Key Definitions
- Atom
- The smallest part of an element that can exist.
- Element
- A substance made of only one type of atom.
- Compound
- A substance made of two or more elements chemically combined in fixed proportions.
- Mixture
- A combination of two or more substances that are not chemically joined together.
- Isotopes
- Atoms of the same element with the same number of protons but different numbers of neutrons.
- Relative Atomic Mass (Ar)
- The weighted average mass of an atom of an element compared with 1/12th of the mass of a carbon-12 atom.
- Empirical Formula
- The simplest whole-number ratio of atoms of each element in a compound.
- Electrolysis
- The decomposition of an electrolyte by an electric current.
States of Matter
Solids
Particles packed tightly in a fixed, regular pattern (lattice). Strong forces hold them in place. Particles vibrate on the spot. Fixed shape and volume; cannot be compressed.
Liquids
Particles close together but arranged randomly. Weaker forces than solids. Particles can move and slide past each other. Fixed volume but take the shape of their container.
Gases
Particles very far apart, arranged randomly. Very weak forces. Particles move quickly and randomly. No fixed shape or volume; easily compressed.
Changes of State
When a substance changes state, the particles gain or lose energy. The chemical bonds are not broken - only the forces between particles change.
- Melting: Solid → Liquid (particles gain energy, overcome some forces, start to move)
- Boiling/Evaporating: Liquid → Gas (particles gain enough energy to overcome all intermolecular forces)
- Freezing: Liquid → Solid (particles lose energy, forces pull them into fixed positions)
- Condensing: Gas → Liquid (particles lose energy, forces bring them closer)
- Sublimation: Solid → Gas directly (e.g. Dry ice, iodine)
State Symbols
In equations, state symbols show the physical state: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).
Limitations of the Particle Model Extended
The simple particle model is useful for explaining states of matter and changes of state, but it has limitations:
- It assumes particles are solid, inelastic spheres; in reality, atoms have complex internal structures with electron clouds.
- It ignores the forces between particles; in reality, intermolecular forces (such as van der Waals forces and hydrogen bonds) play a crucial role in determining properties.
- It ignores the spaces between particles; in reality, the distance between particles varies significantly and affects properties like compressibility.
- It does not show the relative sizes of particles in different states: particles do not actually change size when a substance changes state.
Diffusion & Dilution Experiments
Diffusion is the net movement of particles from an area of higher concentration to an area of lower concentration, down a concentration gradient. It occurs because particles move randomly and collide with each other. This is a passive process that does not require external energy.
Experiment 1: Diffusion of Bromine Gas
A gas jar containing red-brown bromine gas is placed underneath an inverted gas jar containing air, separated by a glass cover. When the cover is removed, the red-brown colour slowly spreads upwards until both jars are a uniform light brown.
Explanation: Bromine and air particles move randomly and collide. Even though bromine is denser than air, the random motion of particles causes them to mix evenly over time.
Experiment 2: Ammonia and Hydrogen Chloride Diffusion
This classic experiment demonstrates that different gases diffuse at different rates:
- A long glass tube has cotton wool soaked in concentrated ammonia solution at one end (releasing NH3 gas) and cotton wool soaked in concentrated hydrochloric acid at the other end (releasing HCl gas).
- After a few minutes, a white ring of solid ammonium chloride (NH4Cl) forms inside the tube.
- Key Observation: The white ring forms closer to the hydrochloric acid end of the tube.
- Equation: NH3(g) + HCl(g) → NH4Cl(s)
- Explanation: Ammonia particles have a lower relative molecular mass (Mr = 17) than hydrogen chloride particles (Mr = 36.5). Therefore, ammonia particles travel faster and diffuse more quickly through the air, meeting the slower HCl particles closer to the acid end.
Experiment 3: Dilution of Potassium Manganate(VII)
When a crystal of potassium manganate(VII) is placed in a beaker of water, the purple colour slowly spreads out from the crystal until the entire solution becomes purple. If more water is added (dilution), the purple colour becomes lighter.
Explanation: Water particles and potassium manganate(VII) particles move randomly, causing the dissolved particles to diffuse throughout the liquid. Dilution spreads the particles further apart, decreasing their concentration.
Solubility & Solubility Curves Extended
In chemistry, we use specific terms to describe how substances dissolve to form mixtures:
- Solute: The substance that dissolves in a liquid (e.g., salt, sugar).
- Solvent: The liquid in which the solute dissolves (e.g., water, ethanol).
- Solution: The mixture formed when a solute has dissolved in a solvent.
- Saturated Solution: A solution that contains the maximum amount of dissolved solute at a specific temperature. Any further solute added will not dissolve.
Definition of Solubility
Solubility is defined as the maximum mass of solute (in grams) that can dissolve in 100 g of solvent at a specific temperature.
For example, if the solubility of sodium chloride in water is 36 g/100 g H₂O at 20°C, it means that a maximum of 36 grams of NaCl will dissolve in 100 grams of water at 20°C.
Core Practical 1.7C: Investigate the Solubility of a Solid in Water
This experiment explains how to determine the solubility of a salt (e.g., ammonium chloride, NH₄Cl) at a specific temperature.
Procedure:
- Set up a water bath at a specific temperature (e.g., 40°C) and place a boiling tube containing water and excess ammonium chloride into the water bath. Stir the mixture until no more salt dissolves to ensure the solution is saturated.
- Weigh an empty evaporating basin and record its mass.
- Carefully decant (pour off) some of the clear saturated solution into the evaporating basin, ensuring that no undissolved solid is transferred.
- Weigh the evaporating basin containing the solution and record the mass.
