Question

Compressibility factor of a gas is given by the equation $Z = \dfrac{{PV}}{{nRT}}$. On this basis, mark the correct statement.
A.When Z$ > 1$, real gases get compressed easily.
B.When Z$ = 1$, real gases get compressed easily.
C.When Z$ > 1$, real gases are difficult to compress.
D.When Z$ = 1$, real gases are difficult to compress.

Answer 1

Hint: Deviation of real gas from ideal behaviour is expressed using compressibility factor.An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

Complete step by step answer:
Compressibility factor of a gas is given by,
$Z = \dfrac{{PV}}{{nRT}}$
For ideal gas, $PV = nRT$
Hence the value of compressibility factor Z will be equal to $1$. For real gases the equation, $PV = nRT$cannot be true. Hence Z cannot be equal to one. Z for real gases will be less than one or greater than one.
When Z$ < 1$, the gas becomes more compressible and when Z$ > 1$, the gas becomes less compressible.
Let us look into the options given.
Option a says that when Z$ > 1$, real gases get compressed easily. This statement is wrong as we discussed. When Z$ > 1$, real gases are easy to compress. Because at this condition the molecular attraction dominates which favours compression. Hence Option a is wrong.
Option b says that when Z$ = 1$, real gases get compressed easily. For real gases Z is not equal to one. Hence this statement is wrong.
Option c says that when Z$ > 1$, real gases are difficult to compress. This statement is correct. When Z$ > 1$, the gas becomes less compressible. The reason for this is that when Z$ > 1$, the forces of attraction between the molecules is weak. The attraction should be strong for compression to happen.
Option d says that When Z$ = 1$, real gases are difficult to compress. Real gases cannot have the value of Z as one. Hence this statement is also wrong.
Hence the correct option is C.

Note:
At $Z > 1$, $PV > nRT$ for real gases. As pressure increases the value of PV increases and gas becomes less compressible. Repulsive forces dominate at this condition.