Ideal gases
Section: 4 States of Matter | Syllabus: Cambridge AS Level Physics 9702
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 vs Ideal Gases 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 Key Point - Units 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 gas What 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 gas 2.00 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 equation A 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 Tip To 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 Key Distinction - Graphite 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 Deduce the s…
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