Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance. 1.Remove all the anions (X) except the central one 2.Replace all the face centered cations (M) by anions (X) 3.Remove all the corner cations (M) 4.Replace the central anion (X) with cation (M)
The value of `(("number of anion s ")/("number of cation s"))` in z is ________.

Answer

`3.00`

Explanation

MX having NaCl structure
No. of `M^(+)` ions = 4, No. of `X^(-)` ions = 4
For structure Z constructed from MX
(i) After removing all `X^(-)` ions except the centred one, No. of `M^(+)` ions = 4 No. of `X^(-) ` ions = 1.
(ii) No. of face centred `M^(+)` ions removed = `6 xx 1/2 = 3`
No. of `M^(+)` ions replaced by `X^(-)` ions = 3
`:.` No. of `M^(+)` ions left = 1 `" " `No. of `X^(-)` ions = `1 + 3 = 4`
(iii) No. of corners `M^(+)` ions = `8 xx 1/8 = 1`.
No. of `M^(+)` ions left = 1 - 1 = 0 `" " ` No. of `X^(-)` ions = 4
(iv) Replaceing central `X^(-)` by `M^(+)`
No. of `M^(+)` ions = `0 + 1 = 1` No. of `X^(-) ions = `4 - 1 = 3`
`("No. of "X^(-)" ions")/("No. of "M^+ " ions") = 3/1 = 3.00`.