JEE Advanced 2018 · Paper 1 · Chemistry Q9

← JEE Advanced 2018 · Paper 1

ChemistryNumerical+3Question 27 of 54

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.

(i) Remove all the anions (X) except the central one

(ii) Replace all the face centered cations (M) by anions (X)

(iii) Remove all the corner cations (M)

(iv) Replace the central anion (X) with cation (M)

The value of $\left(\dfrac{\text{number of anions}}{\text{number of cations}}\right)$ in Z is ______.

Your answer

Answer and worked solution

Official answer: 3

Take the NaCl cell with the central site occupied by an anion. So the anions X are at the edge centres and body centre, and the cations M are at the corners and face centres.

Step	X per cell	M per cell
start	$12\times\tfrac14+1=4$	$8\times\tfrac18+6\times\tfrac12=4$
(i) keep only the central X	1	4
(ii) face-centred M → X	$1+3=4$	1 (corners only)
(iii) remove corner M	4	0
(iv) central X → M	3	1

$\frac{\text{anions}}{\text{cations}}=\frac31=3.$

Answer: 3

Topics:Crystal lattices and unit cells

← Previous question Next question →

JEE Advanced 2018 · Paper 1, Chemistry question 9