X-ray diffraction studies show that edge length of a unit cell of NaCl is 0.56 nm. Density of NaCl was found to be `2.16g//"cc".` What type of defect is found in the solid? Calculate the percentage of `Na^(+)` and `Cl^(-)` ions that are missing.

Explanation

Calculated density , `rho=(ZxxM)/(a^3xxN_0)=(4xx58.5 "g mol"^(-1))/((0.5627xx10^(-7) cm)^3 xx (6.022xx10^23 "mol"^(-1))=2.1809 " g cm"^(-3)`
Observed density =`2.164 "g cm"^(-3)`
As observed density is less than theoretically calculated value, this means that some `Na^+` and `Cl^-` ions missing from their lattice site, i.e., there is Schottky defect.
Actual formula units of NaCl per unit cell can be calculated as follows :
`Z=(a^3xxrhoxxN_0)/M=((0.5627xx10^(-7)cm)^3 xx(2.164 cm^(-3))xx(6.022xx10^23 mol^(-1)))/(58.5 "g mol"^(-1))`=3.968
`therefore` Formula units missing per unit cell=4-3.968=0.032
`therefore` % missing =`0.032/4xx100`=0.8%