1. Counting Particles

Why Do Chemists Need to Count Particles?

Chemistry is concerned with substances made from extremely small particles. Depending on the substance, these particles may be atoms, molecules, ions, or formula units.

A small sample of a substance can contain an enormous number of particles. For example, even a tiny drop of water contains far more water molecules than we could ever count individually.

This creates an important problem:

How can chemists describe and measure such enormous numbers of tiny particles?

Chemists solve this problem by using a special counting unit.

 

 

 

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Counting Units in Everyday Life

We already use special counting units when dealing with groups of objects.

For example:

Counting Unit.	Number of Objects
Pair	2
Half-dozen	6
Dozen	12
Score	20
Gross	144

If someone says they bought 3 dozen eggs, we do not need to count every egg individually.

3 × 12 = 36 eggs

The word dozen is simply a convenient way of representing a particular number.

Chemists use the same basic idea. However, because atoms and molecules are so incredibly small, the chemical counting unit must represent a much larger number than a dozen.

Think About It

Imagine trying to buy sugar by asking for:

3,000,000,000,000,000,000,000 sugar molecules.

A counting unit makes numbers like this much easier to describe and work with.

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What Particles Are We Counting?

Before we can count chemical particles, we need to know what type of particle we are talking about.

Atoms

An atom is the smallest particle of an element that retains the chemical properties of that element.

Examples include:

• He — helium atom
• Na — sodium atom
• Fe — iron atom
• Ne — neon atom

A piece of iron, for example, contains an enormous number of iron atoms.

Molecules

A molecule consists of two or more atoms chemically bonded together as a discrete particle.

Examples include:

• H₂ — hydrogen molecule
• O₂ — oxygen molecule
• H₂O — water molecule
• CO₂ — carbon dioxide molecule

One molecule of water contains:

2 H atoms+1 O atom

Therefore, each H₂O molecule contains 3 atoms in total.

 

 

 

 

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Ions

An ion is an atom or group of atoms that has an electrical charge because electrons have been gained or lost.

Examples include:

• Na⁺ — sodium ion
• Cl⁻ — chloride ion
• Mg²⁺ — magnesium ion
• OH⁻ — hydroxide ion

A positive ion has lost electrons, while a negative ion has gained electrons.

When working with ionic substances, chemists often need to count the number of ions present.

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Formula Units

Ionic compounds such as sodium chloride do not normally exist as individual molecules. Instead, their positive and negative ions form large repeating structures called ionic lattices.

For this reason, we describe ionic compounds using formula units rather than molecules.

For example:

NaCl

One formula unit of NaCl represents the simplest whole-number ratio of ions:

1 Na + : 1 Cl−

Similarly:

CaCl₂

​

represents:

1 Ca₂ + : 2 Cl−

 

Particle Summary

Particle	Description	Example
Atom	Smallest particle of an element	Fe
Molecule	Two or more atoms bonded as a discrete particle	H₂O
Ion	Charged atom or group of atoms	Na⁺
Formula unit	Simplest ratio of ions in an ionic compound	NaCl

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Why Can't We Just Count the Particles?

Atoms and molecules are incredibly small.

Their sizes are typically measured on scales of around:

10⁻¹⁰ m

Because they are so small, even samples that appear tiny to us contain enormous numbers of particles.

Trying to count them one at a time would be completely impractical.

Imagine counting grains of sand on a beach. Now imagine that every grain of sand was itself replaced by billions upon billions of much smaller particles.

Chemists therefore need to connect the microscopic world of particles with measurements that can actually be made in the laboratory.

 

 

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From the Microscopic World to the Laboratory

This is one of the central challenges of chemistry.

At the microscopic level, chemical reactions involve:

• atoms
• molecules
• ions
• formula units

But in the laboratory, chemists measure things such as:

• mass
• volume
• concentration

A chemist cannot normally place one molecule on a laboratory balance.

Instead, the chemist measures a large collection of molecules and uses a counting unit to determine how many particles are represented by that measurement.

This creates a bridge between two worlds:

Microscopic world

atoms, molecules, ions

↓

Chemical counting unit

↓

Macroscopic world

grams, volumes and measurable samples

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8. The Need for a Standard Chemical Counting Unit

A dozen always means 12 objects.

It does not matter whether we are talking about:

• 12 eggs
• 12 pencils
• 12 oranges

Chemists need a similar standard.

The chemical counting unit must represent the same number of particles every time, regardless of the substance being measured.

For example, the same counting unit can be used for:

• carbon atoms
• water molecules
• sodium ions
• sodium chloride formula units

The particles are different, but the number represented by the counting unit remains the same.

This standard chemical counting unit is called the mole.

We will examine the mole and the enormous number it represents in the next topic.

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Did You Know?

If atoms were large enough to count individually by hand, chemistry would be very different. In reality, the number of particles in ordinary laboratory samples is so enormous that counting even billions of particles every second would still be far too slow.

The mole allows chemists to work with these enormous particle numbers using practical laboratory measurements.

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Key Vocabulary

Counting unit — A word or unit representing a fixed number of objects.

Atom — The smallest particle of an element that retains its chemical properties.

Molecule — Two or more atoms chemically bonded together as a discrete particle.

Ion — An atom or group of atoms with an electrical charge.

Formula unit — The simplest whole-number ratio of ions in an ionic compound.

Particle — A general term used to describe atoms, molecules, ions, or formula units.

Mole — The standard counting unit used by chemists for extremely large numbers of particles.

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Key Takeaways

• Chemical substances contain enormous numbers of extremely small particles.
• Counting individual atoms, molecules, or ions directly is impractical.
• We already use counting units such as a dozen to represent groups of objects.
• Chemists use the same idea but require a much larger counting unit.
• Chemical particles may be atoms, molecules, ions, or formula units.
• Molecules are appropriate for discrete covalent substances, while formula units are used for ionic compounds.
• A standard counting unit allows chemists to connect microscopic particles with measurable quantities in the laboratory.
• This standard chemical counting unit is called the mole.

 

 

 

2. The Mole

What Is a Mole?

Chemists often work with enormous numbers of atoms, molecules, and ions. Writing these numbers out every time would be difficult and impractical.

Instead, chemists use a special counting unit called the mole.

A mole (mol) is the SI unit for amount of substance.

One mole contains exactly:

6.02214076×10²³ particles

​

This number is usually written approximately as:

6.02×10²³

​

The particles could be atoms, molecules, ions, or formula units depending on the substance.

 

 

 

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The Mole as a Counting Unit

The mole is similar to counting units we use in everyday life.

