What is the volume of 1 mole real gas at. STP $\left(\mathrm{V}_0=22.4 \mathrm{dm}^3\right)$, if…
What is the volume of 1 mole real gas at. STP $\left(\mathrm{V}_0=22.4 \mathrm{dm}^3\right)$, if compressibility factor of real gas is 1.1 at STP?
- $22.40 \mathrm{dm}^3$
- $23.64 \mathrm{dm}^3$
- $24.64 \mathrm{dm}^3$
- $23.50 \mathrm{dm}^3$
Solution
$\begin{aligned}
& \mathrm{Z}=\frac{\mathrm{V}_{\text {real }}}{\mathrm{V}_{\text {ideal }}} \\
& \mathrm{V}_{\text {real }}=\mathrm{Z} \times \mathrm{V}_{\text {ideal }}=1.1 \times 22.4=24.64 \mathrm{dm}^3
\end{aligned}$
Alternate method:
$\begin{aligned}
\mathrm{Z} & =\frac{\mathrm{PV}}{\mathrm{nRT}} \\
1.1 & =\frac{1 \times \mathrm{V}}{1 \times 0.08206 \times 273} \\
1.1 & =\frac{\mathrm{V}}{0.08206 \times 273} \\
\therefore \quad \mathrm{V} & =24.64 \mathrm{dm}^3
\end{aligned}$
Asked in: MHT CET 2023 (10 May Shift 2)
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