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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`.

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Compressibility factor,
`Z=(pV)/(RT)`
`0.5=(100xxV)/(0.082xx273)`
`therefore" "V=(0.5xx0.082xx273)/(100)=0.1119L`
If volume of molecules is negligible i.e. b is negligible van der Waals equation :
`(p+(a)/(V^(2)))(V)=RT`
`"or "pV=RT-a//V`
`"or "a=RTV-pV^(2)`
`=(0.082xx273xx0.1119)-(100xx0.1119xx0.1119)`
`="1.253 atm L"^(2)"mol"^(-2)`.
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