At $300 \mathrm{~K}, 22 \mathrm{~g}$ of $\mathrm{CO}_2$ gas exerts a pressure of 5 atmosphere. What is…
At $300 \mathrm{~K}, 22 \mathrm{~g}$ of $\mathrm{CO}_2$ gas exerts a pressure of 5 atmosphere. What is volume of the gas at same temperature?
$\left(\mathrm{R}=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
$5.61 \mathrm{dm}^3$
$8.20 \mathrm{dm}^3$
$2.46 \mathrm{dm}^3$
$3.80 \mathrm{dm}^3$
Solution
$\begin{aligned}
& \mathrm{P}_{\mathrm{CO}_2}=5 \mathrm{~atm} \\
& \mathrm{~T}=300 \mathrm{~K}
\end{aligned}$
Moles of gas $=\frac{22}{44}\left(\right.$ Molar mass of $\mathrm{CO}_2$ is 44$)$
$\begin{aligned}
& =0.5 \\
& \mathrm{PV}=\mathrm{nRT} \\
& \mathrm{V}=\frac{\mathrm{nRT}}{\mathrm{P}}=\frac{0.5 \times 0.0821 \times 300}{5} \\
& =2.46 \mathrm{dm}^3
\end{aligned}$