Mole Concept Practice Problems: Questions, Answers, and Solutions

The mole concept is one of the most important topics in chemistry. It helps us calculate the amount of a substance using moles, mass, particles, atoms, molecules, ions, and formula units.

Learning the formulas is important, but solving practice problems is the best way to understand the mole concept. If you are new to the topic, start with this complete guide to the mole concept before working through these problems.

This collection of mole concept practice problems includes basic, intermediate, and multi-step questions. Each problem is followed by a clear solution so you can check your work.

Before starting, make sure you understand the basic mole formulas. You can also learn how to calculate moles step by step if you need a quick review.

Important Mole Concept Formulas

1. Calculate Moles from Mass

n = m ÷ M

Where:

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

For more practice with this type of calculation, see how to convert grams to moles.

2. Calculate Mass from Moles

m = n × M

See how to convert moles to grams for more examples.

3. Calculate Particles from Moles

N = n × N_A

4. Calculate Moles from Particles

n = N ÷ N_A

Avogadro's number is:

N_A = 6.022 × 10²³ particles/mol

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

5. Mole-to-Mole Conversion

Use the coefficients in a balanced chemical equation to determine the mole ratio.

Moles of desired substance = Moles of given substance × Mole ratio

Learn more about mole-to-mole conversion before solving reaction-based problems.

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Part 1: Basic Mole Concept Practice Problems

Problem 1: Calculate Moles from Mass

Question: How many moles are present in 18 g of H₂O?

Solution

Molar mass of H₂O:

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

Use:

n = m ÷ M

n = 18 ÷ 18

n = 1 mol

Answer: 1 mol H₂O

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Problem 2: Calculate Moles from Mass of CO₂

Question: How many moles are present in 88 g of CO₂?

Solution

Molar mass of CO₂:

M = 12 + (2 × 16) = 44 g/mol

n = m ÷ M

n = 88 ÷ 44

n = 2 mol

Answer: 2 mol CO₂

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Problem 3: Calculate Mass from Moles

Question: What is the mass of 3 moles of NaCl?

Solution

Molar mass of NaCl:

M = 23 + 35.5 = 58.5 g/mol

Use:

m = n × M

m = 3 × 58.5

m = 175.5 g

Answer: 175.5 g NaCl

If you need help finding molar mass, see What Is Molar Mass?

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Problem 4: Calculate Mass from Moles of Oxygen

Question: What is the mass of 2 moles of O₂?

Solution

Molar mass of O₂:

M = 2 × 16 = 32 g/mol

m = n × M

m = 2 × 32

m = 64 g

Answer: 64 g O₂

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Part 2: Mole and Particle Practice Problems

Problem 5: Moles to Molecules

Question: How many H₂O molecules are present in 2 moles of water?

Solution

Use:

N = n × N_A

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Answer: 1.2044 × 10²⁴ H₂O molecules

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

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Problem 6: Moles to Atoms

Question: How many carbon atoms are present in 0.5 mole of carbon?

Solution

N = n × N_A

N = 0.5 × 6.022 × 10²³

N = 3.011 × 10²³

Answer: 3.011 × 10²³ carbon atoms

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Problem 7: Particles to Moles

Question: How many moles are present in 3.011 × 10²³ O₂ molecules?

Solution

Use:

n = N ÷ N_A

n = (3.011 × 10²³) ÷ (6.022 × 10²³)

n = 0.5 mol

Answer: 0.5 mol O₂

See how to convert particles to moles for additional practice.

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Problem 8: Particles to Moles

Question: How many moles are present in 1.2044 × 10²⁴ CO₂ molecules?

Solution

n = N ÷ N_A

n = (1.2044 × 10²⁴) ÷ (6.022 × 10²³)

n = 2 mol

Answer: 2 mol CO₂

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Part 3: Counting Atoms in Compounds

Problem 9: Hydrogen Atoms in Water

Question: How many hydrogen atoms are present in 1 mole of H₂O?

Solution

One H₂O molecule contains 2 hydrogen atoms.

One mole of H₂O contains:

6.022 × 10²³ molecules

Therefore:

Number of H atoms = 6.022 × 10²³ × 2

= 1.2044 × 10²⁴

Answer: 1.2044 × 10²⁴ hydrogen atoms

Understanding chemical subscripts is important for these problems. You can review the basics in the complete mole concept guide.

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Problem 10: Oxygen Atoms in Carbon Dioxide

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

Solution

Each CO₂ molecule contains 2 oxygen atoms.

