The edge of the $NaCl$ unit cell is $564 pm$ (molar mass $58.5 g mo l^{- 1}$ , $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ ). The measured density of a crystal sample is $2.155 g c m^{- 3}$ . If the only defects are Schottky pairs and the cell volume is unchanged, what percentage of the formula units are missing? (two decimals)

Numerical answer type, answer in %, tolerance 0.05.

Answer: 0.5 %

Ideal density

= \frac{4 \times 58.5}{6.022 \times 1 0 ^{23} \times ( 5.64 \times 1 0 ^{- 8} ) ^{3}} = 2.1659 g c m^{- 3}

. The observed density is lower in proportion to the mass lost: fraction missing

= 1 - \frac{2.155}{2.1659} = 0.00503

, which is

0.50%