- Heat the evaporating basin gently using a Bunsen burner to evaporate the water.
- Once the water has mostly evaporated, heat the basin gently to avoid spitting (where the solid jumps out of the basin).
- Allow the basin to cool, then weigh it. Re-heat, cool, and re-weigh the basin until a constant mass is obtained. This ensures that all the water has been completely evaporated.
Calculations:
From the recorded masses, we can determine the solubility:
Mass of saturated solution = (Mass of basin + solution) - (Mass of empty basin)Mass of dry residue (solute) = (Mass of basin + dry residue) - (Mass of empty basin)Mass of water evaporated (solvent) = (Mass of saturated solution) - (Mass of dry residue)
Analysis of Errors:
- Spitting of solid: If the solution is heated too strongly, the solid can "spit" out of the basin. This decreases the measured mass of the dry residue, leading to an underestimation of the solubility.
- Incomplete evaporation: If the solid is not heated to a constant mass, water remains in the residue. This increases the measured mass of the residue, leading to an overestimation of the solubility.
Solubility Curves
A solubility curve shows how the solubility of different solutes changes as the temperature of the solvent changes. For most solids, solubility increases with temperature because the water molecules have more kinetic energy to break solute bonds.
Solubility curves for potassium nitrate (solubility increases steeply), sodium chloride (solubility increases very slightly), and cerium(III) sulfate (solubility decreases as temperature rises).
Cooling & Precipitation Calculations
If a saturated solution is cooled, the solubility decreases, and some of the dissolved solute precipitates (crystallises) out of the solution. To calculate the mass of crystals formed, follow this method:
- Find the solubility of the salt at the higher temperature and calculate the mass of solute dissolved in the given mass of water.
- Find the solubility of the salt at the lower temperature and calculate the mass of solute that remains dissolved in the same mass of water.
- Subtract the mass of solute remaining dissolved from the mass originally dissolved.
Worked Example
A saturated solution of potassium nitrate (KNO₃) in 50 g of water is cooled from 60°C to 20°C. Using the solubility curve data below, calculate the mass of crystals that will precipitate out of the solution:
- Solubility of KNO₃ at 60°C = 110 g / 100 g H₂O
- Solubility of KNO₃ at 20°C = 32 g / 100 g H₂O
Step 1: Calculate mass dissolved at 60°C:
In 100 g water, 110 g KNO₃ dissolves.
In 50 g water: 110 × (50 ÷ 100) = 55 g KNO₃ dissolved.
Step 2: Calculate mass dissolved at 20°C:
In 100 g water, 32 g KNO₃ dissolves.
In 50 g water: 32 × (50 ÷ 100) = 16 g KNO₃ remains dissolved.
Step 3: Subtract to find the mass of crystals formed:
Mass of crystals = 55 g - 16 g = 39 g
The mass of potassium nitrate crystals precipitated is 39 g.
Elements, Compounds & Mixtures
What is an Atom?
An atom is the smallest part of an element that can exist. Think of it as the ultimate LEGO brick. Everything in the universe - the air you breathe, the water you drink, and even you - is made of atoms.
Elements
An element is a substance made of only one type of atom. There are about 118 known elements, and each has a unique atomic number (the number of protons in its nucleus). All known elements are catalogued in the periodic table. Examples include Hydrogen (H), Oxygen (O), Carbon (C), and Iron (Fe).
Compounds
A compound is a substance formed when two or more elements are chemically bonded together. The atoms in a compound are held together by chemical bonds (ionic or covalent), and the compound has different properties from the individual elements. A compound can only be separated into its elements by chemical reactions, not by physical methods.
In this example, hydrogen and chlorine (both elements) react to form hydrogen chloride (a compound).
Chemical Equations
Chemical reactions can be represented using word equations and balanced symbol equations. A balanced equation has the same number of each type of atom on both sides - this reflects the law of conservation of mass.
Writing Word Equations
A word equation names the reactants (what goes in) and the products (what comes out), separated by an arrow.
Balancing Symbol Equations
In a balanced symbol equation, the number of atoms of each element must be the same on both sides. You balance by placing numbers in front of formulae - never change the small (subscript) numbers.
Balance: Mg + O₂ → MgO
Step 1: Count atoms: Left has 1 Mg and 2 O. Right has 1 Mg and 1 O - not balanced.
Step 2: Put a 2 in front of MgO: Mg + O₂ → 2MgO. Now right has 2 Mg and 2 O.
Step 3: Put a 2 in front of Mg: 2Mg + O₂ → 2MgO. Both sides: 2 Mg and 2 O ✓
Balanced equation: 2Mg + O₂ → 2MgO
Mixtures
A mixture consists of two or more substances that are not chemically bonded together. The substances retain their individual properties and can be separated by physical methods.
Key Properties of Mixtures
- The components are not chemically combined.
- They retain their original properties.
- They can be separated by physical processes (filtration, distillation, etc.).
- No chemical reaction is needed to separate them.
Examples include air (a mixture of gases), salt water, and alloys like steel.
Separation Techniques
Rf Values
Each substance in a chromatogram can be identified by its Rf value - a ratio that is unique to each substance under specific conditions (same solvent, same temperature).
Calculating an Rf value
Given: A spot has moved 4.2 cm and the solvent front has moved 6.0 cm.
Rf = 4.2 ÷ 6.0 = 0.70
This value can then be compared to known Rf values to identify the substance.
Testing for Purity
Chromatography can determine whether a substance is pure or a mixture:
- A pure substance produces a single spot on the chromatogram.
- A mixture produces two or more spots.
Atomic Structure
Subatomic Particles
Atoms are made up of three types of subatomic particles, each with specific properties:
- Proton: Found in the nucleus. Relative mass = 1, Relative charge = +1.
