Chemistry – Neels Hattingh

Lesson 2.1 – Electron Configuration

Neels Hattingh — Sun, 19 Apr 2026 02:29:32 +0000

Chemistry 2.1: Electron Configuration

Chemistry · Lesson 2.1

Electron Configuration

Shells, Subshells, Orbitals & the Aufbau Principle

In this lesson

Why It Matters Shells & Subshells Orbitals The Three Rules Filling Order Writing Configurations Valence Electrons Exceptions Config Builder Worked Examples Practice Takeaways

Why Electron Configuration Matters

In Tier I we learned that electrons occupy shells around the nucleus. Now we go deeper. The precise arrangement of electrons — their electron configuration — is the single most important factor in determining how an element behaves chemically.

It explains why sodium reacts violently with water while neon is inert. It explains the entire structure of the periodic table, why elements in the same group have similar properties, and how and why chemical bonds form. Every trend you will study in Tier II flows from electron configuration.

The Central Idea

Chemistry is governed by electrons — specifically by the electrons in the outermost shell. Electron configuration tells you exactly how many electrons an atom has and where they are. From that, you can predict almost everything about an element’s chemistry.

Shells & Subshells

Electrons do not orbit the nucleus freely — they occupy specific energy levels called shells (or principal energy levels), numbered 1, 2, 3, 4 outward from the nucleus. The higher the shell number, the greater the energy and the farther from the nucleus.

Each shell is divided into subshells, labelled s, p, d, and f. These differ in shape and energy. The number of subshells in a shell equals the shell number: Shell 1 has only an s subshell; Shell 2 has s and p; Shell 3 has s, p, and d; and so on.

Shell (n)	Subshells present	Max electrons per subshell	Max electrons in shell
1 (K)	1s	s: 2	2
2 (L)	2s, 2p	s: 2 · p: 6	8
3 (M)	3s, 3p, 3d	s: 2 · p: 6 · d: 10	18
4 (N)	4s, 4p, 4d, 4f	s: 2 · p: 6 · d: 10 · f: 14	32

Memory aid — subshell capacities

s holds 2 electrons (1 orbital × 2) · p holds 6 (3 orbitals × 2) · d holds 10 (5 orbitals × 2) · f holds 14 (7 orbitals × 2). The pattern: 2, 6, 10, 14 — each increases by 4.

Orbitals

Each subshell is made up of orbitals — regions of space where there is a high probability of finding an electron. Every orbital can hold a maximum of two electrons, and those two electrons must have opposite spins (one spin-up ↑, one spin-down ↓).

s orbital

Spherical shape. 1 orbital per subshell. Holds up to 2 electrons. Found in every shell (1s, 2s, 3s…). Lowest energy within each shell.

p orbitals

Dumbbell-shaped. 3 orbitals per subshell (px, py, pz), oriented along the x, y, and z axes. Holds up to 6 electrons. Present from Shell 2 onwards.

d orbitals

More complex shapes (cloverleaf). 5 orbitals per subshell. Holds up to 10 electrons. Present from Shell 3 onwards. Responsible for transition metal chemistry.

f orbitals

Most complex shapes. 7 orbitals per subshell. Holds up to 14 electrons. Present from Shell 4 onwards. Associated with the lanthanides and actinides.

Orbital Box Diagram — Nitrogen (Z=7): 1s² 2s² 2p³

2 e⁻ max

6 e⁻ max · Hund’s rule: one e⁻ per orbital before pairing

Notice the 2p subshell: nitrogen has 3 electrons in 2p, and they each occupy a separate orbital with the same spin direction before any pairing begins. This is Hund’s Rule — covered in the next section.

The Three Rules

Three principles govern how electrons fill orbitals. Together they allow you to determine the electron configuration of any element.

1. The Aufbau Principle

German: “building up”

Electrons fill orbitals starting from the lowest available energy level and working upward. The ground state of an atom has electrons in the lowest possible energy arrangement. You fill 1s before 2s before 2p before 3s, and so on — following the Aufbau (filling) order.

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → …

2. The Pauli Exclusion Principle

Wolfgang Pauli, 1925

No two electrons in the same atom can have identical quantum numbers. In practice: each orbital holds at most two electrons, and they must have opposite spins (one ↑ and one ↓). You cannot have two spin-up electrons in the same orbital.

✓ [↑↓] ✗ [↑↑] ✗ [↓↓]

3. Hund’s Rule

Friedrich Hund, 1927

When filling orbitals of equal energy (within the same subshell), electrons occupy separate orbitals with the same spin direction before any pairing begins. Spreading out minimises electron-electron repulsion and gives the atom its lowest energy state.

2p with 3 e⁻: [↑][↑][↑] ✓ not [↑↓][↑][ ] ✗

The Aufbau Filling Order

The order in which subshells are filled does not follow the simple shell sequence — because subshell energies from different shells overlap. The 4s subshell, for example, fills before the 3d because it is slightly lower in energy. This is the single most important sequence to memorise in this lesson.

Aufbau Filling Order — read left to right

1s→ 2s→ 2p→ 3s→ 3p→ 4s→ 3d→ 4p→ 5s→ 4d→ 5p→ 6s→ 4f→ 5d→ 6p

■ s subshell ■ p subshell ■ d subshell ■ f subshell

The 4s / 3d Crossover

4s fills before 3d when building up an atom — but when electrons are removed (ionisation), 4s electrons are lost first. This is because once 3d is occupied, it drops below 4s in energy. So Fe is [Ar] 3d⁶ 4s² but Fe²⁺ is [Ar] 3d⁶ — the two 4s electrons are removed first, not 3d electrons.

Writing Electron Configurations

Electron configuration is written as a sequence of subshell labels, each with a superscript showing the number of electrons it contains. Read the Aufbau order, filling each subshell to capacity before moving to the next.

The format is: shell number + subshell letter + superscript (electron count). Example: 1s² means 2 electrons in the 1s subshell.

Hydrogen — Z = 1

1s¹

1 electron, fills the lowest available subshell (1s) with one electron.

Carbon — Z = 6

1s² 2s² 2p²

6 electrons: 2 fill 1s, 2 fill 2s, 2 go into 2p (one each in two orbitals per Hund’s Rule).

Sodium — Z = 11

1s² 2s² 2p⁶ 3s¹

11 electrons: 1s and 2s fill (2+2=4), 2p fills (6 more = 10 total), lone electron in 3s.

Chlorine — Z = 17

1s² 2s² 2p⁶ 3s² 3p⁵

17 electrons: fills 1s, 2s, 2p (10 total), 3s (12), then 5 into 3p — one orbital short of a full 3p.

Iron — Z = 26

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

26 electrons: fills through 3p (18 total), then 4s (20), then 6 into 3d. Note: 4s fills before 3d.

For heavier elements, chemists use a shorthand called the noble gas configuration. Replace the core electrons (everything up to the previous noble gas) with the noble gas symbol in brackets, then write only the remaining outer electrons.

Iron — Noble Gas Shorthand

[Ar] 3d⁶ 4s²

[Ar] = 1s² 2s² 2p⁶ 3s² 3p⁶ (18 electrons). The shorthand shows only the electrons beyond the argon core.

Valence Electrons

Valence electrons are the electrons in the outermost (highest-numbered) shell of an atom. They are the electrons that participate in chemical bonding — forming ionic bonds by transfer, or covalent bonds by sharing. The core electrons (inner shells) are shielded and generally do not participate in reactions.

For main-group elements (Groups 1–2 and 13–18), the number of valence electrons equals the group number:

Group	Example	Configuration (outer)	Valence e⁻	Typical ion
1	Na	3s¹	1	Na⁺ (loses 1)
2	Mg	3s²	2	Mg²⁺ (loses 2)
13	Al	3s² 3p¹	3	Al³⁺ (loses 3)
14	Si	3s² 3p²	4	Shares (4 bonds)
15	P	3s² 3p³	5	P³⁻ (gains 3)
16	S	3s² 3p⁴	6	S²⁻ (gains 2)
17	Cl	3s² 3p⁵	7	Cl⁻ (gains 1)
18	Ar	3s² 3p⁶	8	No ion (stable)

Notable Exceptions

Two important exceptions to the standard Aufbau filling order arise among the transition metals. They occur because a completely full or exactly half-full d subshell confers extra stability — enough to “steal” an electron from the adjacent s subshell.

Chromium — Z = 24

[Ar] 3d⁵ 4s¹ — not [Ar] 3d⁴ 4s²

A half-filled 3d⁵ (one electron per orbital) is especially stable due to exchange energy. One 4s electron moves to 3d to achieve this arrangement.

Copper — Z = 29

[Ar] 3d¹⁰ 4s¹ — not [Ar] 3d⁹ 4s²

A completely filled 3d¹⁰ subshell is highly stable. One 4s electron migrates to 3d to achieve the full d subshell, sacrificing the 4s pair.

Scope at this level

For Tier II, focus on learning the standard Aufbau order and being able to write configurations for elements Z=1 through Z=36 (up to krypton). Know the chromium and copper exceptions by name. The deeper quantum mechanical reasons for these anomalies are explored in Tier IV.

Configuration Builder

Select an element to see its full electron configuration, noble gas shorthand, and valence electron count.

Electron Configuration Explorer

Element:

Select an element above to see its configuration.

Worked Examples

Example 1Full Configuration from Atomic Number

Write the full electron configuration for: (a) Phosphorus (Z=15), (b) Calcium (Z=20), (c) Iron (Z=26).

Method: Follow the Aufbau order, filling each subshell to capacity before moving to the next. Count electrons against Z.

(a) Phosphorus, Z=15
1s² (2) → 2s² (4) → 2p⁶ (10) → 3s² (12) → 3p³ (15)
1s² 2s² 2p⁶ 3s² 3p³
Valence electrons: 5 (in 3s² 3p³) · Group 15

(b) Calcium, Z=20
1s² 2s² 2p⁶ 3s² 3p⁶ (18, = Ar) → 4s² (20)
[Ar] 4s²
Valence electrons: 2 (in 4s²) · Group 2

(c) Iron, Z=26
[Ar] (18) → 4s² (20) → 3d⁶ (26)
[Ar] 3d⁶ 4s²
Valence electrons: 2 (in 4s²) — transition metals counted by 4s for main bonding

Example 2Configuration of Ions

Write the electron configuration of: (a) Na⁺, (b) Cl⁻, (c) Fe²⁺, (d) Fe³⁺.

Method: Start with the neutral atom’s configuration. Remove electrons for cations (from outermost shell first); add electrons for anions.

(a) Na⁺ — Neutral Na: 1s² 2s² 2p⁶ 3s¹. Remove 1 electron (from 3s):
1s² 2s² 2p⁶ — identical to neon’s configuration.

(b) Cl⁻ — Neutral Cl: 1s² 2s² 2p⁶ 3s² 3p⁵. Add 1 electron (to 3p):
1s² 2s² 2p⁶ 3s² 3p⁶ — identical to argon’s configuration.

(c) Fe²⁺ — Neutral Fe: [Ar] 3d⁶ 4s². Remove 2 electrons from 4s first:
[Ar] 3d⁶

(d) Fe³⁺ — Start from Fe²⁺ ([Ar] 3d⁶). Remove 1 more from 3d:
[Ar] 3d⁵ — a half-filled d subshell, which is notably stable.

Example 3Identifying Elements from Configuration

Identify the element with each configuration: (a) [Ne] 3s² 3p⁴, (b) [Ar] 3d¹⁰ 4s² 4p⁵, (c) [Ar] 3d⁵ 4s¹.

(a) [Ne] 3s² 3p⁴ — [Ne] = 10 electrons. Add 2+4=6 more. Total: 16. Atomic number 16 = Sulfur (S). Valence electrons: 6, Group 16.

(b) [Ar] 3d¹⁰ 4s² 4p⁵ — [Ar] = 18. Add 10+2+5=17 more. Total: 35. Atomic number 35 = Bromine (Br). A halogen with 7 valence electrons.

