Question

A compound $M_p{X}_q$ has cubic close packing (ccp) arrangement of X. The $X^{-}$ ion is present in the corner and at face centers. The empirical formula of the compound is:

• A. $MX$
• B. $M{X}_2$
• C. $M_{2}X$
• D. $M_5{X}_{14}$

Answer 1

The correct option is B $M{X}_2$

Given, Compound $=M_p{X}_q$

Given, the Arrangement of X is CCP arrangement. $X^{-}$ are present in corners and face centers.

No. of $\overline{X}$ ions per lattce for CCP arrangement $=4$

$M^{+}$ ions are present at the four edge centers and at body center.

$\Rightarrow$ No. of $M^{+}$ ions per lattice $=\frac{1}{4}\left(4\right)+1=2$

Now, $M:X=4:2=2:1$

$\Rightarrow$ the empirical formula should be $M{X}_2$

Hence, Option B is the correct answer.