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The density of solid argon (Ar= 40 g//...

The density of solid argon `(Ar= 40 g//"mol")` is `1.68 g//mL` at 40 K . If the argon atom is assumed to be a sphere of radius `1.50 xx10^(-8) cm ` , what `%` of solid Ar is apparently empty space ?

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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