(c) [Ar] 3d⁵ 4s¹ — [Ar] = 18. Add 5+1=6 more. Total: 24. Atomic number 24 = Chromium (Cr). This is the exception — a half-filled 3d⁵ and one 4s electron for extra stability.

Practice Questions

QuizTest your understanding

Q1. What is the maximum number of electrons that can occupy the 3d subshell?

A 2
B 6
C 10
D 14

Q2. Which set of subshells is filled in the correct Aufbau order?

A 1s → 2s → 3s → 2p → 3p
B 1s → 2s → 2p → 3s → 3p → 3d → 4s
C 1s → 2s → 2p → 3s → 3p → 4s → 3d
D 1s → 2p → 2s → 3p → 3s → 4s → 3d

Q3. Hund’s Rule states that electrons in degenerate (equal-energy) orbitals will:

A Pair up in the same orbital before occupying empty orbitals
B Always have opposite spins regardless of orbital
C Occupy separate orbitals with the same spin before pairing
D Fill from the highest energy orbital downward

Q4. An element has the configuration [Ne] 3s² 3p³. How many valence electrons does it have, and which element is it?

A 3 valence electrons · Aluminium
B 2 valence electrons · Magnesium
C 5 valence electrons · Phosphorus
D 6 valence electrons · Sulfur

Q5. When Fe (Z=26) forms an Fe²⁺ ion, which electrons are removed first?

A The two 3d electrons of lowest energy
B One electron each from 3d and 4s
C The two 4s electrons
D Two electrons from the 3p subshell

Key Takeaways

Lesson 2.1 Summary

Electron configuration describes the precise arrangement of electrons in an atom’s shells, subshells, and orbitals — and governs all chemical behaviour.
Shells (n=1,2,3…) contain subshells (s, p, d, f). Subshell capacities: s=2, p=6, d=10, f=14 electrons.
Each orbital holds at most 2 electrons with opposite spins (Pauli Exclusion Principle).
Aufbau Principle: fill from lowest energy upward. Critical crossover: 4s fills before 3d.
Hund’s Rule: within a subshell, electrons occupy separate orbitals (same spin) before pairing.
Noble gas shorthand replaces the inner-electron core with [noble gas symbol] for efficiency.
Valence electrons (outermost shell) determine reactivity and bonding. Group number = valence electrons for main-group elements.
Exceptions: Cr ([Ar] 3d⁵ 4s¹) and Cu ([Ar] 3d¹⁰ 4s¹) gain stability from half-filled and fully-filled d subshells.
For ion configurations: remove electrons from outermost shell first (4s before 3d for transition metals).

lesson 1.8 – Basic Chemical Reactions

Neels Hattingh — Thu, 16 Apr 2026 19:36:02 +0000

Chemistry 1.8: Basic Chemical Reactions

Chemistry · Lesson 1.8

Basic Chemical Reactions

Reactants, Products, Conservation of Mass & Balancing Equations

In this lesson

Writing Equations State Symbols Why Balance? Balancing Method Reaction Types Practice Balancer Worked Examples Practice Takeaways

Writing Chemical Equations

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants on the left, an arrow pointing right, and the products on the right. Coefficients (numbers in front of formulas) show the relative numbers of molecules or formula units involved.

2H₂ + O₂ → 2H₂O

Reactants

Starting materials that are consumed in the reaction. Written to the left of the arrow. In the equation above, H₂ and O₂ are reactants.

Products

New substances formed by the reaction. Written to the right of the arrow. H₂O is the product in the equation above.

Coefficient

A number placed in front of a formula to indicate the relative number of molecules or formula units. The coefficient 2 before H₂ means two molecules of hydrogen.

Subscript

A number written below and to the right of an element symbol within a formula. H₂ means two hydrogen atoms per molecule. Subscripts are part of the formula — never change them when balancing.

The Golden Rule of Balancing

You may only change coefficients — numbers in front of formulas. You must never change subscripts. Changing a subscript changes the substance itself (H₂O becomes H₂O₂ — a completely different compound). Coefficients simply indicate how many molecules of each substance are involved.

State Symbols

Chemical equations often include state symbols in parentheses after each formula. These indicate the physical state of each substance under the reaction conditions. They are particularly important in electrochemistry and thermochemistry.

Symbol	State	Meaning	Example
(s)	Solid	Substance is in the solid phase	NaCl(s), Fe(s), CaCO₃(s)
(l)	Liquid	Substance is in the liquid phase	H₂O(l), Hg(l), Br₂(l)
(g)	Gas	Substance is in the gaseous phase	O₂(g), CO₂(g), HCl(g)
(aq)	Aqueous	Dissolved in water (aqueous solution)	NaCl(aq), HCl(aq), NaOH(aq)

CaCO₃(s) → CaO(s) + CO₂(g)

Why Must Equations Be Balanced?

The Law of Conservation of Mass — established by Lavoisier — states that atoms are neither created nor destroyed in a chemical reaction. They are only rearranged. This means the number of each type of atom must be the same on both sides of a chemical equation.

An unbalanced equation violates this law. Consider the unbalanced combustion of methane:

UNBALANCED CH₄ + O₂ → CO₂ + H₂O

Atom	Left side	Right side	Balanced?
C	1	1	✓
H	4	2	✗
O	2	3	✗

Hydrogen and oxygen are unbalanced. We need to add coefficients to fix this — without touching the subscripts.

BALANCED CH₄ + 2O₂ → CO₂ + 2H₂O

Atom	Left side	Right side	Balanced?
C	1	1	✓
H	4	4	✓
O	4	4	✓

The Balancing Method

There is no single rigid algorithm for balancing equations, but the following systematic approach works for most equations at this level.

1Write the unbalanced equation

Write the correct formulas for all reactants and products. Do not change any subscripts — these are fixed by the chemistry.

Fe + O₂ → Fe₂O₃

2Count atoms on each side

List every element and how many atoms of each appear on each side.

Fe: left=1, right=2 | O: left=2, right=3 — both unbalanced

3Balance the most complex molecule first

Start with the compound containing the most elements. Adjust its coefficient and recount. Here, balance Fe₂O₃ by placing a 4 in front of Fe and a 3 in front of O₂ to fix the ratio.

4Fe + 3O₂ → 2Fe₂O₃

4Verify all atoms balance

Count every atom on both sides again.

Fe: left=4 ✓, right=4 | O: left=6 ✓, right=6 — balanced

5Reduce coefficients if possible

Check if all coefficients share a common factor. If so, divide through to get the simplest whole-number ratio. 4, 3, 2 share no common factor — already in simplest form.

4Fe + 3O₂ → 2Fe₂O₃ ✓

Tips for Tricky Equations

Polyatomic ions (e.g. SO₄²⁻, NO₃⁻): if they appear unchanged on both sides, treat them as a single unit — count the whole ion, not individual atoms.

Odd/even trick: If you have an odd number of atoms of an element that appears in a molecule of 2 (like O₂), multiply everything by 2 first to get even numbers, then halve the coefficients at the end.

Fractions are allowed during working — just multiply through by 2 at the end to get whole numbers.

Reaction Types & Their Equations

Recognising the type of reaction from its equation helps you predict products and balance more efficiently. Here are the five fundamental types with representative balanced equations.

Synthesis

A + B → AB

Two or more substances combine into one. Always produces a single product.

2Mg+O₂→2MgO

Decomposition

AB → A + B

One compound breaks into two or more simpler substances. Always starts with one reactant.

2H₂O→2H₂+O₂

Combustion

fuel + O₂ → CO₂ + H₂O

Rapid reaction with oxygen. Complete combustion of hydrocarbons always produces CO₂ and H₂O.

C₃H₈+5O₂→3CO₂+4H₂O

Single Displacement

A + BC → AC + B

One element displaces another from a compound. Requires the displacing element to be more reactive.

Zn+2HCl→ZnCl₂+H₂

Double Displacement

AB + CD → AD + CB

Two compounds exchange ions. Often produces a precipitate (↓), a gas (↑), or water. Driving force is the removal of an ion from solution.

AgNO₃(aq)+NaCl(aq)→AgCl↓+NaNO₃(aq)

Practice Balancer

Enter the correct coefficients to balance each equation. Type 1 if no coefficient is needed (coefficients of 1 are usually omitted in writing, but enter 1 here to check).

Equation 1 — Formation of water

H₂ + O₂ → H₂O

Equation 2 — Combustion of ethane (C₂H₆)

C₂H₆ + O₂ → CO₂ + H₂O

Equation 3 — Iron(III) oxide formation

Fe + O₂ → Fe₂O₃

Worked Examples

Example 1Balancing by Inspection

Balance the equation: Al + HCl → AlCl₃ + H₂

Step 1 — Count atoms (unbalanced):

Al: L=1, R=1 | H: L=1, R=2 | Cl: L=1, R=3 — H and Cl unbalanced

Step 2 — Fix Cl: Need 3 Cl on left → put 3 in front of HCl.

Al + 3HCl → AlCl₃ + H₂

Step 3 — Recount H: Left=3, Right=2 — still unbalanced. Need H₂ to be 3/2 — use 3/2 H₂, then multiply through by 2.

2Al + 6HCl → 2AlCl₃ + 3H₂

Verify: Al: 2=2 ✓ | H: 6=6 ✓ | Cl: 6=6 ✓ — balanced.

Example 2Combustion Reaction

Balance the complete combustion of propane: C₃H₈ + O₂ → CO₂ + H₂O

Strategy: Balance C first, then H, then O last (O₂ is easy to adjust at the end).

Carbon: 3 C on left → need 3CO₂ on right.
C₃H₈ + O₂ → 3CO₂ + H₂O

Hydrogen: 8 H on left → need 4H₂O on right.
C₃H₈ + O₂ → 3CO₂ + 4H₂O

Oxygen: Right side has 3×2 + 4×1 = 6+4 = 10 O atoms → need 5O₂.
C₃H₈ + 5O₂ → 3CO₂ + 4H₂O

Verify: C: 3=3 ✓ | H: 8=8 ✓ | O: 10=10 ✓

Example 3Identifying and Balancing

Identify the reaction type and balance: NaOH(aq) + H₂SO₄(aq) → Na₂SO₄(aq) + H₂O(l)

Reaction type: Double displacement (acid-base neutralisation). Two ionic compounds exchange partners: NaOH and H₂SO₄ swap to form Na₂SO₄ and H₂O.

Balance Na: Right side has 2 Na in Na₂SO₄ → need 2NaOH.

2NaOH + H₂SO₄ → Na₂SO₄ + H₂O

Balance H: Left has 2+2=4 H → need 2H₂O.

2NaOH(aq) + H₂SO₄(aq) → Na₂SO₄(aq) + 2H₂O(l)

Verify: Na: 2=2 ✓ | O: 2+4=6, 4+2=6 ✓ | H: 2+2=4, 4 ✓ | S: 1=1 ✓

Practice Questions

QuizTest your understanding

Q1. When balancing a chemical equation, you may only change:

A The subscripts within chemical formulas
B The coefficients in front of chemical formulas
C Both subscripts and coefficients
D The element symbols in the formulas

Q2. What are the correct coefficients to balance: __ N₂ + __ H₂ → __ NH₃?

A 1, 1, 1
B 1, 2, 2
C 1, 3, 2
D 2, 3, 2

Q3. The state symbol (aq) indicates that a substance is:

A In its liquid state
B Dissolved in water
C A gaseous product
D An aqueous acid only

Q4. The reaction 2KClO₃ → 2KCl + 3O₂ is classified as:

A Synthesis
B Decomposition
C Combustion
D Single displacement

Q5. How many oxygen atoms are on the right side of the balanced equation: C₄H₁₀ + 13/2 O₂ → 4CO₂ + 5H₂O? (Hint: use the whole-number equivalent: 2C₄H₁₀ + 13O₂ → 8CO₂ + 10H₂O)

A 18
B 8
C 26
D 13

Key Takeaways

Lesson 1.8 Summary

A chemical equation shows reactants (left) and products (right) separated by an arrow. Coefficients indicate relative amounts.
State symbols (s), (l), (g), (aq) indicate the physical state of each substance. (aq) means dissolved in water.
Equations must be balanced because atoms are conserved (Law of Conservation of Mass) — the same number of each atom must appear on both sides.
Only coefficients may be changed when balancing — never subscripts. Changing subscripts changes the substance.
Balancing strategy: write unbalanced equation → count atoms → adjust coefficients starting with the most complex molecule → recount → reduce to simplest whole numbers.
The five reaction types: synthesis (A+B→AB), decomposition (AB→A+B), combustion (fuel+O₂→CO₂+H₂O), single displacement (A+BC→AC+B), double displacement (AB+CD→AD+CB).
For combustion of hydrocarbons: balance C first, then H, then O last.

