States of Matter: Gases and Liquids
States of Matter: Gases and Liquids tests the gas laws, kinetic molecular theory, ideal versus real behavior, van der Waals corrections, liquefaction, vapour pressure, surface tension, viscosity, and related liquid properties.
Core rules
- Ideal gas: PV = nRT. Use T in kelvin and R = 0.0821 L atm mol−1 K−1 or 8.314 J mol−1 K−1.
- Dalton's law: total pressure is the sum of partial pressures. Graham's law compares rates as inverse square roots of molar masses.
- Kinetic theory: average kinetic energy depends only on absolute temperature; molecular speeds follow a distribution.
- Real gases deviate most at high pressure and low temperature, where molecular volume and attractions matter.
- Van der Waals equation: (P + an^2/V^2)(V − nb) = nRT.
- For liquids, vapour pressure rises with temperature; surface tension and viscosity generally fall as temperature rises.
Worked example
A 2.0 g sample of a gas occupies 1.64 L at 1.0 atm and 300 K. Find its molar mass. From PV = nRT, n = PV/RT = (1.0 × 1.64)/(0.0821 × 300) = 0.0666 mol. M = m/n = 2.0/0.0666 = 30.0 g/mol. The gas could be ethane, C2H6, whose molar mass is about 30 g/mol.
Traps
Do not use Celsius in gas-law calculations. Do not assume that a real gas is ideal near liquefaction. Vapour pressure depends on temperature, not on the liquid volume, provided some liquid remains. Do not confuse density with molar mass; density = PM/RT for an ideal gas.