First calculate the number of CO₂ molecules:

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴ molecules

Now calculate oxygen atoms:

1.2044 × 10²⁴ × 2

= 2.4088 × 10²⁴

Answer: 2.4088 × 10²⁴ oxygen atoms

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Problem 11: Total Atoms in CO₂

Question: How many total atoms are present in 1 mole of CO₂?

Solution

Each CO₂ molecule contains:

• 1 carbon atom
• 2 oxygen atoms

Total atoms per molecule:

1 + 2 = 3 atoms

One mole contains:

6.022 × 10²³ molecules

Therefore:

6.022 × 10²³ × 3

= 1.8066 × 10²⁴ atoms

Answer: 1.8066 × 10²⁴ total atoms

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Part 4: Mole Concept Mixed Problems

Problem 12: Mass to Molecules

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

Solution

First convert mass to moles.

Molar mass of H₂O = 18 g/mol.

n = m ÷ M

n = 36 ÷ 18

n = 2 mol

Now convert moles to molecules:

N = n × N_A

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴ molecules

Answer: 1.2044 × 10²⁴ H₂O molecules

This type of problem combines grams-to-moles and moles-to-particles conversions.

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Problem 13: Mass to Atoms

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

Solution

Molar mass of carbon = 12 g/mol.

n = m ÷ M

n = 24 ÷ 12

n = 2 mol

Now:

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Answer: 1.2044 × 10²⁴ carbon atoms

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Problem 14: Molecules to Mass

Question: What is the mass of 3.011 × 10²³ H₂O molecules?

Solution

First convert molecules to moles:

n = N ÷ N_A

n = (3.011 × 10²³) ÷ (6.022 × 10²³)

n = 0.5 mol

Now calculate mass:

m = n × M

m = 0.5 × 18

m = 9 g

Answer: 9 g H₂O

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Problem 15: Mass to Atoms in a Compound

Question: How many oxygen atoms are present in 44 g of CO₂?

Solution

Molar mass of CO₂:

M = 12 + (2 × 16) = 44 g/mol

Therefore:

n = 44 ÷ 44 = 1 mol CO₂

One mole of CO₂ contains:

6.022 × 10²³ CO₂ molecules

Each molecule contains 2 oxygen atoms.

Therefore:

6.022 × 10²³ × 2

= 1.2044 × 10²⁴ oxygen atoms

Answer: 1.2044 × 10²⁴ oxygen atoms

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Part 5: Mole-to-Mole Practice Problems

Problem 16: Hydrogen and Oxygen Reaction

Question: How many moles of H₂O are produced when 4 moles of H₂ react with excess O₂?

Balanced equation:

2H₂ + O₂ → 2H₂O

Solution

Mole ratio:

2 mol H₂ : 2 mol H₂O

Therefore:

4 mol H₂ × (2 mol H₂O ÷ 2 mol H₂)

= 4 mol H₂O

Answer: 4 mol H₂O

For more practice with reaction ratios, see Mole to Mole Conversion.

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Problem 17: Nitrogen and Hydrogen Reaction

Question: How many moles of NH₃ can be produced from 5 moles of N₂?

Balanced equation:

N₂ + 3H₂ → 2NH₃

Solution

Mole ratio:

1 mol N₂ : 2 mol NH₃

Therefore:

5 mol N₂ × (2 mol NH₃ ÷ 1 mol N₂)

= 10 mol NH₃

Answer: 10 mol NH₃

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Problem 18: Decomposition of Calcium Carbonate

Question: How many moles of CO₂ are produced when 3 moles of CaCO₃ decompose?

Balanced equation:

CaCO₃ → CaO + CO₂

Solution

Mole ratio:

1 mol CaCO₃ : 1 mol CO₂

Therefore:

3 mol CaCO₃ → 3 mol CO₂

Answer: 3 mol CO₂

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Problem 19: Potassium Chlorate Decomposition

Question: How many moles of O₂ are produced from 4 moles of KClO₃?

Balanced equation:

2KClO₃ → 2KCl + 3O₂

Solution

Mole ratio:

2 mol KClO₃ : 3 mol O₂

Therefore:

4 mol KClO₃ × (3 mol O₂ ÷ 2 mol KClO₃)

= 6 mol O₂

Answer: 6 mol O₂

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Part 6: Challenge Problems

Problem 20: Mass to Moles to Particles

Question: How many molecules are present in 90 g of H₂O?

Solution

Molar mass of H₂O = 18 g/mol.