A pair means:

2 objects

A dozen means:

12 objects

A mole means:

6.02×10²³ objects

The important idea is that these words describe numbers, not particular objects.

For example:

• 1 dozen eggs = 12 eggs
• 1 dozen pencils = 12 pencils
• 1 dozen oranges = 12 oranges

Similarly:

• 1 mol of carbon atoms = 6.02×10²³ carbon atoms
• 1 mol of water molecules = 6.02×10²³ water molecules
• 1 mol of sodium ions = 6.02×10²³ sodium ions

The type of particle changes, but the number of particles in one mole does not.

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Avogadro's Constant

The number of particles in one mole is called Avogadro's constant.

It is represented by the symbol:

N_A​

and has the value:

N_A​ = 6.02214076×10²³/mol

​

For most school calculations, this is rounded to:

N_A ​ = 6.02×10²³/mol

​

This means that every mole contains approximately 602,000,000,000,000,000,000,000 particles.

That is why chemists need a special counting unit!

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What Does "Amount of Substance" Mean?

In chemistry, amount of substance tells us how many specified particles are present.

Its SI unit is the mole (mol).

For example: 1 mol H₂​O means:

6.02×10²³ H₂​O molecules

while: 2 mol H₂O means:

2(6.02×1023)

or:

1.204×10²⁴ H₂O molecules

The number of moles therefore tells us the amount of substance present.

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Amount of Substance Is Not the Same as Mass

It is important not to confuse amount of substance with mass.

Amount of substance

Amount of substance measures the number of chemical particles.

It is measured in: moles (mol)​

Mass

Mass measures the quantity of matter in a sample.

In laboratory chemistry, mass is commonly measured in: grams (g)​

Two substances can contain the same number of particles but have very different masses.

For example, one mole of hydrogen molecules and one mole of oxygen molecules both contain: 6.02×10²³ molecules

However, the oxygen sample has a much greater mass because an oxygen molecule is heavier than a hydrogen molecule.

 

 

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Moles and Number of Particles

The relationship between moles and particles can be written as:

Number of particles = number of moles×NA​​

or:

N=nNA​​

where:

• N = number of particles
• n = amount of substance in moles
• N_A​ = Avogadro's constant

Example: One Mole of Carbon

How many carbon atoms are present in 1 mol of carbon?

N = nN_A​ =(1)(6.02×10²³)

Therefore: N = 6.02×10²³ carbon atoms​

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Example: Two Moles of Water

How many water molecules are present in 2 mol of H₂O?

N = nNA​ =(2)(6.02×10²³) = 1.204×10²⁴ molecules​.

 

Therefore, 2 mol of water contains approximately: 1.20×10²⁴ H₂​O molecules​

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Example: Half a Mole of Oxygen

How many O₂ molecules are present in 0.5 mol of oxygen?

N = nN_A​ =(0.5)(6.02×10²³) = 3.01×10²³ O₂​ molecules​

Notice the relationship:

• 1 mol → 6.02×10²³ particles
• 2 mol → 1.204×10²⁴ particles
• 0.5 mol → 3.01×10²³ particles

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Different Substances, Same Number of Particles

One of the most important ideas about the mole is that one mole always represents the same number of particles.

Substance.	Amount.	Number of Particles.	Type of Particle
He	1 mol	6.02×1023	atoms
H₂O	1 mol	6.02×1023	molecules
Na⁺	1 mol	6.02×1023	ions
NaCl	1 mol	6.02×1023	formula units

This is similar to saying that a dozen always contains 12 objects, regardless of what the objects are.

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Why Is the Mole So Useful?

The mole connects the microscopic world of atoms and molecules with the macroscopic world that we can measure in a laboratory.

Chemists cannot normally count individual molecules directly.

Instead, they can measure a sample and describe its quantity in moles.

This creates an important connection:

particles⟷moles⟷measurable samples​

Later, we can extend this relationship to include mass:

particles⟷moles⟷mass​

This relationship is one of the foundations of quantitative chemistry.

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Did You Know?

A mole is an unimaginably large number.

If you had a mole of grains of sand, there would be vastly more grains than all the sand found on Earth's beaches.

Chemists need such a huge counting unit because atoms and molecules are extraordinarily small.

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Key Vocabulary

Mole (mol) — The SI unit for amount of substance.

Amount of substance — A measure related to the number of specified particles present, measured in moles.

Avogadro's constant — The number of particles per mole, 6.02214076×10²³/mol.

Particle — A general term that may refer to an atom, molecule, ion, or formula unit.

Mass — A measure of the quantity of matter in a sample, commonly measured in grams in chemistry laboratories.

Formula unit — The simplest whole-number ratio of ions in an ionic compound.

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Key Takeaways

• The mole (mol) is the SI unit for amount of substance.
• One mole contains exactly 6.02214076×10²³ specified particles.
• This value is called Avogadro's constant.
• A mole is a counting unit, just like a dozen, but represents a much larger number.
• One mole can describe atoms, molecules, ions, or formula units.
• Amount of substance and mass are different quantities.
• Different substances can contain the same number of particles but have different masses.
• The relationship between particles and moles is: N=nN_A​​
• The mole provides an essential link between individual chemical particles and quantities that chemists can measure in the laboratory.

 

 

 

3. Avogadro's Number

Avogadro's Number

In chemistry, atoms and molecules are far too small to count individually. Even a tiny sample of a substance contains an enormous number of particles.

Chemists solve this problem using the mole.

One mole of any substance contains a specific number of particles known as Avogadro's number.

Avogadro's number is:

6.022 × 10²³ particles per mole

This means:

1 mol = 6.022 × 10²³ particles

The symbol commonly used for Avogadro's constant is Nₐ.

 

 

 

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Why Is Avogadro's Number So Large?

Atoms, molecules, and ions are incredibly small.

A sample that looks small to us can contain trillions upon trillions of particles.

For example:

1 mole of carbon atoms contains: 6.022 × 10²³ carbon atoms

1 mole of water molecules contains: 6.022 × 10²³ water molecules

1 mole of sodium ions contains: 6.022 × 10²³ sodium ions

The type of particle changes, but the number of particles in one mole does not.

The Mole as a Counting Unit

We use counting words for groups of objects.

For example:

1 pair = 2 objects

1 dozen = 12 objects

1 mole = 6.022 × 10²³ objects

The difference is that a mole represents an enormously larger group.

 

 

 

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The mole is therefore a counting unit.

However, instead of counting eggs or pencils, chemists use moles to count microscopic particles.

What Counts as a Particle?

The word particle can refer to different things depending on the substance.

