Question

Under what conditions do real gases behave like ideal gases?

Answer 1

Hint: A change in conditions like temperature, pressure and volume can significantly impact the physical state of matter. The conditions can be determined by keeping in mind that ideal gases can expand to great volumes and can never be liquefied, which is possible only when the thermal energy is high enough and the forces of attraction are very feeble.

Complete answer:
An ideal gas can be defined on the basis of two important assumptions or postulates of the Kinetic theory of gases.
The volume occupied by the spherical molecules or atoms of gases is negligible in comparison to the volume occupied by the entire gas.
The gaseous particles do not interact with each other at all i.e. there are no forces of attraction between the particles irrespective of the distances between them
The real gases can be distinguished from ideal gas on the basis of the above two assumptions as real gases tend to show significant contribution of volume coming from spherical gaseous particles and forces of attraction also come into existence.
Ideal gases follow all the ideal gas laws and cannot be compressed or cooled enough to transform them into the liquid phase; on the contrary, real gases can be liquefied at specific temperatures and volumes.
The relationship between the physical variable of an ideal gas is given as follows:
\[PV = nRT\]
And the corrected or the non-ideal form of this equation is known as Van der Waals equation:
\[\left( {P + \dfrac{{a{n^2}}}{{{V^2}}}} \right)\left( {V - nb} \right) = nRT\]
Where, \[a\] is the pressure correction term that includes the significant contributions coming from intermolecular forces of attraction and \[b\] is a measure of the excluded volume.
At conditions of high temperature, the gaseous particles have sufficiently high thermal energy to escape the intermolecular forces of attraction, making the \[a\] factor negligible. At conditions of low pressure, the particles are so far apart that their individual volumes can be ignored in calculations, making the \[b\] factor negligible.
Hence, at the conditions of high pressure and low temperature the van der Waals equation reduces to the ideal gas equation and real gases behave like ideal gases.

Note:
The \[a\] factor is not just the pressure correction term but also an indicator of how strongly the particles of a particular gas attract each other at a fixed temperature. Gases that have higher value of \[a\] show stronger forces of attraction and are easy to liquefy as compared to other gases.