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.

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.

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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.

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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

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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

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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.

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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

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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

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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

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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)

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

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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.

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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

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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

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

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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

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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.

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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

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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

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Calculating Mass from Moles

The equation can be rearranged:

mass = moles × molar mass

In symbols:

m = n × M

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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.

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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.

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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

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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.

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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.

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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.

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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.

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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?

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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.