Question

The critical temperature and critical pressure value of four gases are given

Gas	Critical temperature(K)	Critical pressure(atm)
P	5.1	2.2
Q	33	13
R	126	34
S	135	40

Which of the following gases cannot be liquefied at a temperature 100 K and pressure 50 atm.

Answer 1

Hint: The elements that occur in nature mainly belong to either the gaseous state, liquid state, or the solid-state based on the force of intermolecular attraction that operates between them. It is found that the matter in the gaseous state can be turned into the liquid and the liquid can be turned to the solid-state by the application of pressure and decrement of the temperature.

Complete step by step answer:
The critical temperature of the substance is the temperature at and above which the vapors that belong to the substance cannot be liquefied, even if excess pressure is applied.
The critical temperature of the gas is the measure of the strength of the intermolecular forces of attraction. The weaker the intermolecular forces of attraction, the more difficult it is to liquefy the gas, and hence lower would be the critical temperature of the gas.
During the phase change, it is seen that the temperature remains constant though there is an increase in the amount of heat that is being provided to change the phase. It has been inferred that such heat goes into the breaking of the bonds that are essential for the change of matter from one phase to another.
As the temperature is less than 100 K for gas P and gas Q and it is more than 100K for the other two. so the gases, P and Q cannot be liquified at the given temperature.

Note: The ideal gas equation is given as $P = \dfrac{{nRT}}{V}$,
is the equation which states how the gas should act in ideal conditions and what the ideal characteristics are for the gas is also defined. The ideal gas also draws heavily from the kinetic theory of gases but actually, the ideal gas is a hypothetical concept and thus ideal gaseous don't exist in the real world, the gases that exist are called real gases and follow a different rule than that which are laid by the ideal gases.