Question:
At \(27^\circ C\), a real gas of molar mass
\[
44\ \text{g mol}^{-1}
\]
occupies a volume of
\[
0.4\ \text{L}
\]
at a pressure of
\[
40\ \text{atm}.
\]
If the compressibility factor is
\[
Z=0.65,
\]
what is its weight (in g)?
\[
(R=0.082\ \text{L-atm K}^{-1}\text{mol}^{-1})
\]
At \(27^\circ C\), a real gas of molar mass
\[
44\ \text{g mol}^{-1}
\]
occupies a volume of
\[
0.4\ \text{L}
\]
at a pressure of
\[
40\ \text{atm}.
\]
If the compressibility factor is
\[
Z=0.65,
\]
what is its weight (in g)?
\[
(R=0.082\ \text{L-atm K}^{-1}\text{mol}^{-1})
\]
Show Hint
For real gases:
\[
PV=ZnRT.
\]
If \(Z\lt 1\), intermolecular attractions dominate.
Always calculate moles using
\[
n=\frac{PV}{ZRT}
\]
before finding the mass.
Updated On: Jul 29, 2026
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The Correct Option is B
Solution and Explanation
Concept:
For a real gas,
\[
PV=ZnRT
\]
where
\[
Z=\text{compressibility factor}.
\]
Hence,
\[
n=\frac{PV}{ZRT}.
\]
Mass of gas:
\[
m=nM,
\]
where \(M\) is the molar mass.
Step 1: Calculate the number of moles. Given, \[ P=40\ \text{atm}, \] \[ V=0.4\ \text{L}, \] \[ T=27^\circ C=300\ \text{K}, \] \[ Z=0.65, \] \[ R=0.082\ \text{L-atm K}^{-1}\text{mol}^{-1}. \] Therefore, \[ n = \frac{PV}{ZRT} = \frac{40\times0.4} {0.65\times0.082\times300}. \] \[ = \frac{16}{15.99} \approx1. \] \[ n\approx1\ \text{mol}. \]
Step 2: Calculate the mass of the gas. Given molar mass, \[ M=44\ \text{g mol}^{-1}. \] Thus, \[ m=nM. \] \[ m=(1)(44). \] \[ m=44\ \text{g}. \]
Final Answer: \[ \boxed{44\ \text{g}} \] \[ \boxed{\text{Answer = (B)}} \]
Step 1: Calculate the number of moles. Given, \[ P=40\ \text{atm}, \] \[ V=0.4\ \text{L}, \] \[ T=27^\circ C=300\ \text{K}, \] \[ Z=0.65, \] \[ R=0.082\ \text{L-atm K}^{-1}\text{mol}^{-1}. \] Therefore, \[ n = \frac{PV}{ZRT} = \frac{40\times0.4} {0.65\times0.082\times300}. \] \[ = \frac{16}{15.99} \approx1. \] \[ n\approx1\ \text{mol}. \]
Step 2: Calculate the mass of the gas. Given molar mass, \[ M=44\ \text{g mol}^{-1}. \] Thus, \[ m=nM. \] \[ m=(1)(44). \] \[ m=44\ \text{g}. \]
Final Answer: \[ \boxed{44\ \text{g}} \] \[ \boxed{\text{Answer = (B)}} \]
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