Exception 1: $H_{2}$ and He — Always Z > 1 Most gases show Z < 1 at moderate pressures. NOT $H_{2}$ and He. Their 'a' (attraction) values are so small that the 'b' correction (excluded volume, which pushes Z > 1) always dominates.

Exception 2: Water — Anomalous Boiling Point for Its Molecular Mass $H_{2}$O (M = 18) should boil far below 0°C based on the trend of $H_{2}$Se, $H_{2}$S, $H_{2}$Te. Instead it boils at 100°C. Reason: extensive hydrogen bonding network (up to 4 H-bonds per molecule) dramatically raises boiling point.

Exception 3: HF — Anomalously High Boiling Point But Lower Than $H_{2}$O HF (M = 20) has strong H-bonding but less than $H_{2}$O because HF forms chains (one H per molecule), not a 3D network. So HF BP (19.5°C) > HCl (-85°C) but < $H_{2}$O (100°C).

Exception 4: Maxwell-Boltzmann Distribution Tail — Some Molecules Always at Very High Speeds Even at room temperature, a small fraction of molecules have speeds much higher than v_rms. This explains why reactions occur at room temperature even when average KE is below the activation energy — high-speed molecules in the tail can react.

Exception 5: Ideal Gas Cannot Be Liquefied An ideal gas has no intermolecular forces → no condensation → no liquid state → cannot be liquefied under any conditions. This is theoretical — all real gases can be liquefied below T_c.

Exception 6: Above T_c — Supercritical Fluid (Neither Gas Nor Liquid) Above the critical temperature, the substance exists as a supercritical fluid — it has the diffusivity of a gas and the solvating power of a liquid. It is not a gas (too dense) and not a liquid (no surface tension). $CO_{2}$ supercritical state: T > 31.1°C, P > 73.9 atm.

Exception 7: Boyle Temperature — Wide Ideal Range, Not Perfect At T_B = a/(Rb), a real gas approximates ideal behavior over a WIDE pressure range but not perfectly at all pressures. At very high P, excluded volume effects still cause Z > 1 even at T_B.