Ideal gases
Section: 4 States of Matter | Syllabus: Cambridge AS Level Chemistry (9701)
The Ideal Gas
An ideal gas is a theoretical model that simplifies the behaviour of real gases. No gas is perfectly ideal, but many real gases behave approximately ideally at low pressures and high temperatures.
Assumptions of an Ideal Gas
- Gas molecules have zero volume - the volume of the molecules themselves is negligible compared to the volume of the container.
- There are no intermolecular forces of attraction or repulsion between gas molecules (except during collisions).
- Collisions between molecules and with the container walls are perfectly elastic - no kinetic energy is lost.
- Molecules are in constant, random motion.
- The average kinetic energy of the molecules is proportional to the absolute temperature (in Kelvin).
Real gases deviate from ideal behaviour at high pressures (molecules are forced close together - their volume and intermolecular forces become significant) and at low temperatures (molecules slow down - intermolecular attractions become more significant). At low pressure and high temperature, real gases approximate ideal behaviour.
The Ideal Gas Equation
Ideal Gas Equation pV = nRT, where p = pressure (Pa), V = volume (m³), n = amount of gas (mol), R = gas constant (8.31 J K⁻¹ mol⁻¹), T = temperature (K).| Variable | Symbol | SI unit | Common conversions |
|---|---|---|---|
| Pressure | p | Pa (pascals) | 1 atm = 101 325 Pa; 1 kPa = 1000 Pa |
| Volume | V | m³ | 1 dm³ = 0.001 m³; 1 cm³ = 1×10⁻⁶ m³ |
| Amount | n | mol | - |
| Gas constant | R | J K⁻¹ mol⁻¹ | R = 8.31 J K⁻¹ mol⁻¹ |
| Temperature | T | K (kelvin) | T(K) = T(°C) + 273 |
Always convert to SI units before substituting into pV = nRT. The most common errors are using cm³ instead of m³, or °C instead of K. Check: p in Pa, V in m³, T in K.
Figure 4.9: pV = nRT - Variable Relationships
(Three mini graphs: (1) p vs V at constant n,T - hyperbola (Boyle's law). (2) V vs T at constant n,p - straight line through origin (Charles's law). (3) p vs n at constant V,T - straight line through origin. Label each graph axis and the law it represents.)
Calculations Using pV = nRT
Finding the volume of a gasWhat volume does 0.500 mol of an ideal gas occupy at 25°C and 100 kPa?
T = 25 + 273 = 298 K | p = 100 × 10³ = 100 000 Pa | R = 8.31
V = nRT ÷ p = (0.500 × 8.31 × 298) ÷ 100 000 = 0.01238 m³ = 12.38 dm³
Finding the pressure of a gas2.00 mol of gas in a 50.0 dm³ container at 150°C. Find the pressure.
T = 150 + 273 = 423 K | V = 50.0 × 10⁻³ = 0.0500 m³
p = nRT ÷ V = (2.00 × 8.31 × 423) ÷ 0.0500 = 140 556 Pa ≈ 141 kPa
Finding Mᵣ from the ideal gas equationA gas sample of mass 0.236 g occupies 104 cm³ at 25°C and 100 kPa. Find Mᵣ.
T = 298 K | p = 100 000 Pa | V = 104 × 10⁻⁶ = 1.04 × 10⁻⁴ m³
n = pV ÷ RT = (100 000 × 1.04 × 10⁻⁴) ÷ (8.31 × 298) = 4.20 × 10⁻³ mol
Mᵣ = mass ÷ n = 0.236 ÷ 4.20 × 10⁻³ = 56.2 g mol⁻¹
Exam TipTo find Mᵣ: use pV = nRT to find n, then use Mᵣ = mass ÷ n. This is a common exam question - practise the unit conversions carefully.
Physical Properties and Structure - Comparison
The type of structure and bonding determines the physical properties of a substance. Use the table below to compare and predict properties.
| Property | Giant Ionic (NaCl, MgO) | Simple Molecular (I₂, H₂O) | Giant Molecular (Diamond, SiO₂) | Giant Metallic (Cu) |
|---|---|---|---|---|
| Melting / boiling point | High (strong electrostatic attraction) | Low (weak intermolecular forces) | Very high (many strong covalent bonds) | High (strong metallic bonding) |
| Electrical conductivity (solid) | Poor - ions cannot move | Poor - no ions or free electrons | Poor (diamond, SiO₂) / Good along layers (graphite) | Good - delocalised electrons move freely |
| Electrical conductivity (liquid/aq) | Good - ions free to move when melted or dissolved | Poor (non-electrolytes) | Poor - no ions formed | Good (molten metal still conducts) |
| Solubility in water | Often soluble - ion–dipole interactions with water | Polar molecules may dissolve; non-polar molecules do not | Insoluble - covalent bonds too strong to break | Insoluble (reacts with some acids) |
| Hardness | Hard but brittle - lattice shatters when layers shift (like charges meet) | Soft - weak intermolecular forces | Very hard (diamond) / Soft between layers (graphite) | Malleable and ductile - non-directional bonding |
Graphite is the only giant covalent substance that conducts electricity. This is because of its delocalised electrons above and below the hexagonal layers. It is an exception you must know - all other giant covalent substances are insulators.
Deducing Structure and Bonding from Given Information
You can deduce the type of structure from experimental data using the following logic:
- High melting point + conducts when molten/dissolved + does not conduct when solid → giant ionic
- Low melting point + poor conductor in all states + may dissolve in water or organic solvents → simple molecular
- Very high melting point + does not conduct (except graphite) + very hard + insoluble → giant covalent (molecular)
- High melting point + conducts in solid and liquid state + malleable → giant metallic
Substance X: melting point 1713°C, does not conduct electricity in solid or liquid state, insoluble in water, very hard.
High mp + non-conductor + insoluble + hard → giant covalent (molecular) - most likely SiO₂ or diamond.
Deduce the structure of substance YSubstance Y: melting point 114°C, does not conduct electricity, soluble in organic solvents.
Low mp + non-conductor + soluble in organic solvents → simple molecular - most likely iodine (I₂).
Figure 4.10: Decision Tree - Deducing Structure from Properties
(Flowchart: Start → "Does it conduct electricity when solid?" → Yes → Giant metallic. No → "Does it conduct when molten or dissolved?" → Yes → Giant ionic. No → "High or low melting point?" → High → Giant covalent. Low → Simple molecular. Each endpoint labelled with an example substance.)
Interactive revision notes, videos and practice questions load below.