Question

The compressibility factor of He as a real gas at room temperature is :
A.Unity
B.$1 - \dfrac{A}{{RTV}}$
C.$1 + \dfrac{{PB}}{{RT}}$
D.$1 - \dfrac{{RTV}}{{1 - a}}$

Answer 1

Hint: Compressibility factor also known as the compression factor or the gas deviation factor is a correction factor which describes a deviation of a real gas from an ideal gas behavior. An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to inter particle interactions.

Complete step by step answer:
Since there are no attractive or repulsive forces between the molecules of an ideal gas, the actual volume will be the same as the ideal volume. Hence, the compressibility factor is unity.
The compressibility factor is a useful thermodynamic property for modifying the ideal gas law to account for behavior of real gases. It is a measure of how much the thermodynamic properties of a real gas deviate from those expected of an ideal gas.
You can calculate compressibility factor (Z) by, $\dfrac{{PV}}{{RT}}$
Where, P= pressure
              V= volume
              R= gas constant
              T= temperature

Hence the answer is unity i.e. option A is correct.

Additional information:
Properties of ideal gas
-The volume occupied by the gas molecules is insignificant with respect to the volume occupied by the gas
-There are no attractive or repulsive forces between the molecules or between the molecule and the walls of the container.
-All collisions of molecules are perfectly elastic i.e. there is no loss of internal energy upon collision
 Ideal gas law
Also called the general gas equation, is the equation of state of hypothetical gas
  \[PV = \;nRT\]
Where, P= pressure
              V= volume
              N= amount of substance
               T= temperature

Note:
R is universal gas constant. The value of R depends on the units involved but is usually stated with SI units as: R=8.314 \[J/mole\]