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.

Explanation

Density `(rho)=(z xxM)/(N_(o)xx a^(3))`
`= (4xx58.5)/(6.023xx10^(23)xx(0.5627xx10^(-7))^(3))`
`= 2.1805 g//cm^(3)`
Observed density `= 2.164 g//cm^(3)` which is less than calculated density because some ions are missing.
Actual constant units per unit cell can be calculated as :
`z = (rho xx N_(o)xx a^(3))/(M)`
`= (2.164xx6.023xx10^(23)xx(0.5627xx10^(-7))^(3))/(58.5)`
= 3.969
Missing units `= 4-3.969 = 0.031`
`therefore` % missing of `Na^(+)` and `Cl^(-)=(0.031)/(4)xx100 = 0.775 %`