States of matter are governed by the balance between intermolecular forces and kinetic energy, with stronger forces producing solids and weaker forces producing gases. The four gas laws (Boyle, Charles, Gay-Lussac, Avogadro) combine into the ideal gas equation $PV = nRT$, where temperature must always be in Kelvin and R must match the pressure unit. Dalton's law states that total pressure equals the sum of partial pressures, with each gas contributing $p_i = x_i \times P_\text{total}$. Graham's law of diffusion states that rate is inversely proportional to the square root of molar mass, so lighter gases diffuse faster. Kinetic molecular theory derives three molecular speed measures: $v_{mp} < v_{avg} < v_{rms}$, all increasing with temperature and decreasing with molar mass. Real gases deviate from ideal behavior at high pressure and low temperature, where intermolecular forces and molecular volumes become significant. The van der Waals equation corrects for these with constants $a$ (attraction) and $b$ (volume), yielding $(P + an^2/V^2)(V - nb) = nRT$. The compressibility factor $Z = PV/nRT$ equals 1 for ideal gases, less than 1 when attraction dominates, and greater than 1 when repulsion dominates; $H_{2}$ and He always have $Z > 1$ at all pressures. Liquefaction of a gas requires temperature below the critical temperature $T_c$ and pressure above the critical pressure $P_c$. In the liquid state, vapor pressure increases with temperature while surface tension and viscosity both decrease, making these direction-of-change questions straightforward to answer.