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Q.

Consider the following graph of Z $vs \frac{1}{V_{m}}$ drawn at inversion temperature and low pressure (Higher powers of $\frac{1}{V_{m}}$ are not significant) using the virial form of vanderwaal’s equation: $Z = 1 + (b - \frac{a}{R T}) \frac{1}{V_{m}} + \frac{b^{2}}{V_{m^{2}}} + \frac{b^{3}}{V_{m^{3}}} + ...............$
Where Z is compressibility factor and $V_{m}$ is molar volume
Then the critical molar volume $(V_{C}) i n c m^{3}$ is_________

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answer is 6.

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Detailed Solution

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$Z = 1 + (b - \frac{a}{R T}) \frac{1}{V_{m}}$ (at low P)
At inversion temperature
$\begin{array}{l} T = \frac{2 a}{R b} \\ Z = 1 + (b - \frac{a}{\frac{R \times 2 a}{R b}}) = 1 + (b - \frac{b}{2}) \frac{1}{V_{m}} = 1 + \frac{b}{2} \times \frac{1}{V_{m}} \end{array}$

$S l o p e = \frac{b}{2} = \frac{1.02 - 1.01}{0.011 - 0.001} = \frac{0.01}{0.01} = 1 b = 2 c m^{3} V_{c} = 3 b = 6 c m^{3}$

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Consider the following graph of Z vs 1Vm drawn at inversion temperature and low pressure (Higher powers of 1Vm are not significant) using the virial form of vanderwaal’s equation: Z=1+(b−aRT)1Vm+b2Vm2+b3Vm3+...............Where Z is compressibility factor and Vm is molar volume Then the critical molar volume (VC) in cm3 is_________