using X-ray diffraction method , the unit length of NaCl crystal was observed to be 0.5627nm. The density of the crystal was found to be 2.164gcm^-3 what type of defect exist in the crystal ? calculate the percentage Na⁺ and Cl^- missing from missing from the crystal lattice 

Dear Student,

NaCl has an ionic structure. So, the crystal can have only ionic defects.

We know that NaCl has fcc structure.
So , z = 4, M = 58.5 g mol^-1,a = 0.5627 nm=5.627 x 10^-8 cm , N_A = 6.022 x 10²³
Now,
$Density = d = \frac{ZM}{a^3{N}_A}=\frac{4 \times 58.5}{{\left(5.627\times {10}^{-8}\right)}^3\times 6.022 \times {10}^{23}}=2.18 g c{m}^{-3}$
But, observed density= 2.164 < d
Since the stoichiometry of the compound is maintained but the observed density is lesser than the calculated density, it has a Schottky type defect.

Now, change in density = 2.18-2.164 = 0.016 g cm^-3
So , 
$Percentage of ions mis\sin g = Percentage of change in mass = \frac{0.016}{2.18}\times 100=0.734\%$


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