Atomic Mass and the Mole Revision Notes for Grade 10 NSC Matric Physical Sciences

Atomic Mass and the Mole

Introduction to quantitative chemistry

Chemical equations tell us which substances react and which products form, but they don't tell us the quantities involved. For example, in the reaction Fe + S → FeS, we know that iron reacts with sulfur to form iron sulfide, but we don't know how much iron we need or how much product we'll get.

Understanding quantities in chemical reactions is crucial for:

Knowing how many atoms are in a sample
Calculating how much product a reaction will make
Determining how much reactant is needed
Working with industrial chemical processes

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Quantitative chemistry is what makes the difference between theoretical knowledge and practical application. Without understanding quantities, we couldn't manufacture medicines, create materials, or even bake a cake consistently!

The mole concept

The mole is chemistry's way of counting particles (atoms, molecules, or ions). Just like we use dozens to count eggs or years to measure time, chemists use moles to count incredibly small particles.

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Definition: Mole

The mole (abbreviation "mol") is the SI (Standard International) unit for "amount of substance".

Think of the mole as a counting unit - it's much bigger than familiar counting units because atoms and molecules are incredibly small. One mole contains a specific, enormous number of particles.

Avogadro's number

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Definition: Avogadro's number

The number of particles in a mole, equal to 6.022 × 10²³.

This number is so large that if you had this many cold drink cans, you could cover the entire Earth's surface to a depth of over 300 km! If you counted atoms at 10 million per second, it would take 2 billion years to count all the atoms in one mole.

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Key insight: When we measure the relative atomic mass of any element in grams, we have exactly one mole of that element. For example:

12.0 g of carbon = 1 mole of carbon atoms
63.5 g of copper = 1 mole of copper atoms
6.022 × 10²³ copper atoms

Molar mass

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Definition: Molar mass

Molar mass (M) is the mass of 1 mole of a chemical substance. The unit for molar mass is grams per mole or g·mol⁻¹.

The periodic table gives us atomic masses, which can be interpreted in three ways:

Mass of a single atom - the mass in grams of one average atom relative to carbon
Average atomic mass - the average mass of all isotopes of that element
Molar mass - the mass of one mole of the element (this is what we use most in calculations)

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Important relationship: For any element, the relative atomic mass number equals the molar mass number. For example, if carbon has a relative atomic mass of 12.0 u, then carbon has a molar mass of 12.0 g·mol⁻¹.

Key calculation equation

We can calculate the relationship between mass, moles, and molar mass using this equation:

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Key Equation

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

Where:

$n$ = number of moles
$m$ = mass in grams (g)
$M$ = molar mass in grams per mole (g·mol⁻¹)

Memory tip: Think of the triangle diagram. Cover the quantity you want to find, and the triangle shows you the calculation needed.

Important: Always write units next to every number in your calculations. Mass is always in grams (g) and molar mass is always in grams per mole (g·mol⁻¹).

Worked examples

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Worked Example 1: Calculating moles from mass

Question: Calculate the number of moles of iron (Fe) in an 11.7 g sample.

Solution: Step 1: Find the molar mass of iron

From the periodic table, iron has a molar mass of 55.8 g·mol⁻¹.

Step 2: Apply the equation

$n = \frac{m}{M} = \frac{11.7 \text{ g}}{55.8 { g·mol}^{-1}} = 0.21 \text{ mol}$

Therefore, there are 0.21 moles of iron in the sample.

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Worked Example 2: Calculating mass from moles

Question: You have 5 moles of zinc. What is the mass of zinc, and how many zinc atoms are present?

Solution: Step 1: Find the molar mass of zinc (65.4 g·mol⁻¹)

Step 2: Calculate the mass

If 1 mole of zinc = 65.4 g, then 5 moles = 65.4 g × 5 = 327 g

Step 3: Calculate the number of atoms

5 mol × 6.022 × 10²³ atoms·mol⁻¹ = 3.011 × 10²⁴ atoms

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Worked Example 3: Calculating atoms from mass

Question: Calculate the number of atoms in an 81 g sample of aluminium.

Solution: Step 1: Calculate the number of moles

$n = \frac{m}{M} = \frac{81 \text{ g}}{27.0 { g·mol}^{-1}} = 3 \text{ mol}$

Step 2: Calculate the number of atoms

Number of atoms = 3 mol × 6.022 × 10²³ = 1.8069 × 10²⁴ atoms

Extension to compounds

The same principles apply to compounds, but you need to calculate the molar mass of the whole compound by adding up the molar masses of each atom in the formula.

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Worked Example: Calculating molar mass of H₂SO₄

Solution: Step 1: Identify each element and count atoms

Hydrogen: 2 atoms × 1.01 g·mol⁻¹ = 2.02 g·mol⁻¹
Sulfur: 1 atom × 32.1 g·mol⁻¹ = 32.1 g·mol⁻¹
Oxygen: 4 atoms × 16.0 g·mol⁻¹ = 64.0 g·mol⁻¹

Step 2: Add them up

Molar mass of H₂SO₄ = 2.02 + 32.1 + 64.0 = 98.12 g·mol⁻¹

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Important: In balanced chemical equations, the numbers in front of compounds show the mole ratio in which reactants combine to form products.

Key takeaways

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Key Points to Remember:

The mole is a counting unit - like dozen or pair, but much larger (6.022 × 10²³)
Molar mass connects atomic mass to measurable quantities - the number on the periodic table equals the molar mass in g·mol⁻¹
Always use the equation $n = \frac{m}{M}$ for mole calculations, and always include units
For compounds, add up the molar masses of each atom in the formula
Chemical equations show mole ratios - the coefficients tell you how many moles of each substance react

Atomic Mass and the Mole (Grade 10 NSC Matric Physical Sciences): Revision Notes