The pyknometric density of sodium chloride crystal is `2.165xx10^(3)kg m^(-3)` while its `X` ray density is `2.178xx10^(3)kg m^(-3)` the fraction of unoccupied sites in `NaCl` crystal is

Options

A. `5.96 `
B. `5.96 xx 10^(-2)`
C. `5.96 xx 10^(-1)`
D. `5.96 xx 10^(-3)`

Answer

D

Explanation

Molar volume from pyknometer density
`= M/(2.165 xx 10^3) m^3`
Molar volume from X-ray density
`= M/(2.178 xx 10^(3)) m^3`
`:.` Volume unoccupied = `M/(10^3) [1/(2.165) - 1/(2.178)] m^3`
`= (0.013 M xx 10^(-3))/(2.165 xx 2.178)`
`:.` Fraction unoccupied = `(0.013 M xx 10^(-3))/(2.165 xx 2.178) // (M)/(2.165 xx 10^(3))`
=` 5.96 xx 10^(-3)`.