Question

For ${H_2}$ gas, the compressibility factor $Z = \dfrac{{PV}}{{nRT}}$ is:
A.Equal to 1
B.Equal to 0
C.Always greater than 1
D.Initially less than 1 and then becomes greater than 1 at high pressures.

Answer 1

The compressibility factor is a correction factor which describes the deviation of a real gas from ideal gas behavior. It is the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure.

Complete step by step answer:
Ideal gases are the gases which have elastic collisions between their molecules and there are no intermolecular attractive forces. Moreover, when we talk about ideal gases, we assume the following considerations.
a)The molecules of an ideal gas behave as rigid spheres
b)All the collisions are elastic
c)The temperature of the gas is directly proportional to the average kinetic energy of the molecules.
d)The ideal gases are made up of molecules which are in constant motion in random directions.
Now, the compressibility factor or gas deviation factor is a correction factor which describes the deviation of a real gas from ideal gas behavior. It is given as:
$Z = \dfrac{{PV}}{{nRT}}$
Where, P is the pressure, n is the number of moles of gas, T is the absolute temperature and R is the gas constant.
Now, for ideal gas, the compressibility factor is1. But for ${H_2}$ gas, it is always greater than 1.This is observed because the gases like hydrogen show intermolecular repulsive forces which cause the actual volume to be greater than the ideal values.

Hence, option C is correct.

Note: The ideal gas equation holds well as long as the density is kept low. This equation is applicable for single gas or even a mixture of multiple gases where ‘n’ will stand for the total moles of gas particles in the given mixture.