IMAT Chemistry · Free notes

States of Matter and Gas Laws

States of Matter and Gas Laws has 12 past questions since 2011, and the ministry papers from 2023 on have asked 7 of them. More than half are about the gas laws, and the calculations among them are mostly a gas heated in a rigid container. The rest are facts about changes of state, boiling, the density of ice and the units of pressure. The difficulty is rarely the arithmetic: it is converting to kelvin before taking a ratio, telling inverse from direct proportion, and sharing out a pressure by moles rather than mass. Get those three habits right and this chapter is quick marks.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

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Subtopic notes

Formula & revision sheet

8 formulas · 9 reference tables · 20 gotchas across all subtopics — the exam-eve cheat-sheet

Solids, Liquids, Gases and the Kinetic Model

Formulas (1)

Absolute temperature and the average kinetic energy of particles · Kelvin from Celsius, and kinetic energy $T\,(\text{K}) = \theta\,({}^{\circ}\text{C}) + 273.15 \qquad \bar{E}_k \propto T$

Reference tables (2)

The three states of matter in the particle model3 rows

State	Arrangement and spacing	Motion of particles	Shape and volume	Compressible?
Solid	Close together, usually in a regular pattern	Vibrate about fixed positions	Fixed shape and fixed volume	Almost not at all
Liquid	Close together, no regular pattern	Move around and slide past one another	Takes the shape of the container, fixed volume	Almost not at all
Gas	Far apart, random	Fast, random, straight lines between collisions	Fills the whole container	Very easily

A gas at room conditions is mostly empty space: the gaps between molecules are about ten times the size of the molecules.

Water is unusual: ice is less dense than liquid water4 rows

Property	Ice at 0 °C	Liquid water at 0 °C
Density	About 0.92 g/cm³	About 1.00 g/cm³
Volume of 1 kg	About 1.09 L	About 1.00 L
Arrangement	Open lattice held by hydrogen bonds; molecules further apart	Some hydrogen bonds broken; molecules packed closer
Average kinetic energy	Same as the liquid at 0 °C	Same as the ice at 0 °C

Water is one of very few substances whose solid floats on its own liquid.

Watch out for (4)

Particles in a solid still move
→ The three states of matter in the particle model
Only kelvin temperatures can be used in ratios
→ Absolute temperature and the average kinetic energy of particles
At the same temperature, heavier molecules are slower, not more energetic
→ Absolute temperature and the average kinetic energy of particles
The solid is not always the densest state
→ Water is unusual: ice is less dense than liquid water

Changes of State, Boiling and Phase Diagrams

Formulas (1)

Solutes lower the freezing point and raise the boiling point · Freezing point depression $\Delta T_f = i\,K_f\,m \qquad \Delta T_b = i\,K_b\,m$

Reference tables (3)

The six changes of state and their energy6 rows

Change	Name	Energy
Solid to liquid	Melting (fusion)	Absorbed
Liquid to solid	Freezing (solidification)	Released
Liquid to gas	Evaporation or boiling (vaporisation)	Absorbed
Gas to liquid	Condensation	Released
Solid to gas	Sublimation	Absorbed
Gas to solid	Deposition	Released

Vapour pressure, evaporation and the boiling point4 rows

Feature	Evaporation	Boiling
Where	At the surface only	Throughout the liquid, with bubbles
Temperature	Any temperature	Only where vapour pressure equals the external pressure
Speeded up by	Higher temperature, larger surface, wind	Supplying heat faster (the temperature stays the same)
Effect on the liquid	Cools the liquid left behind	Temperature stays at the boiling point

Phase diagrams in outline: triple point and critical point4 rows

Feature	Meaning	Example values
Triple point	Solid, liquid and gas coexist	Water: 0.01 °C and about 0.006 atm
Critical point	End of the liquid to gas line	Water: about 374 °C and 218 atm
Normal melting and boiling points	Where the 1 atm line crosses the two lines	Water: 0 °C and 100 °C
Triple point above 1 atm	No liquid can exist at 1 atm; the solid sublimes	Carbon dioxide: triple point 5.1 atm, so dry ice sublimes at about $-78\ ^\circ\text{C}$ at 1 atm

Watch out for (6)

Freezing means liquid to solid
→ The six changes of state and their energy
The temperature does not rise during melting or boiling
→ The six changes of state and their energy
More pressure on a liquid means a higher boiling point
→ Vapour pressure, evaporation and the boiling point
The triple point of water is not 0 °C at 1 atm
→ Phase diagrams in outline: triple point and critical point
A solute lowers the freezing point; it never raises it
→ Solutes lower the freezing point and raise the boiling point
The solute does not supply the energy to melt ice
→ Solutes lower the freezing point and raise the boiling point

Pressure Units and the Gas Laws

Formulas (3)

Boyle's law: pressure and volume at constant temperature · Boyle's law $P_1 V_1 = P_2 V_2$
Charles's law and Gay-Lussac's law: the effect of temperature · Charles, Gay-Lussac and the combined gas law $\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \frac{P_1}{T_1} = \frac{P_2}{T_2} \qquad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$
Avogadro's law and the molar volume of a gas · Amount of gas from its volume $n = \frac{V}{V_m}$

Reference tables (1)

Units of pressure and their values for one atmosphere6 rows

Unit	Symbol	Value of 1 atm
Pascal	Pa	101 325 Pa
Kilopascal	kPa	101.325 kPa
Bar	bar	1.01325 bar
Millibar (hectopascal)	mbar or hPa	1013.25 mbar
Millimetre of mercury	mmHg	760 mmHg
Torr	Torr	760 torr

Learn 101.3 kPa and 760 mmHg; the others follow from the prefixes.

