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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, number of atoms in or one `ml =(1.65)/(40) xx6.023xx10^(23)`
`:.` Total volume of all atoms of in solid state `= (4)/(3) pi r^(3) xx (1.65)/(40)xx6.023xx10^(23)`
`=(4)/(3)xx(22)/(7)xx(1.54xx10^(-8))xx(1.65)/(40)xx6.023xx10^(23)=0.380 "cm"^(3)`
`=(4)/(3)xx(22)/(7)xx(1.54xx10^(-8))^(3)xx(1.65)/(40)xx6.023xx10^(23)= 0.380 "cm"^(3)`
Volume of solid argon `=1 "cm"^(3)`
`:. %` empty space = `([1-0.380])/(1)xx100=62%`
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