The pyknometric density of `NaCl` crystal is `2.165 xx 10^(3 kg m^(-3)` while its `X`-ray density is `2.178 xx 10^(-3) kg m^(-3)`. The fraction of unoccupied sites in `NaCl` crystal is
a. `5.96` b. `5.96 xx 10^(-2)`
c. `5.96 xx 10^(-1)` d. `5.96 xx 10^(-3)`

Options

A. 5.96
B. `5.96 xx 10^(-2)`
C. 0.596
D. `5.96 xx 10^(-3)`

Answer

D

Explanation

Molar volume from pyknometer density
`=(M)/(2.165xx10^(3))m^(3)`
Molar volume from X - ray density
`=(M)/(2.178xx10^(2))m^(3)`
`therefore" Volume unoccupied"`
`((1)/(2.165)-(1)/(2.178))(M)/(10^(3))m^(3)`
Fraction unoccupied
`=((1)/(2.165)-(1)/(2.165))`
`=(0.013)/(2.165xx178)xx2.165`
`=5.96 xx10^(-3)`