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The compression factor (compressibility ...

The compression factor (compressibility factor) for `1 mol` of a van der Waals gas at `0^(@)C` and `100 atm` pressure is found to be `0.5`. Assuming that the volume of a gas molecule is neligible, calculate the van der Waals constant `a`.

Text Solution

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`Z=(PV)/(RT) =0.5`
`therefore (100xxV)/(0.082xx273)=0.5`
`therefore V=0.112` litre
Now, using van der Waals. equation
`[P+(a)/(V^(2))][V]=RT`
or `[P+(a)/(V^(2))]=(RT)/(V)" "(therefore` b is negligible)
`therefore [100+(a)/((0.112)^(2))]=(0.082xx273)/(0.112)`
`=199.88`
`therefore (a)/((0.112)^(2))=99.88`
`therefore a=1.253" litre"^(2)" mole"^(-2)` atm.
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