Question

The compressibility of a gas is less than unity at STP, therefore:
A. ${V_m} > 22.4L$
B. ${V_m} < 22.4L$
C. ${V_m} = 22.4L$
D. ${V_m} = 44.8L$

Answer 1

Hint: We have to remember that in thermodynamics, the compressibility factor (Z), otherwise called the pressure factor or the gas deviation factor, is a rectification factor that depicts the deviation of a real gas from ideal gas behaviour. It is characterized as the proportion of the molar volume of a gas to the molar volume of an ideal gas at a similar temperature and weight. It is a helpful thermodynamic property for changing the ideal gas law to represent the real gas behaviour.

Complete step by step answer:
For an ideal gas,
\[PV = nRT\]
\[Z = 1\]
We can call the compressibility factor (Z) as the compression factor. The compression factor is defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas. When the temperature and pressure for an ideal gas are the same, the compressibility factor is 1.
The compressibility factor for explicit gases can be perused from summed up compressibility charts that plot Z as an element of weight at a steady temperature.
Because Compressibility $\left( Z \right) = \dfrac{{pV}}{{nRT}}$ for Z less than unity
$\dfrac{{pV}}{{nRT}} < 1$ (or) $pV < nRT$
At standard pressure and temperature,
The value of pressure is one atmosphere.
The value of temperature is $273K$.
The value of the gas constant is $0.0821Latm{K^{ - 1}}$.
i.e$V < 1 \times 0.0821 \times 273$
So, $V < 22.4L$.
When the gas compressibility is less than unity at STP, $V < 22.4L$.

So, the correct answer is Option B.

Note: We need to know that the value of Z increases with pressure and decreases with temperature. We should not get confused between the compressibility factor for the compressibility (otherwise called the coefficient of compressibility or isothermal compressibility) of a material, which is the proportion of the general volume change of a liquid or solid with respect to the change in pressure.