Lesson 1.7 – Atomic Mass & Number

Neels Hattingh — Thu, 16 Apr 2026 19:34:30 +0000

Chemistry 1.7: Atomic Mass & Atomic Number

Chemistry · Lesson 1.7

Atomic Mass & Number

Isotopes, Relative Atomic Mass, Atomic Number & Calculations

In this lesson

Quick Review Atomic Mass Units Isotopes in Depth Relative Atomic Mass Calculations Reading the Table Worked Examples Practice Takeaways

Quick Review

In Lesson 1.5 we introduced the three subatomic particles and the concepts of atomic number and mass number. This lesson builds directly on those foundations, going deeper into how atomic masses are measured, what isotopes mean for real-world chemistry, and how to perform calculations using the periodic table.

Core Relationships — From Lesson 1.5

Z = protons

Atomic number — defines the element

A = protons + neutrons

Mass number — sum of heavy particles in nucleus

N = A − Z

Number of neutrons

e⁻ = Z (neutral atom)

Electrons equal protons in a neutral atom

Atomic Mass Units

Atoms are so small that measuring their masses in grams would produce inconveniently tiny numbers. Instead, chemists use the atomic mass unit (amu), also written as u or Da (dalton).

The atomic mass unit is defined as exactly 1/12 of the mass of a carbon-12 atom. This standard was chosen because carbon-12 is abundant, stable, and easily measured. On this scale, one proton and one neutron each have a mass of approximately 1 amu, while an electron has a mass of only 0.000549 amu — negligible for most calculations.

Atomic Mass Unit (amu)

A unit of mass equal to 1/12 the mass of one carbon-12 atom. Approximately 1.661 × 10⁻²⁷ kg. Used to express the masses of atoms and subatomic particles.

Mass Number vs Atomic Mass

Mass number (A) is always a whole number — it counts protons + neutrons. Atomic mass is a decimal value in amu — it reflects the weighted average of all isotopes.

Why electron mass is ignored

An electron has a mass of 9.109 × 10⁻³¹ kg — about 1836 times lighter than a proton. For nearly all chemistry calculations, electron mass is so small it can be ignored without meaningful error. The mass of an atom is essentially the mass of its protons and neutrons.

Isotopes in Depth

Most elements in nature exist as a mixture of isotopes. Each isotope has the same atomic number (same element) but a different mass number (different neutron count). The proportion of each isotope in a natural sample is called its natural abundance, expressed as a percentage.

Natural abundances are remarkably consistent — a sample of carbon from coal, diamond, human tissue, or a distant meteorite all contain approximately the same ratio of carbon-12 to carbon-13.

Natural Isotope Abundances — Selected Elements

¹H

99.98%

²H

0.02%

¹²C

98.93%

¹³C

1.07%

³⁵Cl

75.77%

³⁷Cl

24.23%

Radioactive Isotopes

Some isotopes are unstable — their nuclei contain an imbalanced ratio of protons to neutrons and decay over time, emitting radiation. These are called radioisotopes. Carbon-14 (used in radiocarbon dating), iodine-131 (used in thyroid cancer treatment), and uranium-235 (nuclear fuel) are important examples. Stable isotopes do not decay.

Relative Atomic Mass

Because most elements exist as mixtures of isotopes, the mass shown on the periodic table is not the mass of any single isotope — it is the relative atomic mass (also called standard atomic weight), which is the weighted average of all naturally occurring isotopes.

A weighted average gives more influence to isotopes that are more abundant. If one isotope makes up 99% of a sample, the average will be very close to its mass.

Weighted Average Atomic Mass Formula

Ar = Σ (isotope mass × fractional abundance)

Where fractional abundance = percentage ÷ 100. Sum over all naturally occurring isotopes of the element.

This is why chlorine has an atomic mass of approximately 35.5 on the periodic table — not 35 or 37. It is the weighted average of ³⁵Cl (75.77%) and ³⁷Cl (24.23%), landing between the two values but closer to 35 because it predominates.

Step-by-Step Calculations

Calculating weighted average atomic mass follows a consistent method. Here is the general approach broken into explicit steps.

Convert percentages to decimals

Divide each isotope’s percentage abundance by 100 to get its fractional abundance.

75.77% → 0.7577 | 24.23% → 0.2423

Multiply each isotope mass by its fractional abundance

This gives each isotope’s contribution to the average.

34.969 × 0.7577 = 26.496 | 36.966 × 0.2423 = 8.956

Sum all contributions

Add together the contributions from all isotopes.

26.496 + 8.956 = 35.452 amu ≈ 35.45 amu

Check your answer

The result should lie between the lightest and heaviest isotope masses, closer to the most abundant one. Compare to the periodic table value.

35.45 amu ✓ — matches the periodic table value for Cl

Using the Periodic Table for Mass Data

The periodic table gives you all the atomic number and mass data you need for calculations. Understanding what each number means — and what it doesn’t mean — prevents common errors.

Atomic Number (Z)

Always a whole number. Never changes for a given element. Use this to find protons, and (for neutral atoms) electrons. Found above the symbol in most periodic tables.

Relative Atomic Mass (Ar)

Usually a decimal. This is the weighted average — not a single isotope’s mass. Use this in mole calculations and stoichiometry. Found below the symbol in most periodic tables.

Mass Number (A)

Always a whole number. Specific to a particular isotope (e.g. ¹²C or ¹⁴C). Use this when calculating neutrons: N = A − Z. Not shown directly on periodic tables.

Neutron Number (N)

N = A − Z. Not shown on the periodic table — you always calculate it. Can vary between isotopes of the same element while Z stays constant.

Common Exam Trap

Students often confuse the relative atomic mass (decimal, periodic table value) with the mass number (whole number, specific to one isotope). You cannot calculate neutrons using the decimal atomic mass — you need the mass number of the specific isotope being described. Always identify which number is being given in a question before calculating.

Worked Examples

Example 1Subatomic Particles from Notation

Determine the number of protons, neutrons, and electrons for: (a) ⁵⁶Fe (neutral), (b) ⁶³Cu²⁺, (c) ³²S²⁻.

(a) ⁵⁶Fe (neutral) — Iron: Z = 26. Protons = 26. Neutrons = 56 − 26 = 30. Electrons = 26 (neutral).

(b) ⁶³Cu²⁺ — Copper: Z = 29. Protons = 29. Neutrons = 63 − 29 = 34. Electrons = 29 − 2 = 27 (lost 2, hence 2+ charge).

(c) ³²S²⁻ — Sulfide ion: Z = 16. Protons = 16. Neutrons = 32 − 16 = 16. Electrons = 16 + 2 = 18 (gained 2, hence 2− charge).

Example 2Weighted Average Atomic Mass

Boron has two naturally occurring isotopes: ¹⁰B (mass 10.013 amu, abundance 19.9%) and ¹¹B (mass 11.009 amu, abundance 80.1%). Calculate the relative atomic mass of boron.

Step 1: Convert to fractional abundances: 19.9% → 0.199; 80.1% → 0.801

Contribution of ¹⁰B = 10.013 × 0.199 = 1.9926
Contribution of ¹¹B = 11.009 × 0.801 = 8.8182
Ar = 1.9926 + 8.8182 = 10.811 amu

This matches the periodic table value for boron (10.81). The result is closer to 11 because ¹¹B is the more abundant isotope (80.1%).

Example 3Back-calculating Isotope Abundance

Gallium has two stable isotopes: ⁶⁹Ga (mass 68.926 amu) and ⁷¹Ga (mass 70.925 amu). The relative atomic mass of gallium is 69.723 amu. Calculate the percentage abundance of each isotope.

Method: Let the fractional abundance of ⁶⁹Ga = x. Then ⁷¹Ga = (1 − x). Set up the weighted average equation.

68.926x + 70.925(1 − x) = 69.723
68.926x + 70.925 − 70.925x = 69.723
−1.999x = 69.723 − 70.925 = −1.202
x = −1.202 ÷ −1.999 = 0.6013
⁶⁹Ga: 60.1% | ⁷¹Ga: 39.9%

Practice Questions

QuizTest your understanding

Q1. The relative atomic mass of an element shown on the periodic table is best described as:

A The mass number of the most common isotope
B The total number of protons and neutrons in one atom
C The weighted average mass of all naturally occurring isotopes
D The mass of one mole of atoms in grams

Q2. An atom of ⁵⁹Co (cobalt, Z = 27) has how many neutrons?

A 27
B 32
C 59
D 86

Q3. Silicon has three isotopes: ²⁸Si (92.23%), ²⁹Si (4.67%), and ³⁰Si (3.10%). Its relative atomic mass will be closest to:

A 29 (the middle isotope)
B 28 (the most abundant isotope)
C 30 (the heaviest isotope)
D Exactly 29 (the average of 28 and 30)

Q4. A ³⁴S²⁻ ion (sulfur, Z = 16) has how many electrons?

A 16
B 14
C 18
D 34

Q5. Magnesium has three isotopes with masses ~24, ~25, and ~26 amu. The periodic table lists magnesium’s atomic mass as 24.305. This tells you that:

A ²⁴Mg is the most abundant isotope, pulling the average close to 24
B ²⁶Mg is the most abundant isotope
C All three isotopes have equal abundance
D Magnesium does not have the isotope ²⁴Mg

Key Takeaways

Lesson 1.7 Summary

The atomic mass unit (amu) = 1/12 the mass of ¹²C. Protons and neutrons each have a mass of ~1 amu; electrons are negligible.
Atomic number (Z) = protons. Mass number (A) = protons + neutrons. Neutrons = A − Z.
Isotopes are atoms of the same element with different neutron counts and mass numbers but identical chemical behaviour.
Natural abundance is the percentage of each isotope found in a naturally occurring sample — consistent worldwide.
Relative atomic mass (Ar) on the periodic table is the weighted average of all naturally occurring isotopes: Ar = Σ(mass × fractional abundance).
The weighted average lies between isotope masses, pulled toward the most abundant isotope.
For ions: electrons = Z ± charge. Adding electrons (anion) makes the charge negative; removing electrons (cation) makes it positive.

Lesson 1.6 – The Periodic Table

Neels Hattingh — Thu, 16 Apr 2026 19:26:56 +0000

Chemistry 1.6: The Periodic Table

Chemistry · Lesson 1.6

The Periodic Table

Layout, Periods, Groups, Metals, Nonmetals & Metalloids

In this lesson

History Layout Reading an Element Key Groups Element Categories Metals, Nonmetals & Metalloids Worked Examples Practice Takeaways

History of the Periodic Table

By the mid-1800s, chemists had identified dozens of elements and were searching for patterns in their properties. Several scientists noticed that elements seemed to repeat certain characteristics at regular intervals — a concept called periodicity.

In 1869, Russian chemist Dmitri Mendeleev published the first widely accepted periodic table. He arranged elements by increasing atomic mass and grouped those with similar properties into vertical columns. Crucially, he left gaps for elements he predicted had not yet been discovered — and his predictions proved correct when gallium, scandium, and germanium were found shortly after, matching his descriptions almost exactly.

The Modern Periodic Table

The modern periodic table, refined in the early 20th century, arranges elements by increasing atomic number (not mass). It contains 118 confirmed elements. The periodic law states: the properties of elements are a periodic function of their atomic numbers.

Layout of the Periodic Table

The periodic table is arranged in rows called periods and columns called groups (or families). Elements in the same group share similar chemical properties because they have the same number of electrons in their outermost shell.