It may refer to:

• atoms
• molecules
• ions
• formula units

You must identify what type of particle the question is asking about.

For example:

1 mol He = 6.022 × 10²³ helium atoms

1 mol H₂O = 6.022 × 10²³ water molecules

1 mol Na⁺ = 6.022 × 10²³ sodium ions

1 mol NaCl = 6.022 × 10²³ formula units of sodium chloride

Atoms

Elements such as helium, iron, copper, and carbon can be counted in atoms.

For example:

1 mol Fe = 6.022 × 10²³ Fe atoms

2 mol Fe = 2 × 6.022 × 10²³ atoms

= 1.2044 × 10²⁴ Fe atoms

Molecules

Covalent substances often exist as molecules.

Examples include:

• H₂O
• CO₂
• O₂
• NH₃
• CH₄

One mole of any molecular substance contains Avogadro's number of molecules.

For example:

1 mol CO₂ = 6.022 × 10²³ CO₂ molecules

 

 

 

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Ions

Ions are charged particles.

Examples include:

Na⁺

Cl⁻

Mg²⁺

O²⁻

One mole of ions contains:

6.022 × 10²³ ions

For example:

0.5 mol Cl⁻ contains:

0.5 × 6.022 × 10²³

= 3.011 × 10²³ chloride ions

Formula Units

Ionic compounds do not normally exist as separate molecules.

Instead, they form giant ionic lattices.

For ionic compounds, we therefore use the term formula unit.

For example:

1 mol NaCl contains:

6.022 × 10²³ formula units of NaCl

Each formula unit contains:

• 1 Na⁺ ion
• 1 Cl⁻ ion

So 1 mol NaCl contains:

6.022 × 10²³ Na⁺ ions

and:

6.022 × 10²³ Cl⁻ ions

Converting Moles to Particles

The most important Avogadro's number calculation is:

Number of particles = number of moles × Avogadro's number

Using symbols:

N = n × Nₐ

where:

N = number of particles

n = number of moles

Nₐ = 6.022 × 10²³ mol⁻¹

 

 

 

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Worked Example: Moles to Atoms

How many atoms are present in 2.0 mol of helium?

Use:

Number of particles = moles × Avogadro's number

N = 2.0 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Therefore:

2.0 mol He contains 1.2044 × 10²⁴ helium atoms.

Worked Example: Moles to Molecules

How many molecules are present in 0.50 mol of water?

N = n × Nₐ

N = 0.50 × 6.022 × 10²³

N = 3.011 × 10²³

Therefore:

0.50 mol H₂O contains 3.011 × 10²³ water molecules.

Worked Example: Moles to Ions

How many Mg²⁺ ions are present in 3.0 mol Mg²⁺?

N = 3.0 × 6.022 × 10²³

N = 1.8066 × 10²⁴

Therefore:

3.0 mol Mg²⁺ contains 1.8066 × 10²⁴ Mg²⁺ ions.

Converting Particles to Moles

Sometimes we know the number of particles and need to determine the number of moles.

Use:

Number of moles = number of particles ÷ Avogadro's number

In symbols:

n = N ÷ Nₐ

Worked Example: Atoms to Moles

A sample contains 1.2044 × 10²⁴ carbon atoms.

How many moles of carbon are present?

n = N ÷ Nₐ

n = (1.2044 × 10²⁴) ÷ (6.022 × 10²³)

n = 2.0

Therefore:

2.0 mol of carbon atoms are present.

Worked Example: Molecules to Moles

A sample contains 3.011 × 10²³ oxygen molecules.

How many moles of O₂ are present?

n = (3.011 × 10²³) ÷ (6.022 × 10²³)

n = 0.50

Therefore:

0.50 mol O₂

The Two Main Calculations

The relationship can be summarized simply.

To go from:

moles → particles

multiply by 6.022 × 10²³.

To go from:

particles → moles

divide by 6.022 × 10²³.

Using Chemical Formulae

Sometimes a question asks for the number of atoms inside molecules.

This requires an extra step.

Consider water:

H₂O

Each water molecule contains:

• 2 hydrogen atoms
• 1 oxygen atom

Therefore, 1 mole of H₂O contains:

• 2 mol H atoms
• 1 mol O atoms

This means 1 mole of water contains a total of:

3 mol of atoms

 

 

 

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Worked Example: Atoms in Water

How many hydrogen atoms are present in 1.0 mol H₂O?

First determine the number of water molecules:

1.0 × 6.022 × 10²³ = 6.022 × 10²³ H₂O molecules

Each molecule contains 2 hydrogen atoms.

Therefore:

2 × 6.022 × 10²³ = 1.2044 × 10²⁴ hydrogen atoms

Worked Example: Oxygen Atoms in Carbon Dioxide

How many oxygen atoms are present in 2.0 mol CO₂?

Each CO₂ molecule contains 2 oxygen atoms.

Therefore:

2.0 mol CO₂ contains:

2 × 2.0 = 4.0 mol O atoms

Now convert to atoms:

N = 4.0 × 6.022 × 10²³

N = 2.4088 × 10²⁴

Therefore:

2.4088 × 10²⁴ oxygen atoms

Worked Example: Total Atoms in Ammonia

How many total atoms are present in 0.25 mol NH₃?

Each NH₃ molecule contains:

1 nitrogen atom + 3 hydrogen atoms = 4 atoms

First determine the number of molecules:

N = 0.25 × 6.022 × 10²³

N = 1.5055 × 10²³ molecules

Each molecule contains 4 atoms.

Total atoms:

4 × 1.5055 × 10²³

= 6.022 × 10²³ atoms

Counting Ions in Ionic Compounds

Chemical formulae can also tell us how many ions are present.

Consider magnesium chloride:

MgCl₂

Each formula unit contains:

• 1 Mg²⁺ ion
• 2 Cl⁻ ions

Therefore:

1 mol MgCl₂ corresponds to:

• 1 mol Mg²⁺ ions
• 2 mol Cl⁻ ions

Worked Example: Ions in Magnesium Chloride

How many chloride ions correspond to 0.50 mol MgCl₂?

Each formula unit contains 2 chloride ions.

Therefore:

0.50 mol MgCl₂ corresponds to:

0.50 × 2 = 1.0 mol Cl⁻

Now convert to ions:

N = 1.0 × 6.022 × 10²³

Therefore:

6.022 × 10²³ chloride ions

A More Challenging Example

How many total ions are represented by 2.0 mol CaCl₂?