- Neutron: Found in the nucleus. Relative mass = 1, Relative charge = 0.
- Electron: Found in shells orbiting the nucleus. Relative mass ≈ 1/2000 (negligible), Relative charge = −1.
How many neutrons does an atom of aluminium-27 have?
Step 1: Aluminium has atomic number 13 (from periodic table), so it has 13 protons.
Step 2: Neutrons = Mass number − Atomic number = 27 − 13 = 14 neutrons
Atomic Size & Mass Distribution
The Scale of an Atom
Atoms are unimaginably small, and the nucleus is even smaller in comparison.
- The atomic radius is approximately 1 × 10⁻¹⁰ metres.
- The radius of the nucleus is about 1 × 10⁻¹⁴ metres.
This means the nucleus is roughly 10,000 times smaller than the entire atom. If an atom were the size of a football stadium, the nucleus would be the size of a pea placed in the centre.
Distribution of Mass
Despite its tiny size, the nucleus contains nearly all of the atom's mass. This is because protons and neutrons (found in the nucleus) each have a relative mass of 1. Electrons have a negligible mass (approximately 1/2000th of a proton or neutron). Therefore, when calculating the mass of an atom, the mass of the electrons is considered to be zero.
Isotopes & Relative Atomic Mass
Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons. Because isotopes have the same number of protons, they also have the same number of electrons - so they have identical chemical properties.
Understanding Isotopes
The key difference between isotopes is their mass number. Let's look at carbon as an example - all carbon atoms have 6 protons:
- Carbon-12: 6 protons + 6 neutrons (Mass number = 12)
- Carbon-13: 6 protons + 7 neutrons (Mass number = 13)
- Carbon-14: 6 protons + 8 neutrons (Mass number = 14)
Relative Atomic Mass (Ar)
The relative atomic mass is the weighted mean mass of an atom of an element, taking into account its naturally occurring isotopes. This is why some elements on the periodic table have mass numbers that are not whole numbers.
Calculating the Ar of Chlorine
In nature, chlorine exists as two isotopes: 75% is Chlorine-35 and 25% is Chlorine-37.
Step 1: Multiply abundance by mass:
(75 × 35) = 2625
(25 × 37)
= 925
Step 2: Add: 2625 + 925 = 3550
Step 3: Divide by 100: 3550 ÷ 100 = 35.5
Electron Shells & Configuration
The way electrons are arranged in an atom is fundamental to chemistry. It dictates how an element behaves, why it reacts, and where it sits in the periodic table.
Rules for Filling Shells
- Electrons always occupy the lowest available energy level first (the innermost shell).
- Shell 1: holds a maximum of 2 electrons.
- Shell 2: holds a maximum of 8 electrons.
- Shell 3: holds a maximum of 8 electrons.
How to Work Out Electron Configurations
Sodium (Na) - Atomic number 11
First shell fills with 2 electrons.
Second shell fills with 8 electrons. (2 + 8 = 10 used).
Remaining 1 electron goes into the third shell.
Electron configuration: 2.8.1
Chlorine (Cl) - Atomic number 17
First shell: 2 electrons.
Second shell: 8 electrons.
Third shell: 7
electrons.
Electron configuration: 2.8.7
Calcium (Ca) - Atomic number 20
First shell: 2 electrons.
Second shell: 8 electrons.
Third shell: 8 electrons.
Fourth shell: 2 electrons.
Electron configuration: 2.8.8.2
Why Electron Arrangement Matters
The electrons in the outermost shell are called valence electrons. The number of valence electrons determines the chemical properties of an element. Elements in the same group have the same number of valence electrons - which is why they have similar chemical properties.
Build your own atoms with protons, neutrons, and electrons using our Atom Builder tool.
The Periodic Table
The periodic table is a masterfully organised chart of all the known chemical elements. It's arranged to reveal patterns in the properties of elements - a concept known as periodicity.
How the Table is Arranged
The modern periodic table arranges elements in order of increasing atomic number (Z). The atomic number is the number of protons - the element's unique ID number.
Periods (Horizontal Rows)
The rows across the periodic table are called periods. The period number tells you how many occupied electron shells an element has.
- Period 1 elements (H, He) have 1 electron shell.
- Period 2 elements (Li to Ne) have 2 electron shells.
- Period 3 elements (Na to Ar) have 3 electron shells.
Groups (Vertical Columns)
The columns down the periodic table are called groups. For the main groups, the group number tells you the number of electrons in the element's outermost shell (valence electrons).
- Group 1 (Alkali Metals): 1 outer electron - very reactive.
- Group 7 (Halogens): 7 outer electrons - very reactive (need one more for a full shell).
- Group 0 (Noble Gases): Full outer shell - stable and very unreactive.
Explore every element and its properties on our Interactive Periodic Table.
Metals & Non-Metals
The periodic table has a fundamental dividing line that separates elements into metals (left and centre) and non-metals (right).
Physical Properties
| Property | Metals | Non-Metals |
|---|---|---|
| Appearance | Shiny (lustrous) | Dull |
| State at room temp | Mostly solid (except mercury) | Solid, liquid or gas |
| Conductivity | Good conductors of heat & electricity | Poor conductors (insulators) |
| Malleability | Malleable & ductile | Brittle (if solid) |
| Melting/Boiling points | Generally high | Generally low |
| Density | Generally high | Generally low |
How Metals and Non-Metals Form Ions
When metals react, they lose their outer electrons to form positive ions (cations). For example, sodium (2.8.1) loses 1 electron to become Na⁺ (2.8).