Period

A horizontal row. There are 7 periods. The period number tells you how many electron shells the atom has. Period 1 has 1 shell, Period 3 has 3 shells, etc.

Group

A vertical column. There are 18 groups. Elements in the same group have the same number of valence electrons (outer electrons) and thus similar reactivity and bonding behaviour.

Valence Electrons

Electrons in the outermost shell. These are the electrons that participate in chemical bonding. The group number (for main-group elements) tells you how many valence electrons the element has.

Periodicity

The repeating pattern of properties across periods. Properties like reactivity, atomic radius, and electronegativity follow predictable trends that repeat with each new period.

Periodic Table — Simplified Layout (Periods 1–4, showing element symbols)

He2

Li3

Be4

Ne10

Na11

Mg12

Al13

Si14

P15

S16

Cl17

Ar18

K19

Ca20

Sc21

Ti22

V23

Cr24

Mn25

Fe26

Co27

Ni28

Cu29

Zn30

Ga31

Ge32

As33

Se34

Br35

Kr36

Alkali metals

Alkaline earth

Transition metals

Post-transition metals

Metalloids

Nonmetals

Halogens

Noble gases

Reading an Element Cell

Each element in the periodic table is represented by a cell containing key information. Being able to read this cell fluently is an essential skill.

Iron

55.85

26 — Atomic number (Z). Iron always has 26 protons. This number defines the element.

Fe — Chemical symbol. From the Latin Ferrum. Symbols are 1–2 letters, capitalised first letter only.

Iron — Full element name.

55.85 — Relative atomic mass (weighted average of all isotopes). Not a whole number because it reflects the natural mixture of isotopes.

Key Groups

Certain groups in the periodic table have special names and distinct properties that you will encounter throughout chemistry. These are the most important to know at this stage.

Grp 1

Alkali Metals

Li, Na, K, Rb, Cs, Fr. Highly reactive metals. 1 valence electron — readily donated to form +1 ions. React vigorously with water to produce hydrogen gas. Reactivity increases down the group. Stored in oil to prevent reaction with air.
Grp 2

Alkaline Earth

Be, Mg, Ca, Sr, Ba, Ra. Reactive metals, less so than Group 1. 2 valence electrons — form +2 ions. Calcium is essential for bones and teeth. Magnesium is the central atom in chlorophyll.
Grp 17

Halogens

F, Cl, Br, I, At. Highly reactive nonmetals. 7 valence electrons — one short of a full shell, so they readily gain 1 electron to form −1 ions. React with metals to form salts. Reactivity decreases down the group.
Grp 18

Noble Gases

He, Ne, Ar, Kr, Xe, Rn. Essentially inert — full outer shell (8 electrons, except He with 2). Extremely stable, colourless, odourless gases. Used in lighting (neon signs), welding (argon), and balloons (helium).
Grps 3–12

Transition Metals

The d-block elements (Fe, Cu, Zn, etc.). Good conductors of heat and electricity. Often form coloured compounds. Can have multiple oxidation states (e.g. Fe²⁺ and Fe³⁺). Many are used as catalysts.
Grp 14

Carbon Group

C, Si, Ge, Sn, Pb. Notably diverse — carbon is the basis of all life; silicon is the basis of semiconductors and computing. 4 valence electrons enable rich bonding chemistry.

Element Categories

Beyond groups, elements are classified into broader categories based on their properties. These categories reflect the block structure of the periodic table.

Alkali Metals

Li · Na · K · Rb · Cs · Fr

Soft, shiny metals. 1 valence electron. Highly reactive, especially with water. Reactivity increases down the group. Never found free in nature.

Alkaline Earth Metals

Be · Mg · Ca · Sr · Ba · Ra

2 valence electrons. Harder and less reactive than alkali metals. Form +2 ions. Calcium and magnesium are biologically essential.

Transition Metals

Fe · Cu · Zn · Ag · Au · Pt

D-block elements. High melting points, good conductors, multiple oxidation states, form coloured compounds, many are catalysts.

Metalloids (Semimetals)

B · Si · Ge · As · Sb · Te

Properties intermediate between metals and nonmetals. Semiconductors — silicon and germanium power all modern electronics and computing.

Nonmetals

C · N · O · P · S · Se

Poor conductors. Brittle as solids. Tend to gain electrons (form anions) or share electrons in covalent bonds. Include the building blocks of life.

Halogens

F · Cl · Br · I · At

7 valence electrons. Most reactive nonmetals. Form salts with metals. Exist as diatomic molecules (F₂, Cl₂, etc.). Used in disinfectants, pharmaceuticals, and PVC.

Noble Gases

He · Ne · Ar · Kr · Xe · Rn

Full outer shells — chemically inert under normal conditions. Monatomic gases. Extremely stable. Their stability is the model for why other elements form bonds.

Post-Transition Metals

Al · Ga · In · Sn · Pb · Bi

P-block metals. Softer and have lower melting points than transition metals. Aluminium is the most abundant metal in Earth’s crust.

Metals, Nonmetals & Metalloids

The most fundamental division in the periodic table is between metals, nonmetals, and metalloids. The dividing line (the “staircase”) runs diagonally from boron to astatine — metals to the left, nonmetals to the right, metalloids along the boundary.

Metals

Good conductors of heat and electricity
Lustrous (shiny) surface
Malleable — can be hammered into sheets
Ductile — can be drawn into wire
Solid at room temperature (except Hg)
Tend to lose electrons (form cations)
About 80% of all elements are metals
E.g. iron, copper, gold, sodium, calcium

Nonmetals

Poor conductors (insulators)
Dull appearance (no metallic lustre)
Brittle as solids — shatter when struck
Not malleable or ductile
Many are gases at room temperature
Tend to gain electrons (form anions)
Include the elements of life: C, H, O, N
E.g. carbon, oxygen, sulfur, chlorine

Metalloids

Intermediate electrical conductivity
Semiconductors — conduct under some conditions
Some metallic appearance
Properties vary between metal and nonmetal
Silicon is the basis of all computer chips
Germanium used in fibre optics
Found along the periodic table “staircase”
E.g. silicon, germanium, arsenic, antimony

Hydrogen — the anomaly

Hydrogen sits alone at the top of Group 1, but it is not an alkali metal. It is a nonmetal gas that can either donate or gain an electron depending on conditions. It forms H⁺ (like a metal) or H⁻ (like a nonmetal). Its placement in Group 1 reflects its 1 valence electron, but its properties are unique.

Worked Examples

Example 1Using the Periodic Table

For each element, state: its group, period, category, number of valence electrons, and whether it is a metal, nonmetal, or metalloid: (a) Sodium (Na, Z=11), (b) Chlorine (Cl, Z=17), (c) Silicon (Si, Z=14).

(a) Sodium (Na) — Group 1, Period 3. Alkali metal · Metal. 1 valence electron. Highly reactive; reacts vigorously with water.

(b) Chlorine (Cl) — Group 17, Period 3. Halogen · Nonmetal. 7 valence electrons. Highly reactive; readily gains 1 electron to form Cl⁻.

(c) Silicon (Si) — Group 14, Period 3. Metalloid · Semiconductor. 4 valence electrons. Neither strongly metallic nor nonmetallic — the basis of modern electronics.

Example 2Predicting Properties from Position

Element X is in Period 4, Group 1. Element Y is in Period 2, Group 17. Without knowing the elements, predict: (a) which is more reactive, X or sodium (Period 3, Group 1)? (b) how many valence electrons does Y have? (c) what charge ion does Y tend to form?

(a) X (Period 4, Group 1) is more reactive than sodium (Period 3, Group 1). Reactivity of alkali metals increases down Group 1 — X is potassium (K), which is indeed more reactive than sodium.

(b) Y is in Group 17 — so it has 7 valence electrons. (Group number = valence electrons for main-group elements.)

(c) With 7 valence electrons, Y needs just 1 more to fill its outer shell. It will gain 1 electron to form a −1 ion (anion). Y is fluorine (F), which forms F⁻.

Practice Questions

QuizTest your understanding

Q1. Elements in the same group of the periodic table have similar chemical properties because they:

A Have the same atomic mass
B Have the same number of valence electrons
C Are in the same period
D Have the same number of neutrons

Q2. Which group contains the noble gases?

A Group 1
B Group 2
C Group 17
D Group 18

Q3. An element is located in Period 3, Group 2. How many electron shells does it have, and how many valence electrons?

A 2 shells, 3 valence electrons
B 2 shells, 2 valence electrons
C 3 shells, 2 valence electrons
D 3 shells, 3 valence electrons

Q4. Which of the following is a property of metals?

A Poor conductors of electricity
B Brittle solids that shatter when struck
C Malleable and ductile with metallic lustre
D Tend to gain electrons to form anions

Q5. Mendeleev’s key contribution to the periodic table was:

A Discovering the electron and its charge
B Arranging elements by atomic number
C Organising elements by properties and predicting undiscovered elements
D Naming the noble gas group

Key Takeaways

Lesson 1.6 Summary

Mendeleev (1869) arranged elements by atomic mass and predicted gaps. The modern table uses atomic number.
Horizontal rows are periods (tell you the number of electron shells). Vertical columns are groups (tell you valence electrons).
Elements in the same group have the same number of valence electrons and similar chemical behaviour.
Key named groups: Alkali metals (1), Alkaline earth metals (2), Halogens (17), Noble gases (18).
Metals (left/centre): conductors, lustrous, malleable, ductile, lose electrons. ~80% of all elements.
Nonmetals (right): insulators, brittle, dull, gain electrons.
Metalloids (along the “staircase”): semiconductors with intermediate properties. Silicon powers modern electronics.
Hydrogen is a unique nonmetal placed in Group 1 due to its 1 valence electron, but it shares few properties with alkali metals.

Lesson 1.5 – Introduction to the Atom

Neels Hattingh — Thu, 16 Apr 2026 04:54:03 +0000

Chemistry 1.5: Introduction to the Atom

Chemistry · Lesson 1.5

Introduction to the Atom

Protons, Neutrons, Electrons & Atomic Structure

In this lesson

History of Atomic Theory Atomic Structure Subatomic Particles Atomic Notation Isotopes Ions Worked Examples Practice Takeaways

History of Atomic Theory

The idea that matter is made of indivisible particles dates back to ancient Greece, but the scientific atomic theory developed only over the last two centuries — through a series of experiments that progressively revealed the atom’s true structure.

Each model below was a major advance over its predecessor, and each was eventually shown to be incomplete. This is how science works — models improve as new evidence emerges.

~400
BC

Democritus

Philosophical Atom

Proposed that all matter is made of tiny, indivisible particles called atomos (Greek: uncuttable). Purely philosophical — no experimental evidence. The idea was largely ignored for 2,000 years in favour of Aristotle’s four-element theory.

1803

John Dalton

Solid Sphere Model

The first scientific atomic theory. Proposed that: all matter is made of atoms; atoms of the same element are identical; atoms cannot be created or destroyed; atoms combine in fixed ratios to form compounds. Pictured atoms as solid, indestructible spheres — like billiard balls.

1897

J.J. Thomson

Plum Pudding Model

Discovered the electron through cathode ray experiments — proving atoms are not indivisible. Proposed a model of negatively charged electrons embedded in a diffuse sphere of positive charge, like plums in a pudding. First model to include subatomic particles.

1911

Ernest Rutherford

Nuclear Model

Gold foil experiment: fired alpha particles at a thin gold foil and found that most passed straight through, but a few deflected sharply — even bouncing back. Concluded that the atom has a small, dense, positively charged nucleus at its centre, surrounded by mostly empty space where electrons orbit.

1913

Niels Bohr

Planetary / Shell Model

Proposed that electrons orbit the nucleus in fixed energy levels (shells) — like planets around a sun. Electrons can jump between shells by absorbing or emitting specific amounts of energy (photons). Explained the hydrogen emission spectrum and forms the basis of our Tier I understanding.