Each formula unit contains:

1 Ca²⁺ + 2 Cl⁻

Total = 3 ions

Therefore:

2.0 mol CaCl₂ corresponds to:

2.0 × 3 = 6.0 mol ions

Number of ions:

N = 6.0 × 6.022 × 10²³

N = 3.6132 × 10²⁴ ions

Scientific Notation

Avogadro's number is written in scientific notation because it is extremely large.

6.022 × 10²³ means:

602,200,000,000,000,000,000,000

Writing:

6.022 × 10²³

is much easier and reduces errors.

Scientific notation is especially important when performing mole calculations.

Using a Calculator

Suppose you need to calculate:

0.35 × 6.022 × 10²³

On a scientific calculator, you may enter something similar to:

6.022 EXP 23 × 0.35

or:

6.022 EE 23 × 0.35

depending on the calculator.

The answer is:

2.1077 × 10²³

Be careful not to enter the exponent incorrectly.

Why Avogadro's Number Matters

Avogadro's number creates a connection between the microscopic and macroscopic worlds.

Chemists cannot practically count individual atoms.

However, they can:

• measure mass
• calculate moles
• use Avogadro's number
• determine the number of particles

 

 

 

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This makes quantitative chemistry possible.

Moles, Mass and Particles

Later calculations often connect three important quantities:

mass ↔ moles ↔ particles

Mass and moles are connected using molar mass.

Moles and particles are connected using Avogadro's number.

For example:

mass → moles → number of molecules

This allows chemists to determine how many microscopic particles are present in a measurable sample.

Avogadro's Number and Chemical Reactions

Chemical equations describe particles reacting in specific ratios.

For example:

2H₂ + O₂ → 2H₂O

At the particle level:

2 molecules H₂ react with 1 molecule O₂.

At the mole level:

2 mol H₂ react with 1 mol O₂.

Because every mole contains the same number of particles, mole ratios allow chemists to scale reactions up from individual molecules to laboratory quantities.

Worked Example: Multi-Step Problem

A sample contains 1.5 mol of CH₄.

How many hydrogen atoms are present?

Step 1: Identify the number of H atoms in each molecule.

CH₄ contains 4 H atoms.

Step 2: Determine moles of H atoms.

1.5 × 4 = 6.0 mol H atoms

Step 3: Convert moles to atoms.

N = 6.0 × 6.022 × 10²³

N = 3.6132 × 10²⁴

Therefore:

1.5 mol CH₄ contains 3.6132 × 10²⁴ hydrogen atoms.

Worked Example: Working Backwards

A sample contains 9.033 × 10²³ molecules of CO₂.

How many moles of CO₂ are present?

Use:

n = N ÷ Nₐ

n = (9.033 × 10²³) ÷ (6.022 × 10²³)

n = 1.5

Therefore:

1.5 mol CO₂

A Useful Problem-Solving Strategy

When solving Avogadro's number problems:

1. Identify what you are given.
2. Identify what the question asks for.
3. Decide whether you need to multiply or divide by Avogadro's number.
4. Check the chemical formula if atoms or ions inside a compound are being counted.
5. Perform the calculation.
6. Include the correct type of particle in your answer.

For example:

Given: moles

Wanted: molecules

Use:

moles × 6.022 × 10²³

Common Misconceptions

Avogadro's number is the mass of one mole.

Incorrect. Avogadro's number tells us the number of particles in one mole.

One mole of every substance has the same mass.

Incorrect. One mole always contains the same number of particles, but different substances have different molar masses.

One mole of H₂O contains 6.022 × 10²³ atoms.

Incorrect. It contains 6.022 × 10²³ water molecules. Each molecule contains three atoms.

Ionic compounds contain molecules.

It is generally more accurate to describe ionic compounds using formula units rather than molecules.

To convert particles to moles, multiply by Avogadro's number.

Incorrect.

Particles → moles means divide by Avogadro's number.

0.5 mol contains 0.5 particles.

Incorrect. Even a fraction of a mole contains an enormous number of particles.

Did You Know?

Avogadro's number is so large that it is difficult to imagine.

If you could count particles at a rate of one billion particles every second, it would still take millions of years to count all the particles in just one mole.

The mole allows chemists to work with this enormous microscopic population using quantities that can actually be measured in a laboratory.

Key Terms

Avogadro's number – The number of particles in one mole: 6.022 × 10²³.

Avogadro constant (Nₐ) – The constant 6.022 × 10²³ mol⁻¹.

Mole (mol) – The amount of substance containing 6.022 × 10²³ specified entities.

Particle – A general term that may refer to an atom, molecule, ion, or formula unit.

Atom – The smallest particle of an element that retains its chemical identity.

Molecule – A group of atoms joined by covalent bonds.

Ion – A charged particle formed when electrons are gained or lost.

Formula unit – The simplest whole-number ratio of ions represented by the formula of an ionic compound.

Scientific notation – A method for expressing very large or very small numbers using powers of ten.

Key Takeaways

• Avogadro's number is 6.022 × 10²³.
• One mole contains 6.022 × 10²³ particles.
• The particles may be atoms, molecules, ions, or formula units.
• Avogadro's number connects microscopic particles with measurable amounts of substances.
• To convert moles to particles, multiply by 6.022 × 10²³.
• To convert particles to moles, divide by 6.022 × 10²³.
• Use N = n × Nₐ to calculate the number of particles.
• Chemical formulae must be considered when counting individual atoms within molecules.
• One mole of H₂O contains one mole of water molecules but two moles of H atoms and one mole of O atoms.
• Ionic formulae can be used to determine the number of individual ions.
• Avogadro's number is fundamental to quantitative chemistry and stoichiometry.

4. Molar Mass

Molar Mass

Molar mass is the mass of one mole of a substance.

Its usual unit is:

grams per mole (g/mol)

For example, one mole of carbon atoms has a mass of approximately 12.01 g.

Therefore:

Molar mass of carbon = 12.01 g/mol

Molar mass creates an important connection between the mass of a substance and the number of moles present.

 

 

 

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The Mole and Molar Mass

A mole is a counting unit used in chemistry.

One mole contains:

6.022 × 10²³ particles

However, different particles have different masses.

Therefore, one mole of different substances will have different masses.

For example:

• 1 mol H atoms ≈ 1.008 g
• 1 mol C atoms ≈ 12.01 g
• 1 mol O atoms ≈ 16.00 g
• 1 mol Fe atoms ≈ 55.85 g

Each sample contains the same number of atoms, but the atoms themselves have different masses.

Molar Mass of an Element

The molar mass of an element can be found using the periodic table.

The relative atomic mass shown on the periodic table has the same numerical value as the element's molar mass in g/mol.

