Answer: Real gases behave ideally under conditions of extremely low pressure and very high temperature.

Explanation based on Van der Waals equation:

1. At Low Pressure: The volume V of the gas is exceptionally large. Consequently, the excluded volume b becomes negligible compared to V (i.e., V - b ≈ V). At the same time, the pressure correction factor
   aV²
   approaches zero because V is vast. Thus, P +
   aV²
   ≈ P.
2. At High Temperature: The kinetic energy of gas molecules increases rapidly, moving them far apart from each other. This reduces intermolecular attractive forces to a virtually non-existent state, making the constant a functionally ineffective.

Substituting these approximations into the Van der Waals equation (P +

)(V - b) = RT, the equation mathematically reduces back to the ideal gas equation:

Answer: The ratio of the actual molar volume of a real gas to the calculated molar volume of an ideal gas under identical temperature and pressure conditions is called the Compressibility Factor (Z).

Mathematically, for 1 mole of any gas, it is expressed as:

Criteria for Gas Behavior:

• For Ideal Gases: Z = 1 under all ranges of temperature and pressure.
• For Real Gases showing Negative Deviation: Z < 1. This indicates that the real gas is more compressible than expected ideally (typically observed at low to moderate pressures for gases like N₂, O₂, and CO₂).
• For Real Gases showing Positive Deviation: Z > 1. This indicates that the real gas is less compressible than expected ideally (observed at very high pressures, and at all pressure ranges for H₂ and He).

Answer: The depth of the downward dip in Amagat’s curve at moderate pressures depends directly on the magnitude of the intermolecular forces of attraction, represented by the Van der Waals constant a.

Carbon Dioxide (CO₂) has a larger molecular size and a significantly higher molecular mass compared to Nitrogen (N₂). Due to its larger electron cloud, the temporary dipole-induced dipole interactions—known as Van der Waals dispersion forces—are substantially stronger in CO₂ than in N₂.

As a result, the value of a for CO₂ is much larger. Since a higher value of a increases the term

in the low-pressure expression Z = 1 -

aRTV

, the value of Z drops more significantly below 1. This mathematically accounts for why CO₂ exhibits a much deeper and more pronounced minimum curve than N₂.

Answer: The specific temperature at which a real gas strictly obeys the ideal gas laws over an extended, appreciable range of pressure is defined as the Boyle Temperature or Boyle Point (T_b).

At this unique thermal state, the effect of the intermolecular attractive force correction (constant a) and the molecular volume correction (constant b) perfectly counterbalance each other within the real gas system. Below the Boyle temperature, real gases exhibit an initial negative deviation (Z < 1) before rising, whereas above the Boyle temperature, they show only positive deviation (Z > 1) from the outset, resembling the behavior of Hydrogen.