When non-metals react, they gain electrons to form negative ions (anions). For example, chlorine (2.8.7) gains 1 electron to become Cl⁻ (2.8.8).
Reactions of Oxides
Metal Oxides are Basic
Metal oxides react with acids in neutralisation reactions to produce a salt and water.
Non-Metal Oxides are Acidic
Non-metal oxides typically react with water to form acidic solutions.
Group 0: The Noble Gases
The elements in Group 0 (Helium, Neon, Argon, etc.) are known as the noble gases. They are chemically inert - extremely unreactive.
Why are Noble Gases So Unreactive?
They all have a full outer shell of electrons:
- Helium: 2
- Neon: 2.8
- Argon: 2.8.8
A full outer shell is the most stable arrangement. They have no tendency to lose, gain, or share electrons, so they exist as individual monatomic atoms.
Trends in Group 0
Boiling points increase as you go down the group. As atoms become larger with more electrons, the weak intermolecular forces of attraction between them become stronger. More energy is needed to overcome these forces.
Uses of Noble Gases
Their inertness makes noble gases useful where unreactive atmospheres are needed:
- Helium: Balloons and airships - low density and non-flammable (safer than hydrogen).
- Neon: Advertising signs - glows bright red-orange when electricity passes through it.
- Argon: Filament lamps and welding - provides an inert atmosphere that prevents the hot metal from reacting with oxygen.
Formulae, Equations & Calculations
Conservation of Mass
The law of conservation of mass states that no atoms are lost or made during a chemical reaction. The total mass of the products equals the total mass of reactants.
This is because the same atoms are present before and after the reaction: they have just been rearranged. This is why we must balance chemical equations.
The same atoms exist before and after: mass is always conserved
Apparent Changes in Mass
Sometimes, the mass of a reaction vessel appears to change:
- If a gas escapes (e.g., CO₂ from a thermal decomposition), mass appears to decrease.
- If a gas is gained from the air (e.g., oxygen during oxidation of metals), mass appears to increase.
In reality, if the system were sealed, the total mass would remain unchanged.
Chemical Measurements & Uncertainty
Whenever a measurement is made, there is always some uncertainty about the result obtained. No measurement is perfectly accurate; all instruments have limitations and all humans introduce small errors when reading scales.
Improving the Quality of Measurements
To increase confidence in results, scientists:
- Repeat measurements and calculate a mean (average).
- Identify and exclude anomalous results (outliers): values that don't fit the pattern. These are usually caused by human error or equipment malfunction.
- Use the range of the measurements about the mean as a measure of uncertainty.
A student records three titre values: 24.50, 24.60, and 24.40 cm³. Calculate the uncertainty.
Step 1: Mean = (24.50 + 24.60 + 24.40) ÷ 3 = 24.50 cm³
Step 2: Range = 24.60 – 24.40 = 0.20 cm³
Step 3: Uncertainty = 0.20 ÷ 2 = ± 0.10 cm³
Result: 24.50 ± 0.10 cm³
Relative Formula Mass (Mr)
The relative formula mass of a compound is the sum of the relative atomic masses of all the atoms in its formula. Ar values are found on the periodic table.
Calculate the Mr of calcium carbonate (CaCO₃)
Ca = 40, C = 12, O = 16
Mr = 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100
Calculate the Mr of magnesium hydroxide (Mg(OH)₂)
Mg = 24, O = 16, H = 1
Mr = 24 + 2 × (16 + 1) = 24 + 34 = 58
Calculate the Mr of aluminium sulfate, Al₂(SO₄)₃
Al = 27, S = 32, O = 16
There are: 2 Al, 3 S, 12 O (3 × 4 = 12)
Mr = (2 × 27) + (3 × 32) + (12 × 16) = 54 + 96 + 192 = 342
Moles & Avogadro's Constant
A mole is simply a number: 6.02 × 10²³ (Avogadro's constant). One mole of any substance contains exactly this number of particles (atoms, molecules, or ions).
The Moles Triangle
mol = mass ÷ Mr
Mr = mass ÷ mol
How many moles in 11 g of CO₂?
Mr of CO₂ = 12 + (2 × 16) = 44
Moles = 11 ÷ 44 = 0.25 mol
What mass is 3 moles of water (H₂O)?
Mr of H₂O = (2 × 1) + 16 = 18
Mass = mol × Mr = 3 × 18 = 54 g
Check your mole calculations instantly with our Moles Calculator - converts between mass, moles, and molar mass.
Reacting Masses
Use a balanced equation plus the moles formula to predict masses used or produced in reactions. Follow these three steps every time:
What mass of magnesium oxide is produced from 6 g of magnesium?
Equation: 2Mg + O₂ → 2MgO
Step 1: Moles of Mg = 6 ÷ 24 = 0.25 mol
Step 2: Ratio: 2Mg : 2MgO = 1:1, so moles of MgO = 0.25 mol
Step 3: Mass of MgO = 0.25 × 40 = 10 g
What mass of iron is produced when 80 g of iron(III) oxide is reduced?
Equation: Fe₂O₃ + 3CO → 2Fe + 3CO₂
Step 1: Mr of Fe₂O₃ = (2 × 56) + (3 × 16) = 160.
Moles = 80 ÷ 160 = 0.5 mol
Step 2: Ratio: 1 Fe₂O₃ : 2 Fe, so moles of Fe = 0.5 × 2 = 1.0 mol
Step 3: Mass of Fe = 1.0 × 56 = 56 g
Limiting Reactants
In many reactions, one reactant is used up before the others. This reactant is called the limiting reactant: it limits the amount of product that can be formed.
The other reactant(s) are said to be in excess.