For example:

Carbon:

Relative atomic mass, Ar = 12.01

Molar mass = 12.01 g/mol

Magnesium:

Ar = 24.31

Molar mass = 24.31 g/mol

Iron:

Ar = 55.85

Molar mass = 55.85 g/mol

 

 

 

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Relative Atomic Mass and Molar Mass

Relative atomic mass, Ar, describes the average mass of an atom relative to 1/12 of the mass of a carbon-12 atom.

Relative atomic mass has no unit because it is a relative value.

Molar mass describes the mass of one mole of atoms.

It has the unit:

g/mol

The numerical values are the same.

For oxygen:

Ar(O) = 16.00

Molar mass of O atoms = 16.00 g/mol

For calcium:

Ar(Ca) = 40.08

Molar mass of Ca atoms = 40.08 g/mol

The important difference is therefore the meaning and units.

Why Are the Values the Same?

Relative atomic mass describes the relative mass of individual atoms.

Molar mass describes the mass of Avogadro's number of those atoms.

The mole is defined so that these numerical values correspond.

For example:

One carbon atom has a relative atomic mass of approximately 12.01.

One mole of carbon atoms has a mass of approximately 12.01 g.

Therefore:

Ar(C) = 12.01

M(C) = 12.01 g/mol

Molar Mass of Molecules

Compounds contain more than one atom.

To calculate the molar mass of a compound, add the atomic masses of all the atoms in its chemical formula.

For example:

Water = H₂O

Each water molecule contains:

• 2 hydrogen atoms
• 1 oxygen atom

Using:

H = 1.008

O = 16.00

Molar mass of H₂O:

M = (2 × 1.008) + 16.00

M = 18.016 g/mol

Usually:

M(H₂O) ≈ 18.02 g/mol

 

 

 

5

A Simple Method

When calculating the molar mass of a compound:

1. Write the chemical formula.
2. Identify each element.
3. Find each atomic mass on the periodic table.
4. Multiply each atomic mass by the number of atoms present.
5. Add the results.
6. Include the unit g/mol.

Worked Example: Carbon Dioxide

Calculate the molar mass of CO₂.

CO₂ contains:

• 1 carbon atom
• 2 oxygen atoms

Atomic masses:

C = 12.01

O = 16.00

Calculate:

M(CO₂) = 12.01 + (2 × 16.00)

M(CO₂) = 12.01 + 32.00

M(CO₂) = 44.01 g/mol

Worked Example: Ammonia

Calculate the molar mass of NH₃.

NH₃ contains:

• 1 nitrogen atom
• 3 hydrogen atoms

Atomic masses:

N = 14.01

H = 1.008

Calculate:

M(NH₃) = 14.01 + (3 × 1.008)

M(NH₃) = 17.034 g/mol

Therefore:

M(NH₃) ≈ 17.03 g/mol

Worked Example: Methane

Calculate the molar mass of CH₄.

CH₄ contains:

• 1 carbon
• 4 hydrogen

M(CH₄) = 12.01 + (4 × 1.008)

M(CH₄) = 16.042 g/mol

Therefore:

M(CH₄) ≈ 16.04 g/mol

Using Subscripts Correctly

The small numbers in chemical formulae are called subscripts.

They tell us how many atoms of each element are present.

For example:

H₂SO₄ contains:

• 2 H atoms
• 1 S atom
• 4 O atoms

Therefore:

M(H₂SO₄) = (2 × H) + S + (4 × O)

 

 

 

4

Using approximate atomic masses:

H = 1.008

S = 32.06

O = 16.00

M(H₂SO₄) = (2 × 1.008) + 32.06 + (4 × 16.00)

M(H₂SO₄) = 2.016 + 32.06 + 64.00

M(H₂SO₄) = 98.076 g/mol

or approximately:

98.08 g/mol

Molar Mass of Ionic Compounds

The same method is used for ionic compounds.

For example:

Sodium chloride = NaCl

Na = 22.99

Cl = 35.45

M(NaCl) = 22.99 + 35.45

M(NaCl) = 58.44 g/mol

Although ionic compounds are described using formula units rather than molecules, their molar masses are calculated in the same way.

Worked Example: Magnesium Chloride

Calculate the molar mass of MgCl₂.

MgCl₂ contains:

• 1 Mg
• 2 Cl

Atomic masses:

Mg = 24.31

Cl = 35.45

M(MgCl₂) = 24.31 + (2 × 35.45)

M(MgCl₂) = 24.31 + 70.90

M(MgCl₂) = 95.21 g/mol

Parentheses in Chemical Formulae

Some chemical formulae contain parentheses.

For example:

Ca(OH)₂

The subscript outside the parentheses applies to everything inside the parentheses.

Ca(OH)₂ contains:

• 1 Ca
• 2 O
• 2 H

 

 

 

4

Calculate:

Ca = 40.08

O = 16.00

H = 1.008

M = 40.08 + (2 × 16.00) + (2 × 1.008)

M = 40.08 + 32.00 + 2.016

M = 74.096 g/mol

Approximately:

74.10 g/mol

A More Challenging Example

Calculate the molar mass of Al₂(SO₄)₃.

First count the atoms.

Al₂(SO₄)₃ contains:

• 2 Al
• 3 S
• 12 O

Why 12 oxygen atoms?

There are 4 oxygen atoms inside the parentheses and 3 groups:

4 × 3 = 12

Using:

Al = 26.98

S = 32.06

O = 16.00

Calculate:

M = (2 × 26.98) + (3 × 32.06) + (12 × 16.00)

M = 53.96 + 96.18 + 192.00

M = 342.14 g/mol

Molar Mass and Chemical Formulae

Correctly reading the chemical formula is often the most important part of a molar mass calculation.

Consider:

CO = 1 C + 1 O

CO₂ = 1 C + 2 O

These substances have different molar masses.

CO:

12.01 + 16.00 = 28.01 g/mol

CO₂:

12.01 + 32.00 = 44.01 g/mol

A small change in the formula changes the number of atoms and therefore changes the molar mass.

Connecting Mass and Moles

Molar mass allows us to convert between:

mass ↔ moles

The main equation is:

number of moles = mass ÷ molar mass

In symbols:

n = m ÷ M

where:

n = number of moles, in mol

m = mass, usually in g

M = molar mass, in g/mol

 

 

 

4

Calculating Moles from Mass

Use:

moles = mass ÷ molar mass

Suppose we have 36.04 g H₂O.

Molar mass of H₂O = 18.02 g/mol

n = 36.04 ÷ 18.02

n = 2.00 mol

Therefore:

36.04 g H₂O = 2.00 mol H₂O

Calculating Mass from Moles

The equation can be rearranged:

mass = moles × molar mass

In symbols:

m = n × M

Worked Example: Moles to Mass

What is the mass of 3.0 mol CO₂?

