 3 moles of oxygen atoms.

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Example 14: Calculate Moles of Hydrogen Atoms in Water

Question

How many moles of hydrogen atoms are present in 4 moles of H₂O?

Each H₂O molecule contains 2 hydrogen atoms.

Therefore:

1 mol H₂O : 2 mol H atoms

So:

4 mol H₂O × (2 mol H ÷ 1 mol H₂O)

= 8 mol H atoms

Answer

4 moles of H₂O contain 8 moles of hydrogen atoms.

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Example 15: Calculate the Number of Atoms in 0.5 Mole of CO₂

Question

How many total atoms are present in 0.5 mole of CO₂?

Each CO₂ molecule contains:

• 1 carbon atom
• 2 oxygen atoms

Total atoms per molecule:

1 + 2 = 3 atoms

Step 1: Find the Number of CO₂ Molecules

N = 0.5 × 6.022 × 10²³

N = 3.011 × 10²³ molecules

Step 2: Find Total Atoms

3.011 × 10²³ × 3

= 9.033 × 10²³ atoms

Answer

0.5 mole of CO₂ contains 9.033 × 10²³ total atoms.

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Example 16: A Multi-Step Mole Concept Problem

Question

How many molecules are present in 90 g of water?

Step 1: Calculate the Molar Mass

For H₂O:

M = 2(1) + 16 = 18 g/mol

Step 2: Convert Mass to Moles

n = m ÷ M

n = 90 g ÷ 18 g/mol

n = 5 mol

Step 3: Convert Moles to Molecules

N = n × N_A

N = 5 × 6.022 × 10²³

N = 3.011 × 10²⁴ molecules

Answer

90 g of H₂O contains 3.011 × 10²⁴ water molecules.

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Mole Concept Problem-Solving Strategy

When solving a mole concept problem, first identify what information is given and what the question asks you to find.

A useful conversion path is:

Mass → Moles → Particles

or:

Particles → Moles → Mass

For chemical reactions, you may use:

Mass → Moles → Mole Ratio → Moles → Mass

This approach helps you solve even complicated chemistry problems step by step.

For more worked problems using these methods, see Mole Concept Practice Problems.

Common Mistakes in Mole Concept Problems

1. Using the Wrong Formula

Make sure you know what you are converting.

• Mass → Moles: n = m ÷ M
• Moles → Mass: m = n × M
• Particles → Moles: n = N ÷ N_A
• Moles → Particles: N = n × N_A

2. Forgetting to Calculate Molar Mass

When converting mass to moles or moles to mass, you need the molar mass of the substance.

3. Confusing Molecules with Atoms

One molecule may contain several atoms.

For example:

H₂O contains 2 hydrogen atoms and 1 oxygen atom.

4. Forgetting Subscripts

The subscript tells you how many atoms of an element are present in one molecule or formula unit.

For example:

CO₂ contains 2 oxygen atoms per molecule.

5. Using an Unbalanced Chemical Equation

For mole-to-mole calculations in chemical reactions, always start with a balanced equation.

6. Making Scientific Notation Errors

Large particle numbers are usually written using scientific notation. Carefully check the exponent when multiplying or dividing.

For more detailed guidance, see Common Mole Calculation Mistakes.

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Practice Problems

Try solving these problems without looking at the answers first.

Problem 1

How many moles are present in 36 g of H₂O?

Problem 2

How many molecules are present in 3 moles of CO₂?

Problem 3

How many carbon atoms are present in 24 g of carbon?

Problem 4

How many moles are present in 1.2044 × 10²⁴ molecules of O₂?

Problem 5

What is the mass of 3 moles of NaCl?

Problem 6

How many moles of oxygen atoms are present in 2 moles of CO₂?

Problem 7

How many molecules are present in 36 g of H₂O?

Problem 8

How many moles of NH₃ can be produced from 4 moles of N₂?

N₂ + 3H₂ → 2NH₃

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Practice Problem Answers

1. 2 mol H₂O
2. 1.8066 × 10²⁴ CO₂ molecules
3. 1.2044 × 10²⁴ carbon atoms
4. 2 mol O₂
5. 175.32 g NaCl
6. 4 mol oxygen atoms
7. 1.2044 × 10²⁴ H₂O molecules
8. 8 mol NH₃

Frequently Asked Questions

What is the mole concept?

The mole concept is a method of measuring the amount of a substance by counting extremely large numbers of particles such as atoms, molecules, ions, or formula units.

For a more detailed explanation, read What Is a Mole in Chemistry?

What is Avogadro's number?

Avogadro's number is 6.02214076 × 10²³. It represents the number of specified elementary entities in one mole.

What is the formula for calculating moles?

When mass is given:

n = m ÷ M

When particles are given:

n = N ÷ N_A

How do I convert moles to particles?

Multiply the number of moles by Avogadro's number:

N = n × N_A

How do I convert particles to moles?

Divide the number of particles by Avogadro's number:

n = N ÷ N_A

How do I solve mole-to-mole problems?

First, balance the chemical equation. Then use the coefficients of the balanced equation as mole ratios.

Why is the mole concept important?

The mole concept allows chemists to connect microscopic particles with measurable quantities such as mass and volume. It is essential for stoichiometry and many chemical calculations.

Key Takeaways

The mole concept becomes much easier when you understand the relationship between mass, moles, particles, and chemical equations.

• Mass → Moles: n = m ÷ M
• Moles → Mass: m = n × M
• Moles → Particles: N = n × N_A
• Particles → Moles: n = N ÷ N_A
• 1 mol = 6.022 × 10²³ particles
• Use balanced chemical equations for mole-to-mole calculations.
• Always pay attention to chemical formulas, subscripts, units, and scientific notation.

With regular practice, mole concept calculations become much easier. Start with simple mass-to-mole and mole-to-particle problems, then move on to multi-step calculations and stoichiometry.