Limiting
Used up first
Excess
Left over
4.8 g of Mg reacts with 14.6 g of HCl. Which is the limiting reactant?
Equation: Mg + 2HCl → MgCl₂ + H₂
Step 1: Moles of Mg = 4.8 ÷ 24 = 0.2 mol
Step 2: Moles of HCl = 14.6 ÷ 36.5 = 0.4 mol
Step 3: The ratio is 1 Mg : 2 HCl. So 0.2 mol Mg needs 0.2 × 2 = 0.4 mol HCl.
Result: We have exactly 0.4 mol HCl - both reactants run out at the same time. Neither is in excess.
If we only had 0.3 mol HCl, then HCl would be limiting (not enough to react with all the Mg).
Concentration
Concentration tells you how much solute is dissolved in a given volume of solution.
The Concentration Triangle
conc = mass ÷ vol
vol = mass ÷ conc
2.5 g of NaOH dissolved in 500 cm³. Find concentration in g/dm³.
Volume = 500 ÷ 1000 = 0.5 dm³
Concentration = 2.5 ÷ 0.5 = 5 g/dm³
Concentration in mol/dm³
4 g of NaOH is dissolved in 250 cm³ of water. Find the concentration in mol/dm³.
Step 1: Mr of NaOH = 23 + 16 + 1 = 40
Step 2: Moles = 4 ÷ 40 = 0.1 mol
Step 3: Volume = 250 ÷ 1000 = 0.25 dm³
Step 4: Concentration = 0.1 ÷ 0.25 = 0.4 mol/dm³
Need to work through a titration calculation? Use our Titration Calculator for step-by-step working with automatic unit conversion.
Percentage Yield Extended
The percentage yield compares the actual amount of product obtained to the theoretical maximum (calculated from stoichiometry).
Three main reasons why yields are always less than 100%:
- The reaction is reversible and does not go to completion.
- Some product is lost during transfer (e.g., filtration, evaporation).
- Side reactions produce unwanted by-products.
A student calculates they should make 10 g of copper sulfate. They actually collect 7.5 g. What is the percentage yield?
% yield = (7.5 ÷ 10) × 100 = 75%
Atom Economy Extended
Atom economy measures the proportion of reactant atoms that become useful product. It evaluates the efficiency of the reaction pathway itself.
High atom economy is desirable. It means less waste, lower costs, and a more sustainable process.
Yield vs Atom Economy
Calculate the atom economy for producing hydrogen from the reaction:
Zn + H₂SO₄ → ZnSO₄ + H₂
Step 1: Mr of desired product (H₂) = 2
Step 2: Mr of all products = ZnSO₄ (161) + H₂ (2) = 163
Step 3: Atom economy = (2 ÷ 163) × 100 = 1.2%
This is very low - most of the atoms end up in the by-product (ZnSO₄), not in the desired product (H₂).
Titrations Extended
A titration is a technique used to find the concentration of an unknown acid or alkali by reacting it with one of known concentration.
The Method
- Use a pipette to measure a fixed volume of alkali into a conical flask.
- Add a few drops of indicator (e.g., phenolphthalein or methyl orange).
- Fill a burette with acid of known concentration.
- Add acid gradually, swirling, until the indicator permanently changes colour: the end point.
- Record the titre (volume of acid added). Repeat until concordant results are achieved (within 0.10 cm³).
Titration Calculations
25 cm³ of NaOH (unknown concentration) is neutralised by 20 cm³ of 0.5 mol/dm³ HCl. Find the concentration of NaOH.
Equation: NaOH + HCl → NaCl + H₂O
Step 1: Moles of HCl = conc × vol = 0.5 × (20 ÷ 1000)
= 0.5 × 0.02 = 0.01 mol
Step 2: Ratio NaOH : HCl = 1:1, so moles of NaOH = 0.01 mol
Step 3: Volume of NaOH = 25 ÷ 1000 = 0.025 dm³
Step 4: Concentration of NaOH = 0.01 ÷ 0.025 = 0.4 mol/dm³
Molar Volume of Gases Extended
At room temperature and pressure (RTP: 20°C, 1 atm), one mole of any gas occupies a volume of 24 dm³ (or 24,000 cm³).
Gas Volume Triangle
mol = vol ÷ 24
(at RTP)
What volume does 0.5 mol of oxygen gas occupy at RTP?
Volume = 0.5 × 24 = 12 dm³
What volume of CO₂ is produced when 5 g of CaCO₃ is decomposed? (at RTP)
Equation: CaCO₃ → CaO + CO₂
Step 1: Mr of CaCO₃ = 40 + 12 + (3 × 16) = 100
Step 2: Moles of CaCO₃ = 5 ÷ 100 = 0.05 mol
Step 3: Ratio 1:1, so moles of CO₂ = 0.05 mol
Step 4: Volume = 0.05 × 24 = 1.2 dm³ (or 1200 cm³)
Explore gas behaviour with our Gas Law Calculator - see how pressure, volume, and temperature are connected.
Empirical & Molecular Formulae
Empirical Formula: The simplest whole-number ratio of the atoms of each element present in a compound.
Molecular Formula: The actual number of atoms of each element present in one molecule of a compound.
Calculating Empirical Formula from Mass or Percentage Composition
To find the empirical formula, follow these steps:
- Write down the mass or percentage of each element.
- Divide each mass/percentage by the relative atomic mass (Ar) of that element to find the number of moles.
- Divide each number of moles by the smallest mole value obtained in step 2.
- If necessary, multiply all numbers to get whole numbers (e.g., if you get 1.5, multiply all by 2).
