U3.6 · Deviation from Ideal Gas LawPractice · 实际气体对理想气体的偏离

In such a small volume the molecules are close together, and the attractions between $\ce{CO2}$ molecules matter: a molecule about to hit the wall is pulled back by the ones behind it, so it hits with less force and the pressure is below the ideal value. The van der Waals equation (CRC values of a and b) gives about 39.6 atm. The molecules’ own volume would push the pressure up (about 53.8 atm from volume alone), but here the attractions win.

At such a high pressure the atoms are crowded, so their own volume matters: the free space is smaller than the container, the atoms hit the walls more often, and the pressure exceeds the ideal value. Attractions between He atoms are tiny (van der Waals a is only 0.0346 L²·bar/mol²), so they hardly count. The van der Waals equation gives about 3.20 × 10² atm. The temperature is fixed, so the average kinetic energy is too.

If the particles didn’t attract each other at all, no amount of cooling would make them cling together as a liquid. Condensation shows the attractions exist: once the particles are too slow to overcome them, they gather together. Diffusion, pressure, and thermal expansion are all explained by the ideal-gas model.

Lower temperature means lower average kinetic energy. The attractions stay the same strength, but slower particles are more easily held by them, so the attractions matter more. At constant pressure the gas also shrinks, putting the particles closer together. The closer to the boiling point, the larger the deviation, until the gas condenses.

Both have 10 electrons, so similar dispersion forces, and their molar masses differ by only 0.99 g/mol. $\ce{NH3}$ is polar with H bonded to N, so its molecules hydrogen-bond and attract each other much more strongly: a is larger (4.225 against 2.283), and NH₃ deviates more from ideal behavior under the same conditions.

PV/nRT below 1 means attractions between molecules make the pressure lower than for an ideal gas; above 1 means the molecules’ own volume is taking up space. Curve C dips lowest (to about 0.65), so it has the strongest attractions: CO₂, which has the most electrons and the strongest dispersion forces (CO₂ is linear and nonpolar). Curve A stays above 1: He, with the weakest attractions. N₂ (B) is in between. A triple bond inside a molecule doesn’t affect attractions between molecules.