MHT CET · Chemistry · States of Matter
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?
\(\left(\mathrm{R}=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)
- A \(5.61 \mathrm{dm}^3\)
- B \(8.20 \mathrm{dm}^3\)
- C \(2.46 \mathrm{dm}^3\)
- D \(3.80 \mathrm{dm}^3\)
Answer & Solution
Correct Answer
(C) \(2.46 \mathrm{dm}^3\)
Step-by-step Solution
Detailed explanation
\(
\begin{aligned}
& \mathrm{P}_{\mathrm{CO}_2}=5 \mathrm{~atm} \\
& \mathrm{~T}=300 \mathrm{~K}
\end{aligned}
\)
Moles of gas \(=\frac{22}{44}\left(\right.\) Molar mass of \(\mathrm{CO}_2\) is 44\()\)
\(
\begin{aligned}
& =0.5 \\
& \mathrm{PV}=\mathrm{nRT} \\
& \mathrm{V}=\frac{\mathrm{nRT}}{\mathrm{P}}=\frac{0.5 \times 0.0821 \times 300}{5} \\
& =2.46 \mathrm{dm}^3
\end{aligned}
\)
\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\()\)
\(
\begin{aligned}
& =0.5 \\
& \mathrm{PV}=\mathrm{nRT} \\
& \mathrm{V}=\frac{\mathrm{nRT}}{\mathrm{P}}=\frac{0.5 \times 0.0821 \times 300}{5} \\
& =2.46 \mathrm{dm}^3
\end{aligned}
\)
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