Worked Example
A compound contains 82.7% carbon and 17.3% hydrogen by mass. Calculate its empirical formula.
| Element | Carbon (C) | Hydrogen (H) |
|---|---|---|
| Mass / % | 82.7 g | 17.3 g |
| Ar | 12 | 1 |
| Moles (Mass ÷ Ar) | 82.7 ÷ 12 = 6.89 mol | 17.3 ÷ 1 = 17.3 mol |
| Divide by smallest (6.89) | 6.89 ÷ 6.89 = 1.0 | 17.3 ÷ 6.89 = 2.51 |
| Multiply by 2 for integers | 1.0 × 2 = 2 | 2.5 × 2 = 5 |
The empirical formula is C2H5.
Calculating Molecular Formula from Empirical Formula and Mr
- Calculate the relative formula mass (Mr) of the empirical formula.
- Divide the given actual Mr of the compound by the empirical formula mass.
- Multiply the empirical formula subscripts by this factor.
Worked Example
The empirical formula of a compound is C2H5 and its relative molecular mass (Mr) is 58. Find its molecular formula.
Step 1: Empirical formula mass of C2H5 = (2 × 12) + (5 × 1) = 29
Step 2: Factor = Actual Mr ÷ Empirical mass = 58 ÷ 29 = 2
Step 3: Molecular formula = (C2H5) × 2 = C4H10
Molar Gas Volume at RTP Extended
Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules.
This means that one mole of any gas (whether carbon dioxide, oxygen, hydrogen, or any other gas) always occupies the same volume under the same conditions:
- At Room Temperature and Pressure (RTP) (defined as 20°C / 293 K and 1 atmosphere pressure), this volume is 24 dm³ (or 24,000 cm³).
- This volume is called the molar volume of a gas.
Formulae for Gas Volumes
To convert between gas volume and moles, use the following relationships:
Worked Examples
Example 1: Volume from Moles
Calculate the volume, in dm³, occupied by 0.25 moles of carbon dioxide gas at RTP.
Working:
Volume = Moles × 24
Volume = 0.25 × 24 = 6.0 dm³
Answer: 6.0 dm³
Example 2: Volume from Mass
Calculate the volume, in cm³, occupied by 8.8 g of propane gas (C₃H₈) at RTP. (A_r: C = 12, H = 1)
Working:
- Find M_r of C₃H₈:
(3 × 12) + (8 × 1) = 44 - Calculate moles:
Moles = Mass ÷ M_r = 8.8 ÷ 44 = 0.20 mol - Calculate volume in cm³:
Volume = Moles × 24,000 = 0.20 × 24,000 = 4,800 cm³
Answer: 4,800 cm³
Example 3: Stoichiometry & Reacting Gas Volumes
On heating, calcium carbonate decomposes to form calcium oxide and carbon dioxide gas:
CaCO₃(s) → CaO(s) + CO₂(g)
Calculate the volume of carbon dioxide gas, in dm³, produced at RTP when 15 g of calcium carbonate is fully decomposed. (M_r of CaCO₃ = 100)
Working:
- Calculate moles of CaCO₃:
Moles = Mass ÷ M_r = 15 ÷ 100 = 0.15 mol - Determine mole ratio from balanced equation: 1 mole of CaCO₃ decomposes to produce 1 mole of CO₂. Therefore,
Moles of CO₂ = 0.15 mol. - Calculate volume of CO₂:
Volume = Moles × 24 = 0.15 × 24 = 3.6 dm³
Answer: 3.6 dm³
Ionic Bonding
Ionic bonding happens between a metal and a non-metal. It involves the transfer of electrons from the metal atom to the non-metal atom.
How Ionic Bonds Form
- Electron Transfer: The metal atom loses outer electrons → positive ion (cation). The non-metal atom gains electrons → negative ion (anion).
- Electrostatic Attraction: The oppositely charged ions are strongly attracted to each other. This powerful force is the ionic bond.
Formation of Sodium Chloride (NaCl)
Sodium (2.8.1) loses 1 electron → Na⁺ (2.8)
Chlorine (2.8.7) gains 1 electron → Cl⁻ (2.8.8)
The Na⁺ and Cl⁻ ions are held together by strong electrostatic attraction.
Formation of Magnesium Oxide (MgO)
Magnesium (2.8.2) loses 2 electrons → Mg²⁺ (2.8)
Oxygen (2.6) gains 2 electrons → O²⁻ (2.8)
Two electrons are transferred. The Mg²⁺ and O²⁻ ions have a strong electrostatic attraction.
Formation of Magnesium Chloride (MgCl₂)
Magnesium (2.8.2) loses 2 electrons - one to each of two chlorine atoms.
Each Chlorine (2.8.7) gains 1 electron → Cl⁻ (2.8.8)
This gives the formula MgCl₂ - one Mg²⁺ ion for every two Cl⁻ ions.
Dot-and-Cross Diagrams for Ionic Bonds
In dot-and-cross diagrams, dots (•) represent electrons from one atom and crosses (×) represent electrons from the other. For ionic bonds, the transferred electrons are shown in the outer shell of the ion that gained them. Square brackets and charges are used around each ion.
The Giant Ionic Lattice
Ionic compounds form a giant ionic lattice - a regular, repeating 3D arrangement of cations and anions. Each ion is strongly attracted to all surrounding ions of the opposite charge.
Properties of Ionic Compounds
High Melting & Boiling Points
Ionic compounds have very high melting and boiling points (e.g., NaCl melts at 801°C). A large amount of energy is needed to overcome the strong electrostatic forces between the ions.
Electrical Conductivity
Whether an ionic compound conducts depends on its state:
- Solid: Does not conduct - ions are held in fixed positions and cannot move.
