Respuesta :
The density of the compound is 4.64 g/[tex]cm^{3}[/tex].
Explanation:
Sodium chloride crystallize as FCC face centered cubic structure. It consist of four atoms of NaCl. So the unknown compound which crytallizes like NaCl wil have volume as:
radius in fcc is calculated as
[tex]\sqrt{2a}[/tex] = 4r
putting the value where a is length of the edge.
[tex]\sqrt{2X461}[/tex]
= 651.9 = 4r so r= 162.98 pm
volume is calculated by the formula:
[tex]\frac{4}{3}[/tex] π[tex]r^{3}[/tex]
putting the values,
[tex]\frac{4}{3}[/tex] x 3.14 x ([tex]1.62 X 10^{-8}[/tex])^3
= 4.25X 10 ^-24
1.7 X [tex]10^{-23}[/tex] [tex]cm^{3}[/tex] = volume of the fcc cell.
mass of the substance = 4 x 120 x 1.6605 x 10^(-24) g/u) (as it contains four atoms)
= 7.9x [tex]10^{-23}[/tex]
density = [tex]\frac{mass}{volume}[/tex]
putting the values
density = [tex]\frac{ 7.9x10^-23 }{1.7 x 10^{-23} }[/tex]
density = 4.64 g/ [tex]cm^{3}[/tex]