First find the moles:

n = 90 ÷ 18 = 5 mol

Now convert moles to molecules:

N = 5 × 6.022 × 10²³

N = 3.011 × 10²⁴

Answer: 3.011 × 10²⁴ H₂O molecules

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Problem 21: Mass to Atoms in CO₂

Question: How many oxygen atoms are present in 88 g of CO₂?

Solution

Molar mass of CO₂ = 44 g/mol.

n = 88 ÷ 44 = 2 mol CO₂

Number of CO₂ molecules:

N = 2 × 6.022 × 10²³

N = 1.2044 × 10²⁴ molecules

Each molecule contains 2 oxygen atoms:

1.2044 × 10²⁴ × 2

= 2.4088 × 10²⁴ oxygen atoms

Answer: 2.4088 × 10²⁴ oxygen atoms

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Problem 22: Reaction Mass Calculation

Question: What mass of H₂O can be produced from 4 moles of H₂?

Balanced equation:

2H₂ + O₂ → 2H₂O

Step 1: Convert H₂ to H₂O

The mole ratio is:

2 mol H₂ : 2 mol H₂O

Therefore:

4 mol H₂ → 4 mol H₂O

Step 2: Convert Moles to Mass

Molar mass of H₂O = 18 g/mol.

m = n × M

m = 4 × 18

m = 72 g

Answer: 72 g H₂O

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Quick Mole Concept Practice Test

Try these questions without looking at the solutions. If you want additional worked examples before attempting the test, see Mole Concept Examples.

1. How many moles are present in 36 g of H₂O?
2. What is the mass of 2 moles of CO₂?
3. How many molecules are present in 0.5 mole of O₂?
4. How many moles are present in 6.022 × 10²³ molecules of H₂O?
5. How many carbon atoms are present in 2 moles of carbon?
6. How many oxygen atoms are present in 1 mole of CO₂?
7. How many moles of NH₃ are produced from 3 moles of N₂?
8. How many grams are present in 5 moles of NaCl?
9. How many H₂O molecules are present in 18 g of water?
10. How many oxygen atoms are present in 44 g of CO₂?

Quick Test Answers

1. 2 mol H₂O
2. 88 g CO₂
3. 3.011 × 10²³ O₂ molecules
4. 1 mol H₂O
5. 1.2044 × 10²⁴ carbon atoms
6. 1.2044 × 10²⁴ oxygen atoms
7. 6 mol NH₃
8. 292.5 g NaCl
9. 6.022 × 10²³ H₂O molecules
10. 1.2044 × 10²⁴ oxygen atoms

Tips for Solving Mole Concept Problems

Follow these steps whenever you face a mole concept problem:

1. Read the question carefully.
2. Identify what is given.
3. Identify what you need to find.
4. Choose the correct formula.
5. Calculate the molar mass if necessary.
6. Keep your units consistent.
7. Check your scientific notation.
8. Write the correct unit in the final answer.

If you make repeated calculation errors, review these common mole calculation mistakes and learn how to avoid them.

Common Mole Concept Mistakes

Using the Wrong Formula

Remember the basic relationships:

n = m ÷ M

m = n × M

N = n × N_A

n = N ÷ N_A

Forgetting Avogadro's Number

When converting between moles and particles, use:

6.022 × 10²³

Ignoring Chemical Subscripts

For example, CO₂ contains two oxygen atoms per molecule. H₂O contains two hydrogen atoms and one oxygen atom.

Using an Unbalanced Equation

Always balance a chemical equation before using its coefficients for mole-to-mole calculations.

Forgetting Units

Always include units such as mol, g, atoms, molecules, ions, or formula units.

Frequently Asked Questions

What is the easiest mole formula to remember?

The most important formulas are:

n = m ÷ M

m = n × M

N = n × N_A

n = N ÷ N_A

How many particles are in one mole?

One mole contains exactly 6.02214076 × 10²³ specified elementary entities. In most school calculations, this is written as 6.022 × 10²³.

How do I know which mole formula to use?

Look at the information given. If mass is given, use molar mass. If particles are given, use Avogadro's number. If a chemical equation is given, use the mole ratio from the balanced equation.

Why do I need to balance a chemical equation?

The coefficients of a balanced chemical equation represent the mole ratios between the substances involved in the reaction.

What is the best way to learn the mole concept?

Start with simple mass-to-mole and mole-to-particle conversions. Then practice particle counting and finally move to multi-step and stoichiometric problems.

Final Summary

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

Remember these four important formulas:

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

Also remember:

1 mol = 6.022 × 10²³ particles

The more problems you solve, the easier mole calculations become. Practice each type separately first, then combine different conversions in multi-step problems.