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4. States of matter

Syllabus
9701–2028–2029
Section
4
Level
AS

4.1 Gases: ideal, real and pV = nRT

Syllabus
9701–2028–2029
Topic
4.1
Level
AS

Gas pressure comes from particles colliding with container walls

Gas molecules move continuously and collide with the container walls. A molecule's momentum changes during a wall collision; the wall exerts a force on the molecule and the molecule exerts an equal and opposite force on the wall.

pressure=forcearea\mathrm{pressure=\frac{force}{area}}

The enormous number of collisions produces a steady average force. Pressure is this average force per unit wall area, so more frequent collisions or a greater momentum change per collision increase the pressure.

At constant temperature, decreasing the container volume shortens the average distance to a wall. Collisions with the walls become more frequent, so the pressure rises even though the number of molecules is unchanged.

Molecule–molecule collisions redistribute momentum, but gas pressure is measured from momentum transferred to the container wall. Pressure is a collective effect of many particles, not a property carried by one stationary molecule.

An ideal gas has zero particle volume and no intermolecular attraction

The ideal-gas model makes two required assumptions: gas particles have zero volume, and there are no intermolecular forces of attraction between them.

Ideal assumption Meaning in the model Why a real gas can deviate
zero particle volume the whole container volume is available for particle motion at high pressure, particles are close and their own volume is no longer negligible
no intermolecular attraction particles do not pull one another away from wall collisions at low temperature, attractions matter more relative to particle kinetic energy

Real gases approach ideal behaviour most closely at low pressure, where particles are far apart, and high temperature, where their kinetic energy makes attractions less significant.

An ideal gas is a simplifying model, not a special real substance. ‘Zero particle volume’ means volume is neglected in the model; it does not mean real molecules literally occupy no space.

Use pV = nRT with SI units before calculating Mᵣ

pV=nRTR=8.31 J K−1 mol−1\mathrm{pV=nRT}\qquad R=8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}

Symbol Quantity SI unit used with R = 8.31
p pressure Pa
V gas volume m³
n amount mol
T absolute temperature K

Convert before substitution: kPa × 1000 gives Pa; cm³ × 10⁻⁶ or dm³ × 10⁻³ gives m³; and T/K = temperature/°C + 273. Keep unrounded values through the calculation.

n=pVRTmolar mass=mn=mRTpV\mathrm{n=\frac{pV}{RT}\qquad molar\ mass=\frac{m}{n}=\frac{mRT}{pV}}

A 0.880 g gas sample occupies 500 cm³ at 100 kPa and 300 K. Using SI units, molar mass = (0.880 × 8.31 × 300) ÷ (100000 × 5.00 × 10⁻⁴) = 43.9 g mol⁻¹, so the numerical value of Mᵣ is 43.9.

Mᵣ is dimensionless, whereas molar mass has unit g mol⁻¹; their numerical values coincide when molar mass is expressed in g mol⁻¹. Never substitute °C, kPa, cm³ or dm³ directly with the SI value of R.

4.2 Bonding and structure

Syllabus
9701–2028–2029
Topic
4.2
Level
AS

Four lattice types differ in their repeating particles and attractions

A lattice is a regular, repeating three-dimensional arrangement of particles. Classify a crystalline solid by identifying the particles repeated through the structure and the attraction holding them together.

Lattice type Repeating particles Attraction throughout the solid Required examples
giant ionic positive and negative ions strong electrostatic attraction between oppositely charged ions NaCl, MgO
simple molecular discrete molecules intermolecular forces between molecules iodine, I₂; buckminsterfullerene, C₆₀; ice, H₂O
giant molecular (giant covalent) atoms covalent bonds in a continuous network SiO₂, graphite, diamond
giant metallic positive metal ions and delocalised electrons electrostatic attraction between the ions and delocalised electrons copper

Graphite is a layered giant covalent network, whereas C₆₀ consists of separate molecules even though both contain only carbon. Ice is simple molecular: covalent O–H bonds lie within each molecule and hydrogen bonds join neighbouring molecules in the lattice.

A formula alone does not establish lattice type. Use evidence about the particles and bonding: SiO₂ is a network, not a collection of separate SiO₂ molecules, while C₆₀ has many atoms but remains a discrete molecule.

Forces and mobile charged particles explain a solid's physical properties

Melting or boiling requires attractions between particles to be overcome. Electrical conduction additionally requires mobile charged particles. Solubility depends on whether new solute–solvent attractions can compensate for attractions within the solid and solvent.

Structure Melting and boiling Electrical conductivity Solubility pattern
giant ionic high: many strong ion–ion attractions must be overcome not when solid; conducts when molten, and in aqueous solution if soluble, because ions can move many dissolve in polar water when ion–dipole attractions and hydration compensate for lattice separation; not all ionic solids are soluble
simple molecular usually low relative to giant structures because only intermolecular forces are overcome; hydrogen bonding can raise the values does not conduct because there are no mobile charged particles depends on polarity and intermolecular forces; substances tend to dissolve in solvents able to form comparable attractions
giant covalent very high because many covalent bonds must be broken usually does not conduct; graphite conducts along its layers using delocalised electrons generally insoluble because separating the network would require breaking covalent bonds
giant metallic often high, but varies with the metal conducts as a solid and liquid because delocalised electrons can move generally insoluble; a metal may react with a solvent instead of simply dissolving

Diamond and SiO₂ have no mobile charge carriers, so they are electrical insulators. Graphite is the important exception: each carbon forms three covalent bonds, leaving delocalised electrons that move along the layers.

Do not infer a property from bond strength alone. In a simple molecular substance, melting separates molecules without breaking their internal covalent bonds; in an ionic solid, melting frees ions to move without turning them into atoms.

Deduce structure by combining melting, conductivity and solubility evidence

Record the conditions attached to every observation, especially whether conductivity was measured in the solid, molten or aqueous state. Match at least two independent properties to a structural model, then explain each match using particles, attractions and charge mobility.

Combined evidence Most likely structure Causal interpretation
low melting/boiling; non-conductor in every pure state simple molecular weak intermolecular forces; no mobile charged particles
high melting; non-conducting solid but conducting melt, and conducting aqueous solution if soluble giant ionic strong ion–ion attractions; ions are fixed in the solid but mobile in melt or solution
high melting; conducting solid and liquid; often malleable giant metallic strong metallic attraction; mobile delocalised electrons
very high melting; insoluble; non-conductor giant covalent such as diamond or SiO₂ continuous covalent network; no mobile charged particles
very high melting; solid conductor; soft or layered graphite giant covalent layers with delocalised electrons and weaker forces between layers

Suppose a solid has a melting point near 800 °C, does not conduct as a solid, but its melt and aqueous solution conduct. The high melting point suggests strong attractions, and conduction only after ions become mobile identifies a giant ionic lattice.

One property is rarely decisive: both ionic and giant covalent solids can have high melting points, while both metals and graphite conduct as solids. A defensible deduction combines the full pattern and states why competing structures are rejected.