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The unit cell length of NaCl is observed...

The unit cell length of NaCl is observed to be 0.5627 nm by X-ray diffraction studies, the measured density of NaCl is 2.164 g `cm^(-3)`. Calculate % of missing `Na^(+) and Cl^(-)` ions.

A

0.00775

B

0.1775

C

0.03939

D

0.0753

Text Solution

Verified by Experts

The correct Answer is:
A
We know that, `Z=(a^(3)xxrhoxxN)/(M)`
where, Z=number of constituent unit per unit cell=4 in fcc
a=edge length`=0.5627xx10^(-7)cm`
`rho`=density, N=Avogadro.s number, M=molar mass
`((0.5627xx10^(-7))^(3)xxrhoxx6.023xx10^(23))/(58.5)=4`
`rho=2.1805g//cm^(3)`
Observed density=2.164`g//cm^(3)` which is less than calculated density because some places are missing.
Actual contituent unit cell can be calculated as:
`Z=((0.5627xx10^(-7))^(3)xx2.164xx6.023xx10^(23))/(58.5)=3.969`
Missing units`=4-3.969=0.031`
%missing=`(0.031)/(4)xx100=0.775%`
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