Watch out for (4)

1 atm is 101.3 kPa, not 1013 kPa
→ Units of pressure and their values for one atmosphere
Inverse proportion, not a direct decrease
→ Boyle's law: pressure and volume at constant temperature
Convert to kelvin before using any gas law ratio
→ Charles's law and Gay-Lussac's law: the effect of temperature
Equal volumes mean equal moles, not equal masses
→ Avogadro's law and the molar volume of a gas

The Ideal Gas Equation and Mixtures of Gases

Formulas (3)

The ideal gas equation PV = nRT · Ideal gas equation $PV = nRT$
Dalton's law of partial pressures · Partial pressure $p_A = x_A\,P_{\text{total}} = \frac{n_A}{n_{\text{total}}}\,P_{\text{total}}$
Graham's law: lighter gases diffuse and effuse faster · Graham's law $\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$

Reference tables (1)

Real gases and the assumptions of the ideal gas model4 rows

Idea	Ideal gas model	Real gas
Volume of the molecules	Negligible	Small but real; matters at high pressure
Forces between molecules	None	Weak attractions; matter at low temperature
Can it be liquefied?	Never	Yes, by cooling and compressing
Closest to ideal	Any gas, at any conditions	Helium and hydrogen, at high temperature and low pressure

Watch out for (4)

Litres with R = 8.314 gives an answer 1000 times wrong
→ The ideal gas equation PV = nRT
Adding gas at constant pressure and volume cools the gas
→ The ideal gas equation PV = nRT
Partial pressures follow moles, not masses
→ Dalton's law of partial pressures
Rate goes with the square root of the molar mass
→ Graham's law: lighter gases diffuse and effuse faster

Pure Substances, Mixtures and Separation Techniques

Reference tables (2)

Elements, compounds and mixtures4 rows

Type	What it is	Examples	How it can be separated
Element	One kind of atom	Iron, oxygen gas, $\mathrm{S_8}$	Cannot be broken down chemically
Compound	Elements bonded in a fixed ratio	Water, sodium chloride, carbon dioxide	Only by a chemical reaction
Homogeneous mixture	Uniform throughout, one phase	Salt water, air, brass	Physical methods such as distillation
Heterogeneous mixture	Not uniform, visible parts	Sand in water, oil and water, granite	Physical methods such as filtration

Separation techniques: filtration, distillation, chromatography and others7 rows

Technique	Separates	Based on	Example
Filtration	Insoluble solid from a liquid	Particle size	Sand from water
Evaporation or crystallisation	Dissolved solid from its solution	The solvent is volatile, the solid is not	Salt from sea water
Simple distillation	Solvent from a solution	Very different boiling points	Pure water from salt water
Fractional distillation	Miscible liquids	Boiling points closer together	Ethanol from water; fractions of crude oil
Chromatography	Dissolved substances in small amounts	Attraction to the stationary and mobile phases	Dyes in an ink; amino acids
Separating funnel	Immiscible liquids	Density; liquids do not mix	Oil from water
Centrifugation	Suspended solid from a liquid	Density	Blood cells from plasma

Watch out for (2)

Looking uniform does not make a substance pure
→ Elements, compounds and mixtures
Filtration cannot remove a dissolved substance
→ Separation techniques: filtration, distillation, chromatography and others

PYQ weightage by concept

17 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

Solids, Liquids, Gases and the Kinetic Model0 PYQs · 0%

Concept	PYQs	Share
The three states of matter in the particle modelfoundation	—	—
Absolute temperature and the average kinetic energy of particlesfoundation	—	—
Water is unusual: ice is less dense than liquid waterfoundation	—	—

Changes of State, Boiling and Phase Diagrams0 PYQs · 0%

Concept	PYQs	Share
The six changes of state and their energyfoundation	—	—
Vapour pressure, evaporation and the boiling pointfoundation	—	—
Phase diagrams in outline: triple point and critical pointfoundation	—	—
Solutes lower the freezing point and raise the boiling pointfoundation	—	—

Pressure Units and the Gas Laws0 PYQs · 0%

Concept	PYQs	Share
Units of pressure and their values for one atmospherefoundation	—	—
Boyle's law: pressure and volume at constant temperaturefoundation	—	—
Charles's law and Gay-Lussac's law: the effect of temperaturefoundation	—	—
Avogadro's law and the molar volume of a gasfoundation	—	—

The Ideal Gas Equation and Mixtures of Gases0 PYQs · 0%

Concept	PYQs	Share
The ideal gas equation PV = nRTfoundation	—	—
Dalton's law of partial pressuresfoundation	—	—
Graham's law: lighter gases diffuse and effuse fasterfoundation	—	—
Real gases and the assumptions of the ideal gas modelfoundation	—	—

Pure Substances, Mixtures and Separation Techniques0 PYQs · 0%

Concept	PYQs	Share
Elements, compounds and mixturesfoundation	—	—
Separation techniques: filtration, distillation, chromatography and othersfoundation	—	—