- Molten/Dissolved: Conducts electricity - ions are free to move and carry charge.
Solubility
Many ionic compounds dissolve in water. Water molecules surround the individual ions, breaking down the lattice and allowing the ions to move freely.
Covalent Bonding
Covalent bonding occurs when two non-metal atoms share pairs of electrons to achieve a full outer shell. Each atom contributes one or more electrons to form a shared pair.
Common Covalent Molecules
Single Bonds (one shared pair)
- H₂ (hydrogen) - each H shares 1 electron
- HCl (hydrogen chloride) - H and Cl each share 1 electron
- H₂O (water) - oxygen shares 1 electron with each of 2 hydrogens
- CH₄ (methane) - carbon shares 1 electron with each of 4 hydrogens
Double Bonds (two shared pairs)
- O₂ (oxygen) - each oxygen shares 2 electrons (O=O)
Triple Bonds (three shared pairs)
- N₂ (nitrogen) - each nitrogen shares 3 electrons (N≡N)
Dot-and-Cross Diagrams for Covalent Bonds
In covalent dot-and-cross diagrams, show the outer shell electrons only. Dots represent electrons from one atom and crosses from the other. The shared pair sits in the overlapping region between the two atoms.
Simple Molecular Substances
Made of individual, discrete molecules. Within each molecule, atoms are held by very strong covalent bonds. However, forces between molecules (intermolecular forces) are very weak.
Properties of Simple Molecules
- Low melting/boiling points: Only a small amount of energy is needed to overcome the weak intermolecular forces. Many are gases or liquids at room temperature.
- Poor electrical conductors: The molecules are neutral with no free-moving electrons or ions to carry charge.
Examples: Hydrogen (H₂), Chlorine (Cl₂), Water (H₂O), Methane (CH₄).
Giant Covalent Structures
Huge numbers of non-metal atoms joined by a continuous network of strong covalent bonds. No separate molecules and no weak intermolecular forces.
Diamond
Each carbon atom forms four strong covalent bonds in a rigid tetrahedral arrangement. Extremely hard, very high melting point, does not conduct electricity (no delocalised electrons).
Graphite
Each carbon forms three covalent bonds, creating flat layers of hexagonal rings. Layers held by weak forces - can slide (soft and slippery). One delocalised electron per carbon allows electrical conductivity along the layers.
Silicon Dioxide (SiO₂)
Similar structure to diamond. Each silicon bonded to four oxygens, each oxygen bonded to two silicons. Very hard, high melting point, does not conduct electricity.
Metallic Bonding
In metals, atoms lose outer electrons to form a regular lattice of positive ions surrounded by a "sea" of delocalised electrons. The metallic bond is the strong electrostatic attraction between the positive ions and the delocalised electrons.
How Metallic Bonding Explains Metal Properties
- Good electrical conductors: Delocalised electrons can move throughout the structure and carry charge.
- Good thermal conductors: Delocalised electrons carry kinetic energy from hotter to cooler regions.
- Malleable & ductile: Layers of ions can slide over each other without breaking the metallic bond.
- High melting points: Strong metallic bonds require a lot of energy to break.
Alloys
Alloys are mixtures of a metal with other elements. Different-sized atoms distort the layers, so they cannot slide as easily. This makes alloys harder and often stronger than pure metals.
Common Alloys
| Alloy | Composition | Use |
|---|---|---|
| Steel | Iron + carbon | Construction, tools, vehicles |
| Stainless steel | Iron + chromium + nickel | Cutlery, surgical instruments |
| Bronze | Copper + tin | Statues, medals, ship propellers |
| Brass | Copper + zinc | Musical instruments, door handles |
| Gold alloys | Gold + copper/silver | Jewellery (harder than pure gold) |
Electrolysis
4.4.3 Electrolysis
Electrolysis uses electricity to decompose an ionic compound. For electrolysis to work, the ions must be free to move. This means the compound must be either molten or dissolved in water (aqueous).
In the solid state, the strong electrostatic forces in the ionic lattice hold the ions in fixed positions, preventing them from carrying charge. When melted or dissolved, the lattice breaks down and the ions become mobile.
Key terminology
- Electrolyte: the ionic compound, either molten or in aqueous solution.
- Electrode: a solid conductor through which the current enters and leaves the electrolyte. Usually made of inert materials like graphite or platinum.
- Cathode (negative electrode): attracts positive ions (cations). Reduction occurs here (cations gain electrons).
- Anode (positive electrode): attracts negative ions (anions). Oxidation occurs here (anions lose electrons).
A simple electrolysis setup. Positive cations migrate to the negative cathode, while negative anions migrate to the positive anode.
Electrolysis of Molten Compounds
For a simple molten binary ionic compound (one containing only two elements), the products are straightforward:
- The metal is always produced at the cathode.
- The non-metal is always produced at the anode.
Example: lead(II) bromide
At the cathode: Pb²⁺ ions gain electrons and form molten lead.
At the anode: Br⁻ ions lose electrons and form bromine gas (brown vapour).
Extraction of Aluminium
Aluminium is too reactive to be extracted by reduction with carbon. It must be extracted by electrolysis of aluminium oxide (Al₂O₃), purified from bauxite ore.
Why is cryolite used?
Pure aluminium oxide has an extremely high melting point (over 2000°C). Melting it directly would be hugely expensive. Instead, the aluminium oxide is dissolved in molten cryolite (Na₃AlF₆), which lowers the operating temperature to about 950°C. This significantly reduces energy costs.
At the electrodes
Both electrodes are made from carbon (graphite).
