Q13 / 150 · MHT CET 2026 (13 April Shift 2) · Chemistry
An ionic compound is formed by elements X and Y. Element Y forms a face-centered cubic (FCC) lattice, and element X occupies one-third of the tetrahedral voids. What is the formula of the compound?
- Correct answerA$X_2Y_3$
- B$XY$
- C$XY_3$
- D$X_2Y$
Solution
Element Y forms a face-centered cubic (FCC) lattice.
Number of Y atoms per unit cell = $4$
Number of tetrahedral voids in an FCC unit cell = $2 \times 4 = 8$
Element X occupies one-third of the tetrahedral voids.
Number of X atoms per unit cell = $\dfrac{1}{3} \times 8 = \dfrac{8}{3}$
Ratio of X to Y = $\dfrac{8}{3} : 4 = 8 : 12 = 2 : 3$
The formula of the compound is $X_2Y_3$.
Number of Y atoms per unit cell = $4$
Number of tetrahedral voids in an FCC unit cell = $2 \times 4 = 8$
Element X occupies one-third of the tetrahedral voids.
Number of X atoms per unit cell = $\dfrac{1}{3} \times 8 = \dfrac{8}{3}$
Ratio of X to Y = $\dfrac{8}{3} : 4 = 8 : 12 = 2 : 3$
The formula of the compound is $X_2Y_3$.
Hence, the correct answer is option: 'A'.