Q.Explain, with reference to the van der Waals equation, why real gases deviate from ideal behaviour at high pressure and low temperature. What does the compressibility factor $Z = \dfrac{PV}{nRT}$ tell us about the direction of this deviation?

[!TLDR] Real gases deviate because molecules have finite volume and attract one another, which the ideal gas model ignores; $Z=PV/nRT$ dips below 1 (attraction dominates) then rises above 1 (volume dominates) as pressure increases. [!ANSWER] $Z<1$ signals inte …

The kinetic theory assumes gas molecules have negligible volume and exert no attractive forces on one another — assumptions that hold well only at low pressure, where molecules are far apart. At higher pressure, both assumptions break down: real molecules do occupy a small but non-zero volume, and they do exert weak attractive forces on their neighbours. The compressibility factor $Z = \dfrac{PV}{nRT}$ measures the size and direction of this deviation, since $Z=1$ exactly for an ideal gas at all conditions. At low to moderate pressure, intermolecular attraction dominates: molecules pull each other slightly closer together than the ideal model predicts, reducing the effective pressure (or volume) below the ideal value, so $Z$ dips below $1$. At high pressure, the molecules are forced close together and their own finite volume becomes a significant fraction of the total gas volume, so the gas resists further compression more than the ideal model predicts, and $Z$ rises above $1$. Plotting $Z$ against $P$ for a real gas therefore gives a characteristic curve start …

Identify which two kinetic-theory postulates fail for real gases, then explain how each failure shi …

Assuming Z always stays below 1 for a real gas, missing that it rises above 1 at sufficiently high …