Question

Compressibility factor for gas under critical condition is :
(A) 3/8
(B) 8/3
(C) 1
(D) 1/4

Answer 1

Hint: Try to find the value of temperature, pressure and volume under critical conditions and then substitute the values in the formula for compressibility factor.
The formula for the compressibility factor is :
 $Z=\dfrac{PV}{nRT}$
Where,
Z stands for compressibility factor,
P stands for pressure,
V stands for volume,
n stands for the number of moles,
T stands for temperature
R stands for the universal gas constant

Complete step by step solution:
-Compressibility factor(Z) is a correction factor which describes the deviation of a real gas from its behaviour of an ideal gas. It is simply the ratio of molar volume of the gas to the molar volume of an ideal gas subjected to the same identical temperature and pressure.
- For ideal gases, Z = 1 as PV = nRT.
However, for real gases, we follow the Van der Waals equation i.e.
$[P+\dfrac{a{{n}^{2}}}{{{V}^{2}}}][V-nb]=nRT$
Where,
P stands for pressure,
V stands for volume,
n stands for the number of moles,
a is pressure correction constant
b is volume correction constant
T stands for temperature
R stands for the universal gas constant

-Under critical conditions we will define the value of pressure, volume and temperature considering n=1.
$\begin{align}
  & {{P}_{c}}=\dfrac{a}{27{{b}^{2}}} \\
 & {{T}_{c}}=\dfrac{8a}{27Rb} \\
 & {{V}_{c}}=3b \\
\end{align}$
Substituting the above values in the formula given for compressibility factor, we get
Z=3/8.

Hence, the correct answer is option (A).

Note:-Critical temperature is defined as the temperature of a substance in its critical state beyond which it cannot be liquefied.
-Critical pressure of a fluid is defined as the vapour pressure of the fluid at the critical temperature.
-Critical volume is the volume occupied by the fluid or substance in its critical state (Critical pressure and temperature).