1926+

Schrödinger / Heisenberg

Quantum Mechanical Model

The modern model. Electrons do not travel in defined orbits — they exist in regions of probability called orbitals. The exact position and momentum of an electron cannot be simultaneously known (Heisenberg Uncertainty Principle). This model will be explored fully in Tier IV.

Atomic Structure

An atom consists of two regions: a tiny, dense nucleus at the centre, and an electron cloud (or electron shells) surrounding it. The nucleus contains protons and neutrons; electrons occupy the space outside.

The nucleus is extraordinarily small relative to the whole atom. If an atom were the size of a football stadium, the nucleus would be about the size of a marble — yet it contains almost all of the atom’s mass.

Bohr Model — Carbon Atom (simplified)

Scale of the Atom

A single hydrogen atom has a diameter of about 0.1 nanometres (1 × 10⁻¹⁰ m). That’s so small that over 1 million hydrogen atoms placed side by side would fit across the width of a human hair. The nucleus is about 100,000 times smaller than the atom itself.

Subatomic Particles

Atoms are composed of three types of subatomic particles, each with a characteristic mass, charge, and location. Knowing these is the absolute foundation of all further chemistry.

Particle	Symbol	Charge	Relative Mass	Location
Proton	p⁺	+1	1 (1.673 × 10⁻²⁷ kg)	Nucleus
Neutron	n⁰	0 (neutral)	1 (1.675 × 10⁻²⁷ kg)	Nucleus
Electron	e⁻	−1	1/1836 (≈ negligible)	Electron shells (outside nucleus)

The number of protons in the nucleus defines what element an atom is — this is the atomic number. Carbon always has 6 protons; oxygen always has 8. Change the number of protons and you change the element entirely.

In a neutral atom, the number of electrons equals the number of protons, so the positive and negative charges cancel out. The atom carries no overall charge.

Why neutrons matter

Neutrons have no charge, but they play two critical roles: they add mass to the nucleus, and they act as a kind of “glue” — the strong nuclear force between neutrons and protons holds the nucleus together against the repulsion between the positively charged protons. Without neutrons, most nuclei would fly apart.

Atomic Number & Mass Number

Two numbers fully describe the composition of any atom’s nucleus. Understanding them lets you calculate the number of protons, neutrons, and electrons in any atom.

Atomic Number (Z)

The number of protons in the nucleus. This number uniquely identifies the element — it never changes for a given element. Carbon always has Z = 6.

Mass Number (A)

The total number of protons + neutrons in the nucleus. Because electron mass is negligible, this approximates the atom’s mass. A = Z + N (where N = neutrons).

12 C 6

12 — Mass number (A): protons + neutrons

C — Element symbol (Carbon)

6 — Atomic number (Z): number of protons

Neutrons = A − Z = 12 − 6 = 6

Key Formulae

Neutrons (N) = Mass number (A) − Atomic number (Z)

For a neutral atom: Electrons = Protons = Atomic number (Z)

For an ion: electrons = Z ± charge (add electrons for negative ions, remove for positive)

Isotopes

Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons. Because the atomic number (proton count) is the same, they are the same element — but their mass numbers differ.

Isotopes have virtually identical chemical properties (because chemistry is governed by electrons, which are the same in all isotopes of an element), but they have different physical properties such as mass and nuclear stability.

¹H

Protium

Protons: 1
Neutrons: 0
Abundance: 99.98%
Stable

²H

Deuterium

Protons: 1
Neutrons: 1
Abundance: 0.02%
Stable

³H

Tritium

Protons: 1
Neutrons: 2
Abundance: trace
Radioactive

The three isotopes of hydrogen are the most well-known example. All three have 1 proton — making them hydrogen — but they have 0, 1, and 2 neutrons respectively. Deuterium is used in nuclear reactors and heavy water; tritium is radioactive and used in nuclear weapons research and self-luminous devices.

Relative Atomic Mass

Because most elements exist as a mixture of isotopes in nature, the atomic mass shown on the periodic table is a weighted average of all naturally occurring isotopes, based on their abundance. This is why chlorine has an atomic mass of 35.5 — it’s a mix of ³⁵Cl (75%) and ³⁷Cl (25%), giving a weighted average that falls between the two.

Ions

A neutral atom has equal numbers of protons and electrons. When an atom gains or loses electrons, it becomes electrically charged — it becomes an ion.

Cation

A positively charged ion formed when an atom loses one or more electrons. Fewer electrons than protons. Metals typically form cations. E.g. Na⁺, Ca²⁺, Fe³⁺.

Anion

A negatively charged ion formed when an atom gains one or more electrons. More electrons than protons. Non-metals typically form anions. E.g. Cl⁻, O²⁻, N³⁻.

Ions are critical to chemistry — they are responsible for ionic bonding, electrical conductivity in solutions, nerve impulses in biology, and a vast range of chemical reactions. You will encounter them throughout this curriculum.

Ions vs Isotopes — a common confusion

Isotopes differ in the number of neutrons — the number of protons (and therefore the element) stays the same. Ions differ in the number of electrons — the number of protons stays the same. Neither changes the element’s identity. Only changing the proton count changes the element.

Worked Examples

Example 1Finding Subatomic Particles

For each atom or ion, state the number of protons, neutrons, and electrons: (a) ²³Na, (b) ³⁵Cl⁻, (c) ⁴⁰Ca²⁺, (d) ¹⁴N.

Method: Protons = atomic number (Z). Neutrons = A − Z. Electrons = protons ± ion charge.

(a) ²³Na — Sodium: Z = 11. Protons = 11. Neutrons = 23 − 11 = 12. Electrons = 11 (neutral atom).

(b) ³⁵Cl⁻ — Chloride ion: Z = 17. Protons = 17. Neutrons = 35 − 17 = 18. Electrons = 17 + 1 = 18 (gained one electron, hence negative charge).

(c) ⁴⁰Ca²⁺ — Calcium ion: Z = 20. Protons = 20. Neutrons = 40 − 20 = 20. Electrons = 20 − 2 = 18 (lost two electrons, hence 2+ charge).

(d) ¹⁴N — Nitrogen: Z = 7. Protons = 7. Neutrons = 14 − 7 = 7. Electrons = 7 (neutral atom).

Example 2Identifying Isotopes

Carbon-12 and Carbon-14 are both isotopes of carbon. Explain how they are similar and how they differ.

Similarities: Both have 6 protons (atomic number = 6) and 6 electrons, making them both carbon atoms with identical chemical behaviour.

Differences: Carbon-12 has 6 neutrons (mass number 12); Carbon-14 has 8 neutrons (mass number 14). Carbon-14 is radioactive and is the basis of radiocarbon dating. Carbon-12 is stable and makes up ~99% of naturally occurring carbon.

Example 3Weighted Average Atomic Mass

Chlorine has two naturally occurring isotopes: ³⁵Cl (75.77% abundant, mass 34.97 u) and ³⁷Cl (24.23% abundant, mass 36.97 u). Calculate the average atomic mass of chlorine.

Method: Multiply each isotope’s mass by its fractional abundance, then sum.

Average mass = (0.7577 × 34.97) + (0.2423 × 36.97)
= 26.496 + 8.958
= 35.45 u

This matches the atomic mass of chlorine on the periodic table (35.45). The value falls between the two isotope masses, closer to ³⁵Cl because it is more abundant.

Practice Questions

QuizTest your understanding

Q1. What determines which element an atom belongs to?

A The number of neutrons in the nucleus
B The number of protons in the nucleus
C The number of electrons in the outer shell
D The total mass of the atom

Q2. An atom has atomic number 8 and mass number 18. How many neutrons does it have?

A 8
B 18
C 10
D 26

Q3. Which of the following correctly describes isotopes?

A Atoms of different elements with the same mass number
B Atoms of the same element with different numbers of electrons
C Atoms of the same element with different numbers of neutrons
D Atoms with the same mass number and different atomic numbers

Q4. A Ca²⁺ ion has atomic number 20 and mass number 40. How many electrons does it have?

A 20
B 22
C 18
D 40

Q5. Rutherford’s gold foil experiment led to the conclusion that:

A Electrons are embedded in a diffuse positive charge
B Atoms are solid, indivisible spheres
C The atom has a small, dense, positively charged nucleus surrounded by mostly empty space
D Electrons travel in fixed circular orbits at defined energy levels

Key Takeaways

Lesson 1.5 Summary

Atomic theory developed progressively: Dalton (solid spheres) → Thomson (plum pudding) → Rutherford (nuclear model) → Bohr (electron shells) → Quantum model.
An atom has a small, dense nucleus containing protons (+) and neutrons (neutral), surrounded by electrons (−) in shells.
Protons define the element (atomic number Z). Neutrons add mass. Electrons determine chemical behaviour.
Atomic number (Z) = number of protons. Mass number (A) = protons + neutrons. Neutrons = A − Z.
In a neutral atom, electrons = protons. Gaining electrons gives a negative ion (anion); losing electrons gives a positive ion (cation).
Isotopes are atoms of the same element with different numbers of neutrons — same chemical behaviour, different masses.
The atomic mass on the periodic table is a weighted average of all naturally occurring isotopes.

lesson 1.4 – Physical vs Chemical Changes

Neels Hattingh — Thu, 16 Apr 2026 04:43:14 +0000

Chemistry 1.4: Physical vs Chemical Changes

Chemistry · Lesson 1.4

Physical vs Chemical Changes

Properties, Reactions, Conservation of Mass & Evidence of Change

In this lesson

Overview Physical Changes Chemical Changes Evidence of Chemical Change Conservation of Mass Reaction Types Worked Examples Practice Takeaways

Overview

Every change that matter undergoes falls into one of two categories: physical or chemical. This distinction is one of the most fundamental in all of chemistry, and learning to classify changes correctly is an essential skill.

The key question is always the same: does the chemical identity of the substance change? If the answer is no, it is a physical change. If a new substance with different properties is produced, it is a chemical change.

Physical Change

Chemical identity is preserved
Only form, shape, or state changes
Generally reversible
No new substances are formed
Original substance can be recovered
Examples: melting, cutting, dissolving, boiling

Chemical Change

Chemical identity is altered
New substance(s) with new properties formed
Generally irreversible
Involves breaking and forming chemical bonds
Original substance cannot be simply recovered
Examples: burning, rusting, cooking, digestion

Physical Changes

A physical change alters the form or appearance of matter without changing its chemical composition. The substance before and after the change is the same substance — it is just in a different state, shape, or arrangement.

Physical changes include all phase changes (melting, freezing, boiling, condensation, sublimation), as well as cutting, bending, dissolving, and mixing. Because no chemical bonds are broken or formed between atoms, the original substance can always be recovered.

Dissolving — Physical or Chemical?

Dissolving is usually a physical change. When salt dissolves in water, the ions separate and disperse, but their chemical identity is unchanged. Evaporate the water and you recover the same salt. However, some substances dissolve by reacting chemically with water — in those cases, dissolving is a chemical change.

Example	What changes	What stays the same	Type
Ice melting	State (solid → liquid)	H₂O molecules	Physical
Cutting paper	Shape and size	Cellulose composition	Physical
Salt dissolving in water	Arrangement of ions	NaCl and H₂O identity	Physical
Gold being hammered flat	Shape	Gold atoms (Au)	Physical
Sugar dissolved in tea	Particle distribution	Sucrose molecule	Physical
Water boiling to steam	State (liquid → gas)	H₂O molecules	Physical

Chemical Changes

A chemical change — also called a chemical reaction — produces one or more new substances with different chemical properties. Atoms are rearranged as chemical bonds are broken and new ones are formed. The starting materials (reactants) are converted into different substances (products).

Chemical changes are typically difficult or impossible to reverse by simple physical means. You cannot un-burn wood or un-rust iron by just heating or cooling it.

