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. `5.99`
B. `5.96 xx 10^(-2)`
C. `5.96 xx 10^(-1)`
D. `5.96 xx 10^(-3)`

Answer

d

Explanation

Mole volume from pyknometric density
`V_(p) = (M)/(2.165 xx 10^(3)) m^(3)`
Molar volume from X-rays density
`V_(x) = (M)/(2.178 xx 10^(3)) m^(3)`
`:.` volume unoccupies`= (M)/(10^(3)) ((1)/(2.165)-(1)/(2.178))`
`= (0.013 xx M xx 10^(-3))/(2.165 xx 2.178 )m^(3)`
`:.` fraction of volume occupied
`= (0.013 xx M xx 10^(3))/(2.165 xx 2.175) //(M xx 10^(-3))/(2.165)`
`= 5.96 xx 10^(-3)`