Question

In the following compressibility factor $(Z)$ versus pressure graph at $300K$, the compressibility of $C{H}_4$ at pressure $<200$ bar deviates from ideal behaviour because

• A. the molar volume of $C{H}_4$ is less than its molar volume in the ideal state
• B. the molar volume of $C{H}_4$ is same as that in its ideal state
• C. inrermolecular interactions between $C{H}_4$ molecules decreases
• D. the molar volume of $C{H}_4$ is more than its molar volume in the ideal state

Answer 1

Answer: (A)

Compressibility factor,$Z=\frac{pV}{nRT}$
For ideal gas $Z=1$ (at all temperature and pressures)
For real gas,$Z>1$(At high pressures) or $Z<1$(At low pressures )
For real gas, $Z=\frac{p{V}_{\text{real}}}{nRT}...(i)$
If the gas shows ideal behaviour, then
$V_{\text{ideal}}=\frac{nRT}{p}$
or $\frac{p}{nRT}=\frac{1}{V_{\text{ideal}}}...(ii)$
Putting $(ii)$ in $(i)$
$Z=\frac{V_{\text{real}}}{V_{\text{ideal}}}$
If we consider molar volume, then
$Z=\frac{(V_m{)}_{\text{real}}}{(V_m{)}_{\text{ideal}}}$
As in given case
$Z=\frac{(V_m{)}_{\text{real}}}{(V_m{)}_{\text{ideal}}}<1$ at $p<200$ bar
$\therefore (V_m{)}_{C{H}_4}$ real $<(V_m{)}_{C{H}_4}$ ideal