Example	Reactants	Products formed	Type
Wood burning	Cellulose + O₂	CO₂ + H₂O + ash	Chemical
Iron rusting	Fe + O₂ + H₂O	Fe₂O₃ (iron oxide)	Chemical
Cooking an egg	Liquid proteins	Denatured proteins (solid)	Chemical
Baking soda + vinegar	NaHCO₃ + CH₃COOH	CO₂ + H₂O + NaCH₃COO	Chemical
Digesting food	Complex molecules	Simpler molecules (sugars, amino acids)	Chemical
Silver tarnishing	Ag + H₂S	Ag₂S (silver sulfide)	Chemical

Reactants & Products

In chemistry, we write chemical reactions as equations. The reactants appear on the left side of the arrow, and the products appear on the right. The arrow (→) means “reacts to form” or “yields.”

Reactants → Products

e.g. CH₄ + 2O₂ → CO₂ + 2H₂O

Evidence of Chemical Change

How do you know a chemical change has occurred? Since a new substance is formed, it will often have noticeably different properties from the reactants. There are six key indicators to look for — though none on their own is definitive proof. The true test is whether a new substance has formed.

Gas Production

Bubbles or fizzing indicate a gas is being produced. E.g. adding vinegar to baking soda releases CO₂ bubbles. Distinct from air bubbles produced by boiling.

Colour Change

A permanent change in colour (not from mixing coloured liquids). E.g. iron turning orange-brown as rust forms; a copper roof turning green (patina).

Precipitate Formation

A solid forms from two clear solutions being mixed. E.g. mixing lead nitrate and potassium iodide solutions produces a bright yellow precipitate of lead iodide.

Temperature Change

Heat is absorbed or released. Exothermic reactions feel hot (combustion, hand warmers); endothermic reactions feel cold (dissolving ammonium nitrate in water).

Light Emission

Some reactions produce light. Combustion reactions glow or flame; chemiluminescent reactions (glow sticks) produce cold light without significant heat.

Odour Change

A new or different smell often signals a new substance. E.g. meat cooking, milk souring, or the distinctive smell of sulfur dioxide when a match is struck.

Important Caveat

These indicators are evidence of a chemical change, not proof. A colour change might just be mixing two differently coloured solutions physically. A temperature change can occur during dissolving (a physical process). Always ask: has a new substance with new properties been formed?

Conservation of Mass

One of the most important laws in chemistry governs what happens to mass during a chemical reaction. French chemist Antoine Lavoisier established this principle experimentally in the late 18th century.

Law of Conservation of Mass

Mass of reactants = Mass of products

In any chemical reaction, matter is neither created nor destroyed — it is only rearranged. The total mass of the substances entering a reaction equals the total mass of the substances produced. Atoms are simply reorganised into new arrangements; none are lost or gained.

This law has a profound practical consequence: it is why we balance chemical equations. A balanced equation has the same number of each type of atom on both sides. We will explore equation balancing in detail in Lesson 1.8.

Why does burning wood seem to lose mass?

When wood burns, the solid residue (ash) weighs far less than the original wood. This seems to contradict conservation of mass — but it doesn’t. The “missing” mass has become gases: carbon dioxide and water vapour that escape into the air. If you could collect all the gases produced and weigh them, total mass would be conserved.

Reactants

The starting substances in a chemical reaction. They appear on the left side of a chemical equation, before the arrow.

Products

The new substances formed during a chemical reaction. They appear on the right side of the equation, after the arrow.

Exothermic Reaction

A reaction that releases energy (usually as heat) to the surroundings. The products have less energy than the reactants. E.g. combustion, rusting, respiration.

Endothermic Reaction

A reaction that absorbs energy from the surroundings. The products have more energy than the reactants. E.g. photosynthesis, dissolving ammonium nitrate.

Introduction to Reaction Types

Chemical reactions can be grouped into broad categories based on what happens to the reactants and products. You will study each of these in depth later in the curriculum — for now, learn to recognise the basic pattern of each.

Synthesis

Two or more substances combine to form a single new substance. Also called a combination reaction.

A + B → AB | 2H₂ + O₂ → 2H₂O
Decomposition

A single compound breaks down into two or more simpler substances. The reverse of synthesis.

AB → A + B | 2H₂O → 2H₂ + O₂
Combustion

A substance reacts rapidly with oxygen, releasing heat and light. Complete combustion of hydrocarbons produces CO₂ and H₂O.

fuel + O₂ → CO₂ + H₂O | CH₄ + 2O₂ → CO₂ + 2H₂O
Single Displacement

One element replaces another in a compound. Only occurs if the replacing element is more reactive than the one it displaces.

A + BC → AC + B | Zn + CuSO₄ → ZnSO₄ + Cu
Double Displacement

Two compounds exchange partners (ions) to form two new compounds. Often produces a precipitate, gas, or water.

AB + CD → AD + CB | NaCl + AgNO₃ → NaNO₃ + AgCl↓

Worked Examples

Example 1Classifying Changes

Classify each as physical or chemical: (a) a log being chopped into firewood, (b) the firewood burning, (c) chocolate melting, (d) milk souring, (e) a nail bending.

Key test: Is the chemical identity of the substance the same before and after?

(a) Chopping wood — Physical. The shape changes but the cellulose in the wood is chemically unchanged.

(b) Firewood burning — Chemical. The cellulose reacts with oxygen to form CO₂, H₂O, and ash — entirely new substances with different properties.

(c) Chocolate melting — Physical. The chocolate changes state from solid to liquid, but its chemical composition is unchanged. It will re-solidify on cooling.

(d) Milk souring — Chemical. Bacteria convert lactose (sugar) into lactic acid — a new substance. The change is irreversible; you cannot “un-sour” milk by cooling it.

(e) Nail bending — Physical. The iron atoms are rearranged but the iron remains iron (Fe). No new substance is formed.

Example 2Conservation of Mass

4.0 g of hydrogen reacts completely with 32.0 g of oxygen. What mass of water is produced?

Apply Conservation of Mass: Mass of reactants = mass of products.

Mass of H₂ + mass of O₂ = mass of H₂O
4.0 g + 32.0 g = 36.0 g of water produced

No matter is created or destroyed — all 36.0 g of reactants become 36.0 g of product.

Example 3Identifying Reaction Type

Identify the reaction type: (a) 2Mg + O₂ → 2MgO, (b) 2HgO → 2Hg + O₂, (c) C + O₂ → CO₂, (d) Fe + CuCl₂ → FeCl₂ + Cu.

(a) 2Mg + O₂ → 2MgO — Synthesis. Two substances (Mg and O₂) combine to form one product (MgO).

(b) 2HgO → 2Hg + O₂ — Decomposition. One compound (HgO) breaks down into two simpler substances (Hg and O₂).

(c) C + O₂ → CO₂ — Combustion (also synthesis). Carbon burns in oxygen to produce carbon dioxide with the release of energy.

(d) Fe + CuCl₂ → FeCl₂ + Cu — Single displacement. Iron (more reactive) displaces copper from copper chloride, forming iron chloride and copper metal.

Practice Questions

QuizTest your understanding

Q1. Which of the following is a chemical change?

A Water freezing into ice
B Glass being shattered
C Iron rusting in the presence of water
D Salt dissolving in water

Q2. The Law of Conservation of Mass states that in a chemical reaction:

A Energy is always released to the surroundings
B The total mass of reactants equals the total mass of products
C The number of molecules is conserved
D Mass increases slightly due to energy release

Q3. A student mixes two clear solutions and a yellow solid forms at the bottom of the flask. This is evidence of:

A A physical change, because the solutions are still liquid
B A chemical change — a precipitate (new solid substance) has formed
C A phase change from liquid to solid
D Dissolving in reverse

Q4. The reaction 2H₂O → 2H₂ + O₂ is best classified as:

A Synthesis
B Decomposition
C Combustion
D Single displacement

Q5. 12 g of carbon reacts completely with 32 g of oxygen to form carbon dioxide. What is the mass of CO₂ produced?

A 32 g
B 12 g
C 44 g
D 20 g

Key Takeaways

Lesson 1.4 Summary

A physical change alters form, shape, or state but not chemical identity. The original substance can be recovered.
A chemical change (reaction) produces one or more new substances with different properties. It is generally irreversible.
Evidence of chemical change: gas production, colour change, precipitate formation, temperature change, light emission, odour change.
The Law of Conservation of Mass: mass of reactants = mass of products. Atoms are rearranged, not created or destroyed.
Reactants appear before the arrow in a chemical equation; products appear after.
Exothermic reactions release energy; endothermic reactions absorb energy from surroundings.
The five basic reaction types are synthesis, decomposition, combustion, single displacement, and double displacement.

lesson 1.3 – Pure Substances & Mixtures

Neels Hattingh — Wed, 15 Apr 2026 19:48:17 +0000

Chemistry 1.3: Pure Substances & Mixtures

Chemistry · Lesson 1.3

Pure Substances & Mixtures

Elements, Compounds, Solutions & Separation Techniques

In this lesson

Classification of Matter Pure Substances Mixtures Comparison Separation Techniques Worked Examples Practice Takeaways

Classification of Matter

All matter can be systematically classified based on its composition. The first division is between pure substances — which have a fixed, uniform composition — and mixtures — which are combinations of two or more substances that are physically, but not chemically, combined.

This classification is the framework that underpins much of chemistry. Understanding where a substance falls in this scheme tells you how it can be separated, what properties it has, and how it will behave in reactions.

Classification Tree — Matter

Pure Substances

A pure substance has a fixed composition throughout — every sample of it is identical, with the same properties regardless of its source. Pure substances have sharp, definite melting and boiling points. They can only be separated into simpler substances through chemical means, not physical ones.

Pure substances are divided into two categories: elements and compounds.

Element

A pure substance composed of only one type of atom. Cannot be broken down into simpler substances by chemical means. There are 118 known elements, each with a unique symbol on the periodic table.

Compound

A pure substance formed when two or more different elements are chemically bonded together in a fixed ratio. Has properties completely different from the elements that make it up.

Elements vs Compounds — A Critical Distinction

Hydrogen (H₂) and oxygen (O₂) are both elements — colourless, flammable or reactive gases. When they chemically combine in a 2:1 ratio, they form water (H₂O) — a liquid at room temperature with completely different properties. The compound is not a simple mix of the two gases; it is an entirely new substance with its own unique identity.

Some elements exist as diatomic molecules — pairs of atoms bonded together — in their standard state. The common diatomic elements are: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂. Memorising these is important — when you write “oxygen” in a chemical equation, it appears as O₂, not O.

Law of Definite Proportions

A compound always contains the same elements in the same ratio by mass, regardless of how it was made or where it was found. Water from the ocean, a river, or a laboratory is always 88.9% oxygen and 11.1% hydrogen by mass. This law, established by Joseph Proust in 1799, is a defining feature of compounds.

Mixtures

A mixture is a combination of two or more substances that are physically combined — not chemically bonded. The components retain their individual properties. Mixtures have variable composition: you can have saltwater with a little salt or a lot of salt — both are still saltwater.

Crucially, the components of a mixture can always be separated by physical means — without any chemical reaction occurring.

Homogeneous Mixture

Uniform composition throughout — every sample from any point is identical. Also called a solution. The components are not visibly distinguishable. E.g. saltwater, vinegar, air, brass (copper + zinc).

Heterogeneous Mixture

Non-uniform composition — different parts of the mixture have different compositions. Components are visibly distinguishable. E.g. sand and water, oil and water, pizza, granite, blood.

Solutions: Solute & Solvent

In a solution (homogeneous mixture), the substance present in the larger amount is the solvent and the substance dissolved in it is the solute. In saltwater, water is the solvent and salt is the solute. The solvent does not have to be water — in many industrial and pharmaceutical applications, organic solvents like ethanol or acetone are used.

Colloids & Suspensions

Between homogeneous and heterogeneous mixtures sit two intermediate types. A colloid contains particles larger than dissolved molecules but too small to settle — milk, fog, and gelatin are colloids. A suspension contains larger particles that will eventually settle — muddy water and orange juice with pulp are suspensions.

