Question

The compressibility of a gas is less than unity at STP. Therefore?

• A. ${\mathrm{V}}_{\mathrm{m}}$ greater than $22.4\mathrm{L}$
• B. ${\mathrm{V}}_{\mathrm{m}}$ less than $22.4\mathrm{L}$
• C. ${\mathrm{V}}_{\mathrm{m}}$ equal to $22.4\mathrm{L}$
• D. ${\mathrm{V}}_{\mathrm{m}}$ equal to $44.8\mathrm{L}$

Answer 1

The correct option is B

${\mathrm{V}}_{\mathrm{m}}$ less than $22.4\mathrm{L}$

The explanation for the correct option:

Option(B):$\mathrm{Vm}$ less than $22.4\mathrm{L}$

Step 1: Given data:

The gas is given at STP, hence at standard pressure and temperature,

The value of pressure = $1\mathrm{atm}$

The value of temperature = $273\mathrm{K}$

The value of the gas constant = $0.0821\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}$

Step 2: Formula for compressibility factor:

For an Ideal gas, $\mathrm{PV}=\mathrm{nRT}$,the compressibility factor $\mathrm{Z}=1$

We know the compressibility factor (Z) is given as = $\frac{\mathrm{pV}}{\mathrm{nRT}}$

Step 2: Calculating condition for the given gas:

For the given gas, the compressibility factor (Z) is given as less than the unity

$$\begin{gathered} \Rightarrow \frac{{\mathrm{PV}}_{\mathrm{m}}}{\mathrm{nRT}}<1 \\ \Rightarrow {\mathrm{PV}}_{\mathrm{m}}<\mathrm{nRT} \\ \Rightarrow {\mathrm{V}}_{\mathrm{m}}<1\mathrm{x}0.0821\mathrm{x}273 \\ \Rightarrow {\mathrm{V}}_{\mathrm{m}}<22.4\mathrm{L} \end{gathered}$$

Thus, when the gas compressibility is less than unity at STP, ${\mathrm{V}}_{\mathrm{m}}$ less than $22.4\mathrm{L}$, option (B) is the correct answer.