🧊 States of Matter & Real vs Ideal Gases

Matter exists in several physical forms: solid, liquid, gas, and plasma are observable in daily life. Intermediate states like liquid crystals exist, while exotic states (Bose‑Einstein condensates, neutron‑degenerate matter, quark‑gluon plasma) occur only under extreme conditions (ultra‑cold, ultra‑dense, or extremely high energy). Understanding gas behaviour is crucial because real gases deviate from the ideal gas law under many conditions.

📊 Comparison: Ideal Gas vs Real Gas

📈 Fig. 1: Compressibility factor Z as a function of pressure for H₂, N₂, and CO₂ at constant temperature. H₂ shows Z>1 (repulsion dominant). N₂ and CO₂ dip below 1 (attraction dominant) then rise. CO₂ has the deepest dip because it liquefies most easily.

🧪 Compressibility Factor (Z): Measuring Deviation

To quantify how much a real gas deviates from ideal behaviour, we use the compressibility factor Z:

For an ideal gas, \(Z = 1\) under all conditions. For a real gas:

• \(Z < 1\) → attractive forces dominate (gas is more compressible than ideal).
• \(Z > 1\) → repulsive forces dominate (gas is less compressible).

The farther \(Z\) is from 1, the greater the non‑ideality.

🌡️ Effect of Temperature on Deviation: Boyle Temperature

As temperature increases, gas molecules have higher kinetic energy, overcoming intermolecular attractions. The deviation from ideality decreases. At a specific temperature called the Boyle temperature (T_B), the gas behaves ideally over a range of pressures – Z ≈ 1. Below T_B, Z dips below 1 first; above T_B, Z > 1.

📉 Fig. 2: Effect of temperature on compressibility factor Z for N₂. At low temperature (T₁), a deep dip (Z<1). As temperature increases (T₂, T₃), the dip becomes shallower. At the Boyle temperature (T_B), the curve is nearly horizontal (Z ≈ 1). At higher temperatures (T₄), Z > 1.

🔥 Boyle Temperature – Key Concept

Every gas has a characteristic Boyle temperature (T_B) at which the second virial coefficient becomes zero and the gas obeys Boyle’s law (\(PV = \text{constant}\)) over a moderate pressure range. For nitrogen, T_B ≈ 332 K. At this temperature, attractive and repulsive forces balance, making the gas nearly ideal.

⚙️ Interactive: Compressibility Factor Calculator

📘 Summary: Real Gas Behaviour

• All real gases show ideal behaviour at low pressure and high temperature.
• At high pressure, repulsive forces dominate → Z > 1.
• At moderate pressures and low temperatures, attractive forces dominate → Z < 1 (gas more compressible).
• The Boyle temperature is where the gas behaves ideally over a range of pressures.
• Gases that liquefy easily (e.g., CO₂, NH₃) show larger deviations.