- Cathode: Al³⁺ + 3e⁻ → Al (molten aluminium sinks to the bottom and is tapped off).
- Anode: 2O²⁻ → O₂ + 4e⁻ (oxygen gas is produced).
Electrolysis of Aqueous Solutions Extended
When an ionic compound is dissolved in water, there is an added complication: water itself partially ionises, introducing extra H⁺ and OH⁻ ions into the solution. This means there are competing ions at each electrode.
Rules for the cathode (negative electrode)
Both the metal cations and H⁺ ions from water migrate to the cathode. Which one is discharged depends on reactivity:
- If the metal is more reactive than hydrogen (e.g. Sodium, calcium, aluminium), hydrogen gas is produced at the cathode.
- If the metal is less reactive than hydrogen (e.g. Copper, silver), the metal is deposited at the cathode.
Rules for the anode (positive electrode)
Both the non-metal anions and OH⁻ ions from water migrate to the anode:
- If halide ions (Cl⁻, Br⁻, I⁻) are present, the halogen is produced (e.g. Chlorine gas, bromine).
- If no halide ions are present, oxygen gas is produced (from the discharge of OH⁻ ions).
Predicting products: electrolysis of copper sulfate solution
Cathode: Cu²⁺ and H⁺ are present. Copper is less reactive than hydrogen, so copper metal is deposited. Observation: pink/brown solid coats the cathode.
Anode: SO₄²⁻ and OH⁻ are present. No halide ions are present, so oxygen gas is produced. Observation: bubbles at the anode.
Predicting products: electrolysis of sodium chloride solution
Cathode: Na⁺ and H⁺ are present. Sodium is more reactive than hydrogen, so hydrogen gas is produced. Observation: bubbles; squeaky pop with a lighted splint.
Anode: Cl⁻ and OH⁻ are present. Halide ions are present, so chlorine gas is produced. Observation: bubbles; bleaches damp litmus paper.
Predicting products: electrolysis of copper(II) bromide solution
Cathode: Cu²⁺ and H⁺ are present. Copper is less reactive than hydrogen, so copper metal is deposited. Observation: brown/pink solid coats the cathode.
Anode: Br⁻ and OH⁻ are present. Bromide is a halide ion, so bromine is produced. Observation: orange/brown colour near the anode.
Practice: write the half-equations for the electrolysis of copper(II) bromide solution
Cathode (reduction): Cu²⁺(aq) + 2e⁻ → Cu(s)
Anode (oxidation): 2Br⁻(aq) → Br₂(aq) + 2e⁻
Check: 2 electrons lost at the anode = 2 electrons gained at the cathode. ✔
Electrolysis of Brine
Brine is a concentrated solution of sodium chloride (NaCl). Its electrolysis is an important industrial process because it produces three useful products:
- Chlorine gas (Cl₂) at the anode - used in bleach, PVC plastics, and water purification/disinfection.
- Hydrogen gas (H₂) at the cathode - used as a fuel and in the manufacture of margarine (hardening vegetable oils).
- Sodium hydroxide solution (NaOH) left in the solution - used in soap, paper and ceramics manufacturing, and oven cleaners.
Half-equations
Testing the products
- Chlorine: bleaches damp litmus paper (turns it white).
- Hydrogen: squeaky pop with a lighted splint.
- Sodium hydroxide: turns universal indicator blue/purple (alkaline).
Ionic Half-Equations in Electrolysis
At the electrodes, ions either gain or lose electrons. These reactions are represented by ionic half-equations. By looking at these, we can identify which species are oxidized and which are reduced.
OIL RIG: Oxidation Is Loss (of electrons), Reduction Is Gain (of electrons).
- At the Cathode (negative electrode), positive ions (cations) gain electrons. This is reduction.
- At the Anode (positive electrode), negative ions (anions) lose electrons. This is oxidation.
Worked Examples of Electrode Reactions
1. Electrolysis of Molten Lead(II) Bromide (PbBr2)
- At the Cathode: Lead ions gain electrons to form lead metal (reduction).
Pb2+ + 2e- → Pb(l) - At the Anode: Bromide ions lose electrons to form bromine gas (oxidation).
2Br- → Br2(g) + 2e-
2. Electrolysis of Aqueous Sodium Chloride (NaCl)
- At the Cathode: Hydrogen ions from water are reduced in preference to sodium ions (reduction).
2H+ + 2e- → H2(g) - At the Anode: Chloride ions are oxidized in preference to hydroxide ions (oxidation).
2Cl- → Cl2(g) + 2e-
3. Electrolysis of Dilute Sulfuric Acid (H2SO4)
- At the Cathode: Hydrogen ions are reduced to hydrogen gas.
2H+ + 2e- → H2(g) - At the Anode: Hydroxide ions from water are oxidized to oxygen gas and water.
4OH- → O2(g) + 2H2O(l) + 4e-
4. Electrolysis of Aqueous Copper(II) Sulfate (CuSO4)
- Using Carbon (Inert) Electrodes:
- Cathode: Copper ions are reduced, forming a brown copper coating.
Cu2+ + 2e- → Cu(s) - Anode: Hydroxide ions are oxidized, forming oxygen bubbles.
4OH- → O2(g) + 2H2O(l) + 4e-
- Cathode: Copper ions are reduced, forming a brown copper coating.
- Using Active Copper Electrodes:
- Cathode: Copper ions are reduced to copper metal (the cathode increases in mass).
Cu2+ + 2e- → Cu(s) - Anode: The copper anode itself oxidizes and dissolves (the anode decreases in mass).
Cu(s) → Cu2+ + 2e-
- Cathode: Copper ions are reduced to copper metal (the cathode increases in mass).