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The density of a particular crystal of L...

The density of a particular crystal of LiF is `2.65g//"cc"`. X-analyses shows that `Li^(+)` and `F^(-)` ions are arranged in a cubic array at a spacing of `2.01Å`. From this data, apparent Avogadro's constant is `x xx10^(23)`. Calculate the value of x (Given atomic mass of Li = 6.939, F = 18.998)

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In this problem, we are to calculate the value of Avogadro's number ltBrgt Molar mass of LiF = `6.939+18.998=25.937g`
Density of LiF = 2.65 g/cc
`"Volume of 1 mole LiF"=("Molar mass")/("Density")=((25.937g))/((2.65g//"cc"))=9.78"cc"`
LiF is cubic in structure and let the edge length of the cube be a
`therefore` Volume of the cube `(a^(3))=9.78"cc"`
Edge length `=(9.78)^(1//3)=2.138cm`
No. of ions present in one edge =`((2.138cm))/((2.01xx10^(-8)cm))=1.063xx10^(8)`
No. of ions `(Li^(+)+F^(-))` present in the cube = `(1.063xx10^(8))^(3)`
`=1.201xx10^(24)`
Since each molecules of LiF has two ions, ltBrgt No. of LiF molecules per mole `=(1.201xx10^(24))/(2)=6.01xx10^(23)`
Value of x = `6.01~~6`.
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