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The density of solid argon is 1.65g//mL ...

The density of solid argon is `1.65g//mL ` at `-233^(@)C` . If the argon atom is assumed to be sphere of radius `1.54xx10^(-8)cm`, what percentage of solid argon is apparentaly empty space ? `(At. Wt. of Ar=40)`

Text Solution

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Volume of one atom of `Ar=(4)/(3)pir^(3)`
Also, No. of atoms in `1.65g=(1.65)/(40)xx6.023xx10^(23)`
`therefore` Total volume of all atoms of Ar in solid state `=(4)/(3)pir^(3)xx(1.65)/(40)xx6.023xx10^(23)`
`=(4)/(3)xx(22)/(7)xx(1.54xx10^(-8))^(3)xx(1.65)/(40)xx6.023xx10^(23)=0.380cm^(3)`
Volume of solid argon =1 `cm^(3)`
`therefore` %empty space = `([1-0.380])/(1)xx100=62%`
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