Gases, Kinetic Theory and States of Matter
This domain tests the ideal gas equation, kinetic theory and the behaviour of real gases. STPM expects correct unit conversion and explanations of deviations from ideality.
Ideal gas equation
PV = nRT, with R = 8.31 J K−1 mol−1. Temperature must be in kelvin, pressure in pascals and volume in m3. Dalton’s law states that total pressure is the sum of partial pressures; partial pressure = mole fraction × total pressure.
Kinetic theory
The model assumes gas particles have negligible volume, exert no intermolecular forces, move randomly and collide elastically, and that average kinetic energy is proportional to absolute temperature. Real gases deviate at high pressure and low temperature because particle volume and intermolecular attractions become significant. The van der Waals equation corrects for these: (P + an2/V2)(V − nb) = nRT.
States and phase changes
Solids have fixed shape and volume; liquids have fixed volume but take the container shape; gases fill the container. Melting, boiling and sublimation involve energy changes without temperature change at the transition point.
Worked example
0.500 g of a gas occupies 200 cm3 at 27 °C and 101 kPa. V = 200×10−6 m3, T = 300 K, P = 101000 Pa. n = PV/RT = (101000 × 200×10−6)/(8.31 × 300) = 20.2/2493 = 8.10×10−3 mol. M = 0.500/8.10×10−3 = 61.7 g mol−1.
Traps that cost marks
Convert °C to K and cm3 to m3. Use total pressure for a mixture, not the partial pressure of one gas. Do not assume real gases obey PV = nRT at extreme conditions. Kinetic theory assumptions are models, not exact descriptions.