Comparison: Elements, Compounds & Mixtures

Property	Element	Compound	Mixture
Composition	One type of atom only	Two or more elements in a fixed ratio	Two or more substances in any ratio
Chemical formula	Single symbol: Fe, O₂, Au	Fixed formula: H₂O, NaCl, CO₂	No fixed formula
Properties	Unique to that element	Entirely different from component elements	Each component retains its own properties
Melting/boiling point	Sharp, definite point	Sharp, definite point	Range, varies with composition
Separation method	Cannot be separated chemically	Only by chemical reaction	Physical methods (filtration, distillation, etc.)
Examples	Gold, nitrogen, sulfur, silicon	Water, salt, sugar, aspirin	Air, seawater, soil, bronze

Separation Techniques

Because the components of a mixture retain their individual physical properties, those properties can be used to separate them. The key is choosing the right technique based on the difference in properties between the components.

Filtration

Based on: particle size

A mixture is passed through filter paper or a porous material. Solid particles (residue) too large to pass through are retained; liquid (filtrate) passes through.

Example: separating sand from water

Distillation

Based on: boiling point

A liquid mixture is heated until one component vaporises, the vapour is cooled and condensed back into a liquid in a separate container. Used for liquids with sufficiently different boiling points.

Example: separating ethanol from water; producing pure water

Evaporation

Based on: volatility

The solvent is evaporated by heating, leaving the dissolved solute behind as a solid residue. Works when the solute is non-volatile (does not evaporate at the boiling point of the solvent).

Example: recovering salt from saltwater

Chromatography

Based on: solubility & affinity

Components in a mixture travel through a medium (paper, silica) at different rates depending on their affinity for the stationary phase vs the moving solvent. Separates mixtures into their components as distinct bands or spots.

Example: separating pigments in ink; identifying drugs

Crystallisation

Based on: solubility difference

A hot, concentrated solution is cooled slowly. The desired solute crystallises out (precipitates) as a pure solid while impurities remain dissolved. Produces very pure crystals.

Example: purifying copper sulfate; refining sugar

Magnetic Separation

Based on: magnetic properties

A magnet is used to attract and remove magnetic components from a non-magnetic mixture. Simple and effective when one component is magnetic.

Example: separating iron filings from sand

Fractional Distillation

When a mixture contains several liquids with similar but different boiling points, fractional distillation is used — a tall column allows repeated vaporisation and condensation, separating components into “fractions.” This is how crude oil is refined into petrol, diesel, kerosene, and other products.

Worked Examples

Example 1Classifying Substances

Classify each as an element, compound, or mixture: (a) silver (Ag), (b) carbon dioxide (CO₂), (c) stainless steel, (d) baking soda (NaHCO₃), (e) orange juice.

(a) Silver (Ag) — Element. A single type of atom; found on the periodic table with symbol Ag.

(b) Carbon dioxide (CO₂) — Compound. Carbon and oxygen chemically bonded in a fixed 1:2 ratio. Has a definite formula.

(c) Stainless steel — Mixture (homogeneous). An alloy — a solid solution of iron, chromium, and other metals. Variable composition; no fixed formula.

(d) Baking soda (NaHCO₃) — Compound. Sodium, hydrogen, carbon, and oxygen bonded in a fixed ratio. Has a definite chemical formula.

(e) Orange juice — Mixture (heterogeneous if it contains pulp; approximately homogeneous if filtered). Contains water, sugars, acids, vitamins in variable amounts.

Example 2Choosing a Separation Technique

Suggest a suitable separation technique for each mixture and explain why: (a) salt and water, (b) iron filings and sulfur powder, (c) alcohol and water, (d) a mixture of coloured dyes in solution.

(a) Salt and water — Evaporation. Water evaporates when heated, leaving salt as a solid residue. Salt does not evaporate at the boiling point of water.

(b) Iron filings and sulfur — Magnetic separation. A magnet attracts the iron filings, while the non-magnetic sulfur is left behind. Quick and effective.

(c) Alcohol and water — Distillation. Ethanol boils at 78°C and water at 100°C. Heating the mixture causes ethanol to vaporise first; it is condensed and collected separately.

(d) Coloured dyes — Chromatography. Different dye molecules travel at different speeds through a medium, separating into distinct bands that can be identified individually.

Practice Questions

QuizTest your understanding

Q1. Which of the following is a pure substance?

A Seawater
B Granite
C Carbon dioxide (CO₂)
D Bronze (copper and tin alloy)

Q2. A compound differs from a mixture in that a compound:

A Can be separated by physical means
B Has variable composition depending on how it was made
C Has a fixed composition and its components are chemically bonded
D Always exists as a liquid at room temperature

Q3. Which separation technique would best separate a mixture of sand (insoluble solid) and water?

A Distillation
B Filtration
C Chromatography
D Crystallisation

Q4. Air is classified as a homogeneous mixture because:

A It is made of a single element (nitrogen)
B Its components are chemically bonded in a fixed ratio
C It has uniform composition throughout and its components retain individual properties
D It can only be separated by chemical means

Q5. The Law of Definite Proportions states that:

A Elements always combine in whole number ratios by volume
B A compound always contains the same elements in the same mass ratio, regardless of its source
C The mass of products in a reaction equals the mass of reactants
D Mixtures can contain elements in any ratio

Key Takeaways

Lesson 1.3 Summary

All matter is classified as either a pure substance (fixed composition) or a mixture (variable composition).
Pure substances are either elements (one type of atom) or compounds (two or more elements chemically bonded in a fixed ratio).
Compounds have completely different properties from the elements that form them — water and hydrogen/oxygen are nothing alike.
The Law of Definite Proportions: a compound always has the same composition by mass, regardless of its origin.
Mixtures are homogeneous (uniform, e.g. solutions) or heterogeneous (non-uniform, e.g. sand in water).
The components of a mixture retain their individual properties and can be separated by physical methods.
Separation techniques exploit differences in physical properties: filtration (size), distillation (boiling point), evaporation (volatility), chromatography (affinity), crystallisation (solubility), and magnetic separation (magnetic properties).

lesson 1.2 – States of Matter

Neels Hattingh — Wed, 15 Apr 2026 19:46:41 +0000

Chemistry 1.2: States of Matter

Chemistry · Lesson 1.2

States of Matter

Solids, Liquids, Gases, Plasma & Phase Changes

In this lesson

The Four States Kinetic Theory Phase Changes Heating Curve Temperature & Pressure Worked Examples Practice Takeaways

The Four States of Matter

Matter can exist in four distinct states — sometimes called phases. The state a substance is in depends on two factors: temperature and pressure. These factors determine how much energy the particles have and how close together they are.

In everyday chemistry you will mainly encounter solids, liquids, and gases. Plasma is the fourth state and the most common in the universe, though rarely encountered in a laboratory setting.

Solid

Definite shape · Definite volume

Particles are tightly packed in a regular, ordered arrangement. They vibrate in fixed positions but do not move past each other. Solids are incompressible and maintain their shape.

High density; particles close together
Very low compressibility
No flow — rigid structure
Examples: ice, iron, salt, diamond

Liquid

Definite volume · Variable shape

Particles are close together but not in a fixed arrangement. They can slide past each other, giving liquids the ability to flow and conform to any container shape.

High density; nearly as dense as solids
Very low compressibility
Flows freely; takes container shape
Examples: water, mercury, ethanol, oil

Gas

Variable shape · Variable volume

Particles are far apart and move rapidly in random directions. Gases have no fixed shape or volume — they expand to fill any container. They are highly compressible.

Very low density; particles far apart
Highly compressible
Fills any container completely
Examples: oxygen, nitrogen, steam, CO₂

Plasma

Ionised gas · Extreme conditions

At extremely high temperatures, electrons are stripped from atoms, creating a soup of ions and free electrons. Plasma behaves differently from gas and responds to magnetic fields.

Most common state in the universe
Found in stars, lightning, auroras
Used in neon signs, plasma TVs
Requires temperatures of thousands of °C

Kinetic Molecular Theory

The Kinetic Molecular Theory (KMT) is the model that explains the behaviour of matter in terms of particles in constant motion. It was developed to explain the properties of gases, but its principles extend to solids and liquids.

Core Postulates

All matter is made of tiny particles (atoms or molecules) that are in constant, random motion. The average kinetic energy of particles is directly proportional to temperature. Particles collide with each other and with container walls — these collisions are the origin of pressure in a gas.

Property	Solid	Liquid	Gas
Particle arrangement	Regular, ordered lattice	Close, but disordered	Random, widely spaced
Particle motion	Vibrate in fixed positions	Slide and flow past each other	Move rapidly in all directions
Intermolecular forces	Very strong — hold structure rigid	Moderate — allow flow	Negligible — particles barely interact
Compressibility	Almost none	Almost none	High — large empty space between particles
Energy level	Lowest	Intermediate	Highest (of the three common states)

Temperature is a measure of the average kinetic energy of particles in a substance. This is a crucial distinction: temperature measures the average, not the total. Two objects can have the same temperature but different total thermal energies if they have different masses or compositions.

Phase Changes

A phase change is the transition of matter from one state to another. Phase changes are physical changes — the chemical identity of the substance does not change, only the arrangement and energy of its particles.

All phase changes involve the absorption or release of energy. The temperature remains constant during a phase change, even as energy is being added or removed — all that energy is being used to break or form intermolecular forces, not to speed up particles.

Phase Change Diagram — Names & Directions

Solid

e.g. ice

Melting

⇄

Freezing

Liquid

e.g. water

Vaporisation

⇄

Condensation

Gas

e.g. steam

Melting

Solid → Liquid. Occurs at the melting point. Requires energy input (endothermic) to overcome the rigid lattice structure.

Freezing

Liquid → Solid. Occurs at the freezing point (same temperature as melting point). Energy is released as intermolecular bonds form.

Vaporisation

Liquid → Gas. Can occur as evaporation (surface only, below boiling point) or boiling (throughout liquid, at boiling point).

Condensation

Gas → Liquid. Energy is released as gas particles slow down and intermolecular forces pull them together. E.g. dew forming on glass.

Sublimation

Solid → Gas directly, without passing through the liquid state. E.g. dry ice (solid CO₂) sublimes at room temperature and pressure.

Deposition

Gas → Solid directly. E.g. frost forming when water vapour deposits onto a cold surface without first becoming liquid.

Endothermic vs Exothermic Phase Changes

Endothermic (absorb energy): melting, vaporisation, sublimation — going from lower to higher energy states.

Exothermic (release energy): freezing, condensation, deposition — going from higher to lower energy states.

The Heating Curve

A heating curve shows how the temperature of a substance changes as heat is continuously added. It reveals something important: temperature does not rise during phase changes. The energy added goes into breaking intermolecular forces instead of increasing kinetic energy.

Heating Curve — Water (H₂O), starting from ice below 0°C

Notice the two flat sections (plateaus) on the curve. These are the phase changes. During melting (at 0°C) and boiling (at 100°C for water at sea level), the temperature stays constant while all the added energy goes into overcoming intermolecular forces.

Latent Heat

The energy required to complete a phase change without changing temperature is called latent heat. The latent heat of fusion applies to melting/freezing; the latent heat of vaporisation applies to boiling/condensation. Water has an unusually high latent heat of vaporisation — which is why sweating cools you so effectively.

Temperature & Pressure Effects

The state a substance adopts depends on both temperature and pressure. Increasing temperature gives particles more energy, pushing transitions toward the gas phase. Increasing pressure compresses particles, favouring the liquid or solid state.

Boiling Point & Altitude

Water boils at 100°C at sea level (1 atm pressure). At higher altitudes, atmospheric pressure is lower, so water boils at a lower temperature. On top of Mount Everest, water boils at around 70°C — which is why food takes longer to cook there.

Melting Point vs Freezing Point

For a pure substance, the melting point and the freezing point are the same temperature — the difference is only the direction of the phase change. Water melts at 0°C and freezes at 0°C. Impurities (like salt dissolved in water) lower the freezing point — the reason roads are salted in winter.

Worked Examples

Example 1Identifying Phase Changes

Name the phase change in each: (a) liquid water forming on the outside of a cold drink, (b) mothballs gradually disappearing, (c) lava cooling to form rock, (d) water evaporating from a puddle.

(a) Condensation — water vapour in the air (gas) transitions to liquid water on the cold surface.

(b) Sublimation — the solid naphthalene in mothballs transitions directly to gas without becoming liquid.