Molar mass of CO₂ = 44.01 g/mol

m = n × M

m = 3.0 × 44.01

m = 132.03 g

Therefore:

3.0 mol CO₂ has a mass of approximately 132 g.

Worked Example: Mass to Moles

How many moles are present in 117 g NaCl?

M(NaCl) = 58.44 g/mol

n = m ÷ M

n = 117 ÷ 58.44

n ≈ 2.00 mol

Therefore:

117 g NaCl contains approximately 2.00 mol NaCl.

Worked Example: A Smaller Sample

How many moles are present in 5.00 g of calcium?

M(Ca) = 40.08 g/mol

n = 5.00 ÷ 40.08

n ≈ 0.125 mol

Therefore:

5.00 g Ca ≈ 0.125 mol Ca

Connecting Mass, Moles and Particles

Molar mass can be combined with Avogadro's number.

The overall relationship is:

mass ↔ moles ↔ particles

To convert:

mass → moles

divide by molar mass.

moles → mass

multiply by molar mass.

moles → particles

multiply by 6.022 × 10²³.

particles → moles

divide by 6.022 × 10²³.

 

 

 

5

Worked Example: Mass to Molecules

How many water molecules are present in 9.01 g H₂O?

Step 1: Calculate moles.

M(H₂O) = 18.02 g/mol

n = 9.01 ÷ 18.02

n = 0.500 mol

Step 2: Convert moles to molecules.

Number of molecules = 0.500 × 6.022 × 10²³

= 3.011 × 10²³

Therefore:

9.01 g H₂O contains approximately 3.01 × 10²³ water molecules.

Worked Example: Particles to Mass

A sample contains 6.022 × 10²³ CO₂ molecules.

Step 1: Convert molecules to moles.

6.022 × 10²³ molecules = 1.00 mol

Step 2: Find molar mass.

M(CO₂) = 44.01 g/mol

Step 3: Calculate mass.

m = 1.00 × 44.01

m = 44.01 g

Therefore:

6.022 × 10²³ CO₂ molecules have a mass of 44.01 g.

Molar Mass and Chemical Reactions

Molar mass is extremely important in chemical reactions.

Chemical equations give relationships in moles, but substances in a laboratory are usually measured by mass.

For example:

2H₂ + O₂ → 2H₂O

The equation tells us:

2 mol H₂ react with 1 mol O₂ to produce 2 mol H₂O.

Molar mass allows these mole quantities to be converted into measurable masses.

This is one of the foundations of stoichiometry.

A Useful Calculation Strategy

When solving molar mass problems:

1. Write the correct chemical formula.
2. Count the number of atoms of each element.
3. Find the atomic masses on the periodic table.
4. Multiply each atomic mass by the number of atoms.
5. Add the values.
6. Write the unit g/mol.
7. If necessary, use the molar mass to convert between mass and moles.

For multi-step problems, it can help to think:

What do I know? → What do I need? → Do I need to pass through moles?

Common Misconceptions

Molar mass and relative atomic mass have exactly the same meaning.

They have the same numerical value for an element, but different meanings. Relative atomic mass is a relative value without units, while molar mass is the mass of one mole and is measured in g/mol.

Every substance has a molar mass of 6.022 × 10²³ g.

Incorrect. 6.022 × 10²³ is Avogadro's number and represents a number of particles.

One mole of every substance has the same mass.

Incorrect. One mole always contains the same number of specified particles, but different particles have different masses.

To calculate compound molar mass, add each element only once.

Incorrect. You must account for the number of each type of atom shown by the formula.

The 2 in H₂O means two water molecules.

Incorrect. The subscript 2 means there are two hydrogen atoms in each water molecule.

The 2 in Ca(OH)₂ applies only to hydrogen.

Incorrect. It applies to everything inside the parentheses: two oxygen atoms and two hydrogen atoms.

Did You Know?

One mole of water contains the same number of molecules as one mole of carbon dioxide:

6.022 × 10²³ molecules

However, their masses are different.

1 mol H₂O ≈ 18.02 g

1 mol CO₂ ≈ 44.01 g

This is because a CO₂ molecule contains heavier atoms and therefore has a greater molecular mass.

The number of particles is the same, but the mass is different.

Key Terms

Molar mass – The mass of one mole of a substance.

Mole – The amount of substance containing 6.022 × 10²³ specified entities.

Relative atomic mass (Ar) – The average relative mass of an atom compared with 1/12 of carbon-12.

Relative formula mass (Mr) – The sum of the relative atomic masses in a chemical formula.

Avogadro's number – 6.022 × 10²³ particles per mole.

Chemical formula – Symbols showing the elements and their proportions in a substance.

Subscript – A small number in a chemical formula showing the number of atoms.

Formula unit – The simplest whole-number ratio of ions in an ionic compound.

Stoichiometry – The quantitative study of amounts of substances in chemical reactions.

Key Takeaways

• Molar mass is the mass of one mole of a substance.
• Molar mass is usually measured in g/mol.
• The periodic table can be used to determine the molar mass of an element.
• An element's molar mass in g/mol has the same numerical value as its relative atomic mass.
• Relative atomic mass has no unit, while molar mass has units of g/mol.
• Compound molar mass is calculated by adding the atomic masses of all atoms in the formula.
• Subscripts must be included when counting atoms.
• Parentheses must be interpreted carefully.
• Use n = m ÷ M to calculate moles from mass.
• Use m = n × M to calculate mass from moles.
• Molar mass connects measurable mass with the mole.
• Molar mass and Avogadro's number together allow conversion between mass, moles, and particles.
• Molar mass is essential for quantitative chemical calculations and stoichiometry.

5. Converting Between Moles and Particles

Converting Between Moles and Particles

Chemistry often requires us to move between three different ways of describing an amount of substance:

• mass
• moles
• number of particles

These quantities are connected by two important ideas:

Avogadro's number = 6.022 × 10²³ particles per mole

Molar mass = mass of one mole of a substance, in g/mol

Together, these allow us to convert between:

mass ↔ moles ↔ particles

 

 

 

4

The Mole as the Central Quantity

The mole acts as a bridge between mass and particles.

You usually cannot convert directly from mass to particles in one simple step.

Instead:

mass → moles → particles

Similarly:

particles → moles → mass

This means many chemistry problems are solved by first converting to moles.

