Exactly one mole of a real gas at is compressed in a cylinder. The gas exhibits a measured compressi — States of Matter and Gaseous State Chemistry Question
Question
Exactly one mole of a real gas at $300\text{ K}$ is compressed in a cylinder. The gas exhibits a measured compressibility factor $Z = 0.65$ under these conditions and occupies a volume of $0.4\text{ L}$. Calculate the pressure exerted by the gas in $\text{atm}$. (Use $R = 0.0821\text{ L atm K}^{-1}\text{ mol}^{-1}$ and round off to the nearest integer).
Answer: 40
💡 Solution & Explanation
The compressibility factor is defined as $Z = PV / nRT$. Substituting the given values: $0.65 = (P \times 0.4) / (1 \times 0.0821 \times 300)$. $0.65 = 0.4P / 24.63$. Solving for $P$: $P = (0.65 \times 24.63) / 0.4 = 16.0095 / 0.4 = 40.023\text{ atm}$. Rounding to the nearest integer gives 40.
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