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(A) The compressibility factor is defined as $Z = \frac{p V}{n R T}$.For an ideal gas,$Z = 1$ at all temperatures and pressures.For a real gas,$Z = \f

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the molar volume of $CH_{4}$ is less than its molar volume in the ideal state

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(A) The compressibility factor is defined as $Z = \frac{p V}{n R T}$.For an ideal gas,$Z = 1$ at all temperatures and pressures.For a real gas,$Z = \frac{p V_{real}}{n R T} \quad (i)$.If the gas shows ideal behaviour,then $V_{ideal} = \frac{n R T}{p}$,which implies $\frac{p}{n R T} = \frac{1}{V_{ideal}} \quad (ii)$.Substituting $(ii)$ into $(i)$,we get $Z = \frac{V_{real}}{V_{ideal}}$.Considering molar volume,$Z = \frac{(V_{m})_{real}}{(V_{m})_{ideal}}$.From the given graph,$Z Therefore,$\frac{(V_{m})_{real}}{(V_{m})_{ideal}} < 1$,which implies $(V_{m})_{CH_{4}, real} < (V_{m})_{CH_{4}, ideal}$.

In the following compressibility factor $(Z)$ versus pressure graph at $300 \, K$,the compressibility of $CH_{4}$ at pressure $< 200 \, bar$ deviates from ideal behaviour because

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