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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)`. Correlate the difference of observed and calculated densities and calculate % of missing `Na^(+)` and `Cl^(-)` ions.

Text Solution

Verified by Experts

We know that,
`Z=(a^(3)xxrhoxxN)/(M)`
where, Z =number of constituent units 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=2.1805 g//cm^(3)`
Observed density=`2.164g//cm^(3)` which is less than calculated density because some places are missing.
`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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