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Calculate density of NaCl if edge length of nacl unit cell is 564 pm

Calculate density of NaCl if edge length of nacl unit cell is 564 pm

Grade:12

1 Answers

Arun
25750 Points
5 years ago
The volume of a unit cell, Vcell, is given by: 
Vcell = ZM/dN 
where Z is the formula units per unit cell 
M is the molar mass per formula unit 
d is the density in g cm^-3 
N is the Avogadro constant 

NaCl has a fcc lattice and for fcc, Z = 4 
For NaCl, M = 58.44 g mol^-1 

As the unit cell is a cube, the edge length 564 pm = 3√Vcell 
5.64 x 10^-8 cm = 3√(ZM/dN) 
(5.64 x 10^-8 cm)^3 = (ZM/dN) 
dN = ZM/(5.64 x 10^-8 cm)^3 
d = [ZM/(5.64 x 10^-8 cm)^3]/N 
d = [(4 x 58.44 g mol^-1)/(5.64 x 10^-8 cm)^3)]/6.022 x 10^23 mol^-1 
d = 2.16 g cm^-3

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