Chemistry - Solid State Question with Solution | TestHub

Problem: FeO crystallize according rock salt structure, where ${\mathrm{O}}^{-2}$ is equivalent to ${\mathrm{Cl}}^{\ominus }$ ion. Due to some crystal defect, lattice becomes ${\mathrm{Fe}}_{0.75}\mathrm{O}$. Find number of effective ${\mathrm{Fe}}^{+2}$ ions per unit cell.

Correct Answer: 1

Solution:

In a rock salt (NaCl) structure, there are 4 ${\mathrm{O}}^{2-}$ ions per unit cell.

For ${\mathrm{Fe}}_{0.75}\mathrm{O}$, the ratio of Fe to O is 0.75:1.

Let the number of ${\mathrm{Fe}}^{2+}$ ions be $x$ and ${\mathrm{Fe}}^{3+}$ ions be $y$.

Total Fe ions = $x+y=0.75\times 4=3$.

Total negative charge from ${\mathrm{O}}^{2-}$ ions = $4\times (-2)=-8$.

To maintain charge neutrality, total positive charge from Fe ions must be +8.

$2x+3y=8$.

Solving $x+y=3$ and $2x+3y=8$:

From $x+y=3$, $y=3-x$.

Substitute into the second equation: $2x+3(3-x)=8$

$2x+9-3x=8$

$-x=-1$

$x=1$.

So, there is 1 effective ${\mathrm{Fe}}^{2+}$ ion per unit cell.