The Mole and Conversions Revision Notes for HSC SSCE Chemistry

The Mole and Conversions

What is a mole?

The mole is one of the most fundamental concepts in chemistry. It provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure in the laboratory.

Scientists discovered that the carbon-12 atom has a mass of $1.993 \times 10^{-23}$ g. This means there are exactly $6.022 \times 10^{23}$ atoms in 12 g of carbon-12. This huge number is called Avogadro's constant.

chatImportant

Key definition: A mole of a substance is the quantity that contains as many elementary units (atoms, ions or molecules) as there are atoms in exactly 12 g of the carbon-12 isotope.

Avogadro's constant ( $N_A$ ) is the number of particles in one mole:

$N_A = 6.022 \times 10^{23} \text{ particles per mole}$

The concept extends to all elements and compounds. For any element, if you take a mass in grams equal to its relative atomic mass, you will have exactly $6.022 \times 10^{23}$ atoms.

infoNote

Examples of molar quantities:

Copper has a relative atomic mass of 63.55, so 63.55 g of copper contains $6.022 \times 10^{23}$ atoms
Titanium has a relative atomic mass of 48, so 48 g of titanium contains $6.022 \times 10^{23}$ atoms
Water (H₂O) has a relative molecular mass of 18, so 18 g of water contains $6.022 \times 10^{23}$ molecules

Two ways of understanding a mole

There are two complementary ways to think about a mole, and both are equally important for solving chemistry problems.

As a number of particles: One mole contains exactly $6.022 \times 10^{23}$ elementary units (atoms, ions, or molecules).

As a mass: One mole has a mass in grams numerically equal to the relative atomic mass (for elements) or relative molecular mass (for compounds).

This dual nature is what makes the mole so useful. We can measure mass easily in the lab, but we can then use this to work out how many particles we have.

infoNote

Understanding the dual nature:

One mole of silver (relative atomic mass 108) can be described as:

$6.022 \times 10^{23}$ atoms of silver, OR
108 g of silver

Similarly, one mole of sucrose (relative molecular mass 342) is:

$6.022 \times 10^{23}$ molecules of sucrose, OR
342 g of sucrose

Molar mass

Molar mass is the mass of one mole of a substance. This term can be used for both elements and compounds, making it very convenient.

Molar mass is expressed in grams per mole, written as g mol⁻¹ or g/mol.

infoNote

Key points about molar mass:

For elements: molar mass equals the relative atomic mass in g mol⁻¹
For compounds: molar mass equals the relative molecular mass (or relative formula mass) in g mol⁻¹

Examples:

The molar mass of copper is 63.6 g mol⁻¹
The molar mass of nitrogen dioxide (NO₂) is 46 g mol⁻¹

chatImportant

Important abbreviation: The accepted abbreviation for mole is mol, such as 3.9 mol of zinc or $4.3 \times 10^{-3}$ mol of carbon. The word 'molecule' is always written in full to avoid confusion.

Special case: Gaseous elements

When dealing with gaseous elements that exist as diatomic molecules (such as oxygen, nitrogen, chlorine, hydrogen), you must be careful to specify whether you mean atoms or molecules.

chatImportant

Critical distinction for gaseous elements:

Oxygen example:

One mole of oxygen atoms has a mass of 16 g (relative atomic mass = 16)
One mole of oxygen molecules (O₂) has a mass of 32 g (relative molecular mass = 32)
One mole of oxygen molecules contains two moles of oxygen atoms

Chlorine example:

One mole of chlorine atoms has a mass of 35.5 g
One mole of chlorine gas (Cl₂ molecules) has a mass of $2 \times 35.5 = 71$ g

This distinction is important when writing calculations and interpreting results. Always specify whether you're referring to atoms or molecules of gaseous elements.

Converting between mass and moles

One of the most common calculations in chemistry involves converting between the mass of a substance and the number of moles present.

The key equation is:

$n = \frac{m}{MM}$

where:

$n$ = number of moles (mol)
$m$ = mass (g)
$MM$ = molar mass (g mol⁻¹)

This equation can be rearranged to find mass if you know moles:

$m = n \times MM$

The diagram shows this relationship visually. To go from mass to moles, you divide by the molar mass. To go from moles to mass, you multiply by the molar mass.

lightbulbExample

Worked Example: Mass to moles calculation

Let's calculate the number of moles in 4.63 g of magnesium chloride (MgCl₂).