---

Converting Moles to Particles

To convert moles to particles:

Number of particles = moles × Avogadro's number

In symbols:

N = n × Nₐ

where:

N = number of particles

n = number of moles

Nₐ = 6.022 × 10²³ mol⁻¹

---

Worked Example: Moles to Atoms

How many atoms are present in 2.5 mol of helium?

Use:

N = n × Nₐ

N = 2.5 × 6.022 × 10²³

N = 1.5055 × 10²⁴

Therefore:

2.5 mol He contains 1.51 × 10²⁴ helium atoms.

---

Worked Example: Moles to Molecules

How many molecules are present in 0.40 mol H₂O?

N = 0.40 × 6.022 × 10²³

N = 2.4088 × 10²³

Therefore:

0.40 mol H₂O contains 2.41 × 10²³ water molecules.

---

Converting Particles to Moles

To convert particles to moles:

Moles = number of particles ÷ Avogadro's number

In symbols:

n = N ÷ Nₐ

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Worked Example: Molecules to Moles

A sample contains 1.2044 × 10²⁴ CO₂ molecules.

How many moles are present?

n = N ÷ Nₐ

n = (1.2044 × 10²⁴) ÷ (6.022 × 10²³)

n = 2.0

Therefore:

2.0 mol CO₂

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A Quick Rule

To move:

moles → particles

multiply by 6.022 × 10²³

To move:

particles → moles

divide by 6.022 × 10²³

 

 

 

5

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Converting Mass to Moles

Mass and moles are connected by molar mass.

Use:

Moles = mass ÷ molar mass

In symbols:

n = m ÷ M

where:

n = moles

m = mass in grams

M = molar mass in g/mol

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Worked Example: Mass to Moles

How many moles are present in 36.0 g of water?

Molar mass of H₂O ≈ 18.0 g/mol

n = 36.0 ÷ 18.0

n = 2.0 mol

Therefore:

36.0 g H₂O = 2.0 mol H₂O

---

Converting Moles to Mass

To calculate mass:

Mass = moles × molar mass

In symbols:

m = n × M

---

Worked Example: Moles to Mass

What is the mass of 3.0 mol CO₂?

Molar mass of CO₂:

12.01 + (2 × 16.00)

= 44.01 g/mol

Now calculate:

m = 3.0 × 44.01

m = 132.03 g

Therefore:

3.0 mol CO₂ has a mass of approximately 132 g.

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The Main Conversion Map

These relationships can be summarized as:

Mass → Moles

divide by molar mass

Moles → Mass

multiply by molar mass

Moles → Particles

multiply by Avogadro's number

Particles → Moles

divide by Avogadro's number

 

 

 

6

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Converting Mass to Particles

This is a two-step calculation.

You cannot usually jump directly from mass to particles.

Instead:

mass → moles → particles

Step 1:

moles = mass ÷ molar mass

Step 2:

particles = moles × 6.022 × 10²³

---

Worked Example: Mass to Molecules

How many molecules are present in 9.0 g H₂O?

Step 1: Find molar mass.

H₂O:

M = (2 × 1.0) + 16.0

M = 18.0 g/mol

Step 2: Convert mass to moles.

n = 9.0 ÷ 18.0

n = 0.50 mol

Step 3: Convert moles to molecules.

N = 0.50 × 6.022 × 10²³

N = 3.011 × 10²³

Therefore:

9.0 g H₂O contains approximately 3.01 × 10²³ molecules.

---

Worked Example: Mass to Atoms

How many atoms are present in 24.0 g of carbon?

Molar mass of carbon ≈ 12.0 g/mol

Step 1: Calculate moles.

n = 24.0 ÷ 12.0

n = 2.0 mol

Step 2: Convert moles to atoms.

N = 2.0 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Therefore:

24.0 g carbon contains approximately 1.20 × 10²⁴ atoms.

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Converting Particles to Mass

This is also a two-step calculation.

Use:

particles → moles → mass

Step 1:

moles = particles ÷ Avogadro's number

Step 2:

mass = moles × molar mass

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Worked Example: Molecules to Mass

A sample contains 3.011 × 10²³ molecules of O₂.

What is its mass?

Step 1: Convert molecules to moles.

n = (3.011 × 10²³) ÷ (6.022 × 10²³)

n = 0.50 mol

Step 2: Find molar mass.

O₂ contains 2 oxygen atoms.

M = 2 × 16.00

M = 32.00 g/mol

Step 3: Calculate mass.

m = 0.50 × 32.00

m = 16.0 g

Therefore:

3.011 × 10²³ O₂ molecules have a mass of 16.0 g.

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Types of Particles

Always identify what kind of particle the question refers to.

Possible particle types include:

• atoms
• molecules
• ions
• formula units

For example:

1 mol Ne = 6.022 × 10²³ neon atoms

1 mol CO₂ = 6.022 × 10²³ carbon dioxide molecules

1 mol Na⁺ = 6.022 × 10²³ sodium ions

1 mol NaCl = 6.022 × 10²³ formula units

---

Counting Atoms Inside Molecules

Sometimes a question asks for the number of individual atoms inside a molecular sample.

You must use the chemical formula.

For example:

H₂O contains:

• 2 H atoms
• 1 O atom

Therefore each H₂O molecule contains:

3 atoms total

 

 

 

4

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Worked Example: Hydrogen Atoms in Water

How many hydrogen atoms are present in 2.0 mol H₂O?

Each H₂O molecule contains 2 H atoms.

Therefore:

2.0 mol H₂O contains:

4.0 mol H atoms

Now convert moles of atoms to number of atoms.

N = 4.0 × 6.022 × 10²³

N = 2.4088 × 10²⁴

Therefore:

2.0 mol H₂O contains 2.41 × 10²⁴ hydrogen atoms.

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Worked Example: Total Atoms in Carbon Dioxide

How many total atoms are present in 0.50 mol CO₂?

Each CO₂ molecule contains:

1 C + 2 O = 3 atoms

Therefore:

0.50 mol CO₂ corresponds to:

0.50 × 3 = 1.5 mol atoms

Now:

N = 1.5 × 6.022 × 10²³

N = 9.033 × 10²³

Therefore:

0.50 mol CO₂ contains 9.03 × 10²³ total atoms.

---

Counting Ions in Ionic Compounds

Ionic compounds require the same careful attention to chemical formulae.

Consider:

CaCl₂

Each formula unit contains:

• 1 Ca²⁺ ion
• 2 Cl⁻ ions

Therefore:

1 mol CaCl₂ corresponds to:

• 1 mol Ca²⁺
• 2 mol Cl⁻
• 3 mol ions total

---

Worked Example: Chloride Ions

How many chloride ions are present in 0.25 mol CaCl₂?

Each formula unit contains 2 chloride ions.