(c) Freezing (solidification) — the liquid lava loses heat and transitions to a solid as it cools.

(d) Evaporation — a form of vaporisation occurring at the liquid surface, below the boiling point, as faster-moving molecules escape into the gas phase.

Example 2Interpreting a Heating Curve

On the heating curve for water, explain why the temperature stays at 0°C for a period of time even though heat is continuously being added.

Answer: During the melting phase change, the energy being added is not increasing the kinetic energy of the particles — instead, it is being used to break the intermolecular hydrogen bonds that hold the water molecules in the solid lattice structure. Until all those bonds are broken (i.e. all the ice has melted), the temperature cannot rise. This energy is called the latent heat of fusion.

Practice Questions

QuizTest your understanding

Q1. Which of the following correctly describes the particle arrangement in a liquid?

A Particles are in a regular, ordered lattice and vibrate in fixed positions
B Particles are close together but can slide past each other
C Particles are far apart and move rapidly in random directions
D Particles are ionised and respond to magnetic fields

Q2. What happens to the temperature of water during the boiling phase change?

A It continues to rise steadily as heat is added
B It drops temporarily before rising again
C It remains constant while the heat breaks intermolecular forces
D It rises rapidly because gas particles move faster than liquid particles

Q3. Dry ice (solid CO₂) transitions directly from solid to gas. This phase change is called:

A Evaporation
B Condensation
C Sublimation
D Deposition

Q4. Which of the following phase changes is exothermic (releases energy)?

A Melting
B Sublimation
C Vaporisation
D Condensation

Q5. Water boils at a lower temperature at high altitude because:

A The air is colder at altitude, which lowers the boiling point
B Atmospheric pressure is lower, so less energy is needed for molecules to escape
C Water molecules are lighter at altitude due to reduced gravity
D High altitude reduces the latent heat of vaporisation of water

Key Takeaways

Lesson 1.2 Summary

Matter exists in four states: solid (fixed shape and volume), liquid (fixed volume, variable shape), gas (no fixed shape or volume), and plasma (ionised gas at extreme temperatures).
The Kinetic Molecular Theory explains the properties of matter in terms of constantly moving particles whose average kinetic energy equals temperature.
Phase changes are physical changes — the substance’s chemical identity remains the same, only the arrangement and energy of particles changes.
The six phase changes: melting, freezing, vaporisation, condensation, sublimation, and deposition.
Temperature remains constant during a phase change — all added energy goes into breaking or forming intermolecular forces (latent heat).
A heating curve shows temperature vs heat added, with flat plateaus at the melting and boiling points.
Boiling point decreases with lower atmospheric pressure — which is why water boils below 100°C at high altitude.

Lesson 1.1 – What is Chemistry

Neels Hattingh — Wed, 15 Apr 2026 19:43:09 +0000

Chemistry 1.1: What is Chemistry?

Chemistry · Lesson 1.1

What is Chemistry?

Matter, Energy & the Science of Everything

In this lesson

Defining Chemistry Matter Energy Branches Scientific Method Lab Safety Worked Examples Practice Takeaways

Defining Chemistry

Chemistry is the branch of science that studies the composition, structure, properties, and transformations of matter. In practical terms, it asks: what is everything made of, and what happens when things interact?

Chemistry connects to physics at one end and flows into biology at the other, becoming the molecular language of life. This is why it is often called the central science.

Key Idea

Chemistry is the science of matter and the changes it undergoes. From the food you digest to the steel in a bridge, virtually every substance and process you encounter involves chemistry.

Chemistry

The scientific study of the composition, structure, properties, and reactions of matter — especially at the atomic and molecular scale.

Matter

Anything that has mass and takes up space. All physical substances — solids, liquids, gases — are matter.

Substance

Matter with a definite, uniform composition throughout. Substances are either pure elements or compounds.

Property

A characteristic that describes matter. Can be physical (colour, density) or chemical (flammability, reactivity).

Matter

Matter is defined by two properties: it has mass (resists being moved) and it has volume (occupies space). Light and sound are not matter — they carry energy but have no mass.

Matter exists in different states, depending on particle arrangement and energy content.

Solid

Fixed shape and volume. Particles packed tightly in a regular arrangement, vibrating in place.

Liquid

Fixed volume, variable shape. Particles close together but able to slide past each other.

Gas

No fixed shape or volume. Particles move freely at high speed, spreading to fill any container.

Plasma

Super-heated ionised gas. Found in stars, lightning, and neon signs. Most common state in the universe.

Element

A pure substance made of only one kind of atom. Cannot be broken down chemically. E.g. gold (Au), oxygen (O).

Compound

A pure substance formed when two or more elements chemically bond in a fixed ratio. E.g. water (H₂O), salt (NaCl).

Homogeneous Mixture

Uniform composition throughout. Also called a solution. E.g. saltwater, air, steel.

Heterogeneous Mixture

Visibly different components, non-uniform composition. E.g. sand and water, granite, salad.

Physical vs Chemical Properties

Physical properties can be observed without changing chemical identity: colour, melting point, density.

Chemical properties describe how a substance reacts: iron rusts in oxygen; wood burns in air. Observable only during a chemical change.

Energy

Every chemical reaction involves an exchange of energy. Reactions can release energy (burning wood) or absorb it (dissolving ammonium nitrate in water produces a cold sensation). Energy is the capacity to do work or produce heat.

Kinetic Energy

Energy of motion. Atoms and molecules are always moving. Temperature is a measure of average particle kinetic energy.

Potential Energy

Stored energy based on position or composition. Chemical potential energy is stored in bonds — released when fuels combust.

Thermal Energy (Heat)

Total kinetic energy of all particles in a substance. Flows from hot objects to cold ones — governs many chemical reactions.

Chemical Energy

Energy stored in chemical bonds. Breaking and forming bonds exchanges energy with the surroundings — exothermic or endothermic.

Law of Conservation of Energy

Energy cannot be created or destroyed — only transformed. When petrol burns, chemical energy converts to heat and light. The total energy in the universe is unchanged.

Branches of Chemistry

Chemistry is a vast discipline. As you progress through this curriculum you will encounter each of these major branches.

Organic
The chemistry of carbon-containing compounds. Includes molecules of life — proteins, DNA, carbohydrates — and pharmaceuticals, plastics, and fuels.
Inorganic
Chemistry of elements and compounds not based on carbon. Covers metals, minerals, salts, and transition metals.
Physical
Applies physics to chemical problems. Studies thermodynamics, kinetics, and quantum mechanics of matter.
Analytical
Develops methods to identify and quantify substances using spectroscopy, chromatography, and titration.
Biochemistry
Chemistry of living organisms — metabolic pathways, enzymes, genetic information, and the molecular basis of life.
Nuclear
Concerned with atomic nuclei — radioactive decay, fission, fusion, and their applications in medicine and energy.

The Scientific Method

Chemistry is an experimental science. Knowledge is built through systematic observation and testing, not speculation. The scientific method is the framework that guides this process.

Observation

Notice a phenomenon. Gather data using senses or instruments — carefully and without bias.

Question

Formulate a specific, testable question based on your observations.

Hypothesis

Propose a possible explanation. Must be falsifiable — possible to prove wrong through testing.

Experiment

Design and conduct a controlled test. Change one variable (independent), measure another (dependent), and hold all others constant (controlled).

Analysis

Record and interpret results. Use tables, graphs, and calculations to find patterns in the data.

Conclusion

Does the data support or refute the hypothesis? Communicate findings. Science advances through repeated testing and peer review.

Scientific Law

Describes an observed pattern in nature, usually mathematically. Describes what happens, not why. E.g. Law of Conservation of Mass.

Scientific Theory

A well-tested explanation for a broad set of observations, supported by overwhelming evidence. Explains why. E.g. Atomic Theory.

Note on “Theory”

In everyday language, “theory” means a guess. In science, a theory is the highest standard of explanation — one that has survived rigorous testing across vast ranges of evidence. Scientific theories are never mere guesses.

Laboratory Safety

Before entering any laboratory, you must understand the rules that protect people from harm. Chemical reactions can be unpredictable, and many substances are corrosive, flammable, or toxic.

Wear PPE at all times. Safety goggles, lab coat, and closed-toe shoes are non-negotiable when working with chemicals.
Know the location of safety equipment. Fire extinguisher, eyewash station, emergency shower, and first aid kit — before you begin.
Never smell chemicals directly. Use the wafting technique — fan vapours gently toward your nose from a distance.
Read every label before use. Identify hazard symbols, handling instructions, and first aid measures.
Handle glassware carefully. Never use cracked glassware. Use heat-resistant glass when heating.
Dispose of chemicals properly. Never pour substances down a drain without checking the protocol.
Tie back hair and loose clothing. Both can catch fire or dip into chemicals unexpectedly.
Report all accidents immediately. Even minor incidents can escalate if ignored.
Never work alone. Always have a partner or supervisor present during experiments.

Worked Examples

Example 1Classifying Matter

Classify each: (a) copper wire, (b) a cup of coffee, (c) table salt, (d) muddy river water.

Approach: Is it a pure substance or a mixture? If pure — element or compound? If a mixture — homogeneous or heterogeneous?

(a) Copper wire — Pure substance · Element. Copper (Cu) is a single element on the periodic table.

(b) Cup of coffee — Homogeneous mixture (solution). Water, caffeine, oils, and dissolved compounds uniformly distributed.

(c) Table salt — Pure substance · Compound. Sodium chloride (NaCl) — sodium and chlorine bonded in a fixed 1:1 ratio.

(d) Muddy river water — Heterogeneous mixture. Soil particles are visibly distinct from the water and unevenly distributed.

Example 2Physical vs Chemical Change

Physical or chemical? (a) Melting ice, (b) burning paper, (c) dissolving sugar in water, (d) iron rusting.

Key test: Does the chemical identity of the substance change?

(a) Melting ice — Physical. H₂O changes state from solid to liquid but remains H₂O.

(b) Burning paper — Chemical. Cellulose reacts with oxygen to produce CO₂, water vapour, and ash — entirely new substances.

(c) Dissolving sugar — Physical. Sugar molecules disperse but remain chemically unchanged. Evaporate the water and you recover the sugar.

(d) Iron rusting — Chemical. Iron reacts with oxygen and water to form iron oxide (Fe₂O₃) — a different compound with different properties.

Practice Questions

QuizTest your understanding

Q1. Which of the following is a chemical property of iron?

A Its density is 7.87 g/cm³
B It is a shiny grey solid at room temperature
C It reacts with oxygen to form rust
D It melts at 1538°C

Q2. Air is best described as a:

A Pure element
B Compound
C Homogeneous mixture
D Heterogeneous mixture

Q3. When ice melts into liquid water, this is best described as:

A A chemical change because the state changes
B A physical change because the chemical identity is unchanged
C A chemical change because energy is absorbed
D Neither physical nor chemical

Q4. Matter is defined as anything that:

A Carries energy and travels at the speed of light
B Exists only as a solid or liquid
C Has mass and occupies space
D Is composed exclusively of carbon atoms

Q5. A scientific theory is best described as:

A An educated guess about how something works
B A pattern observed repeatedly in nature
C A well-tested explanation supported by extensive evidence
D A law that has been proven beyond all doubt

Key Takeaways

Lesson 1.1 Summary

Chemistry is the science of matter and the changes it undergoes — called “the central science” because it bridges physics and biology.
Matter is anything with mass and volume. It exists in four states: solid, liquid, gas, and plasma.
Matter is classified as pure substances (elements or compounds) or mixtures (homogeneous or heterogeneous).
Physical properties are observed without changing chemical identity; chemical properties describe a substance’s reactivity.
Energy exists as kinetic or potential. Chemical reactions always involve an exchange of energy with the surroundings.
The scientific method — observe, question, hypothesise, experiment, analyse, conclude — is the foundation of all scientific knowledge.
A scientific theory is a well-tested, evidence-supported explanation — far more than an everyday “guess.”
Laboratory safety is non-negotiable: PPE, hazard awareness, and correct procedure at all times.