Step 1: Identify the formula

Magnesium chloride is MgCl₂

Step 2: Calculate the molar mass

\begin{aligned} MM \text{ of MgCl}_2 &= 24.31 + (2 \times 35.45) \\ MM &= 95.21 \text{ g mol}^{-1} \end{aligned}

Step 3: Use the formula to calculate moles

$n = \frac{m}{MM} = \frac{4.63}{95.21} = 0.0486 \text{ mol}$

The answer is rounded to 3 significant figures because the given mass (4.63 g) has 3 significant figures.

Converting between moles and number of particles

To convert from moles to the actual number of atoms or molecules, we use Avogadro's constant.

The equation is:

$N = n \times N_A$

where:

$N$ = number of atoms or molecules
$n$ = number of moles (mol)
$N_A$ = Avogadro's constant ( $6.022 \times 10^{23}$ mol⁻¹)

To convert in the opposite direction (from number of particles to moles):

$n = \frac{N}{N_A}$

The diagram illustrates this bidirectional conversion. Multiply by Avogadro's constant to go from moles to particles. Divide by Avogadro's constant to go from particles to moles.

Complete conversion pathway: Mass to particles

To convert from mass to number of atoms or molecules (or vice versa), you must work through two steps using both equations. You cannot go directly from mass to particles.

infoNote

The pathway is:

Convert mass to moles using $n = \frac{m}{MM}$
Convert moles to particles using $N = n \times N_A$

lightbulbExample

Worked Example 1: From mass to number of atoms

How many atoms are in a pure copper coin weighing 2.56 g? (Relative atomic mass of copper = 63.6)

Step 1: Calculate moles of copper

Molar mass of copper = 63.6 g mol⁻¹

$n = \frac{m}{MM} = \frac{2.56}{63.6} = 0.0403 \text{ mol}$

Step 2: Calculate number of atoms

$N = n \times N_A = 0.0403 \times 6.022 \times 10^{23} = 2.43 \times 10^{22} \text{ atoms}$

lightbulbExample

Worked Example 2: From number of molecules to mass

What is the mass of $1.0 \times 10^{12}$ molecules of sulfur dioxide (SO₂)?

Step 1: Convert molecules to moles

$n = \frac{N}{N_A} = \frac{1.0 \times 10^{12}}{6.022 \times 10^{23}} = 1.66 \times 10^{-12} \text{ mol}$

Step 2: Calculate molar mass of SO₂

\begin{aligned} MM &= 32.07 + (2 \times 16.00) \\ MM &= 64.07 \text{ g mol}^{-1} \end{aligned}

Step 3: Calculate mass

$m = n \times MM = 1.66 \times 10^{-12} \times 64.07 = 1.1 \times 10^{-10} \text{ g}$

Exam tips

infoNote

When solving mole problems:

Always start by identifying what you're given and what you need to find
Draw a simple diagram showing the conversion pathway (mass → moles → particles)
Write down all formulas before substituting numbers
Keep track of units throughout your calculation
Round your final answer to the appropriate number of significant figures
For gaseous elements, always specify whether you mean atoms or molecules

chatImportant

Common mistakes to avoid:

Trying to convert directly from mass to number of particles without going through moles
Forgetting to use the molecular mass for diatomic gases (O₂, Cl₂, etc.)
Using the wrong units (mixing grams and kilograms)
Not maintaining significant figures correctly

bookmarkSummary

Key Points to Remember:

A mole is $6.022 \times 10^{23}$ particles (atoms, ions, or molecules)
One mole of any substance has a mass in grams equal to its relative atomic mass (for elements) or relative molecular mass (for compounds)
The key conversion formulas are: $n = \frac{m}{MM}$ and $N = n \times N_A$
To convert from mass to number of particles, you must always work through moles as an intermediate step
For gaseous elements like oxygen and chlorine, always specify whether you're referring to atoms or molecules, as this affects the molar mass

The Mole and Conversions (HSC SSCE Chemistry): Revision Notes