Therefore:

0.25 × 2 = 0.50 mol Cl⁻

Now convert to ions.

N = 0.50 × 6.022 × 10²³

N = 3.011 × 10²³

Therefore:

0.25 mol CaCl₂ contains 3.01 × 10²³ chloride ions.

---

Multi-Step Problem: Mass to Atoms

How many oxygen atoms are present in 44.0 g CO₂?

Step 1: Find molar mass.

M(CO₂) = 12.0 + (2 × 16.0)

M = 44.0 g/mol

Step 2: Convert mass to moles.

n = 44.0 ÷ 44.0

n = 1.0 mol CO₂

Step 3: Account for oxygen atoms.

Each CO₂ molecule contains 2 oxygen atoms.

Therefore:

1.0 mol CO₂ = 2.0 mol O atoms

Step 4: Convert to atoms.

N = 2.0 × 6.022 × 10²³

N = 1.2044 × 10²⁴

Therefore:

44.0 g CO₂ contains approximately 1.20 × 10²⁴ oxygen atoms.

---

Multi-Step Problem: Mass to Ions

How many sodium ions are represented by 11.7 g NaCl?

Step 1: Find molar mass.

Na = 22.99

Cl = 35.45

M(NaCl) = 58.44 g/mol

Step 2: Convert mass to moles.

n = 11.7 ÷ 58.44

n ≈ 0.200 mol

Step 3: Use the formula.

Each NaCl formula unit contains 1 Na⁺ ion.

Therefore:

0.200 mol NaCl = 0.200 mol Na⁺

Step 4: Convert to ions.

N = 0.200 × 6.022 × 10²³

N ≈ 1.20 × 10²³

Therefore:

11.7 g NaCl contains approximately 1.20 × 10²³ sodium ions.

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Multi-Step Problem: Particles to Mass

A sample contains 1.8066 × 10²⁴ molecules of NH₃.

What is its mass?

Step 1: Convert molecules to moles.

n = (1.8066 × 10²⁴) ÷ (6.022 × 10²³)

n = 3.0 mol

Step 2: Find molar mass.

NH₃:

N = 14.01

H = 1.008

M = 14.01 + (3 × 1.008)

M ≈ 17.03 g/mol

Step 3: Calculate mass.

m = 3.0 × 17.03

m ≈ 51.1 g

Therefore:

1.8066 × 10²⁴ NH₃ molecules have a mass of approximately 51.1 g.

---

A Problem-Solving Road Map

A useful way to solve these problems is to identify your starting point and your destination.

If the question gives:

mass and asks for particles

use:

mass → moles → particles

If the question gives:

particles and asks for mass

use:

particles → moles → mass

If the question gives:

moles and asks for mass

use:

moles → mass

If the question gives:

moles and asks for particles

use:

moles → particles

 

 

 

5

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Dimensional Thinking

Units can help you decide which operation to perform.

For example:

20.0 g ÷ 40.0 g/mol

The grams cancel:

g ÷ (g/mol) = mol

So the result is in moles.

Similarly:

2.0 mol × 6.022 × 10²³ particles/mol

The mol units cancel:

mol × particles/mol = particles

Checking units is a powerful way to catch mistakes.

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Scientific Notation

Particle calculations usually produce very large numbers.

For example:

6.022 × 10²³

1.204 × 10²⁴

3.011 × 10²²

Scientific notation makes these values easier to read and calculate.

Remember:

10²⁴ is ten times larger than 10²³

and:

10²² is ten times smaller than 10²³

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Using a Scientific Calculator

For a calculation such as:

2.50 × 6.022 × 10²³

you may enter:

2.50 × 6.022 EXP 23

depending on your calculator.

For division:

3.011 × 10²³ ÷ 6.022 × 10²³

use brackets if necessary to ensure the entire scientific notation value is entered correctly.

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Significant Figures

Final answers should normally reflect the precision of the information given.

For example:

2.0 mol × 6.022 × 10²³

The value 2.0 has two significant figures.

So a suitable answer is:

1.2 × 10²⁴ particles

rather than writing many unnecessary digits.

---

Common Misconceptions

Mass can be converted to particles by multiplying directly by Avogadro's number.

Incorrect. Mass should first be converted to moles using molar mass.

Moles to particles means divide by Avogadro's number.

Incorrect. Moles to particles means multiply.

Particles to moles means multiply by Avogadro's number.

Incorrect. Particles to moles means divide.

One mole means one particle.

Incorrect. One mole contains 6.022 × 10²³ particles.

Every substance has the same molar mass.

Incorrect. Every mole contains the same number of particles, but substances have different molar masses.

One mole of H₂O contains one mole of atoms.

Incorrect. One mole of H₂O contains one mole of molecules but three moles of atoms in total.

The subscript in a chemical formula can be ignored.

Incorrect. Subscripts determine how many atoms or ions are present and are essential in multi-step problems.

---

Did You Know?

A laboratory balance measures macroscopic quantities such as grams, but chemical reactions occur between microscopic particles.

The mole connects these two scales.

For example, a chemist can weigh a sample of water, convert its mass to moles, and then calculate how many individual water molecules are present.

This means the pathway:

mass → moles → particles

is one of the most important links between what chemists can measure and what is actually happening at the atomic level.

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Key Terms

Mole – An amount of substance containing 6.022 × 10²³ specified entities.

Avogadro's number – 6.022 × 10²³ particles per mole.

Molar mass – The mass of one mole of a substance, usually measured in g/mol.

Particle – A general term for atoms, molecules, ions, or formula units.

Atom – The smallest particle of an element that retains its chemical identity.

Molecule – A group of atoms joined by covalent bonds.

Ion – An electrically charged particle.

Formula unit – The simplest whole-number ratio of ions in an ionic compound.

Scientific notation – A method of expressing very large or small numbers using powers of ten.

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Key Takeaways

• Moles connect measurable amounts of substances with microscopic particles.
• 1 mol = 6.022 × 10²³ particles.
• To convert moles to particles, multiply by Avogadro's number.
• To convert particles to moles, divide by Avogadro's number.
• To convert mass to moles, divide by molar mass.
• To convert moles to mass, multiply by molar mass.
• Mass-to-particle problems usually follow mass → moles → particles.
• Particle-to-mass problems usually follow particles → moles → mass.
• Chemical formulae must be considered when counting individual atoms or ions.
• Subscripts tell you how many atoms or ions are present.
• Scientific notation is important when expressing particle numbers.
• Units can help determine whether to multiply or divide.
• Multi-step chemistry calculations become much easier when moles are treated as the central conversion point.