Question

A solid is formed by two elements $P$ and $Q$. The element $Q$ forms cubic close packing and atoms of $P$ occupy one-third of tetrahedral voids. The formula of the compound is

• A. $PQ_{3}$
• B. $P_{3}Q$
• C. $P_{2}Q_{3}$
• D. $P_{3}Q_{2}$

Answer 1

Answer: (C)

$P_{2}Q_{3}$

Answer 2

Let the number of atoms in cubic close packing be $x$.
$\therefore$ Number of tetrahedral voids $=2 x$
Since, $Q$ forms cubic close packing, the number of $Q$ atoms $=x$
$P$ occupy one third of tetrahedral voids, the number of $p$ atoms $=\frac{2}{3} x$
$\frac{\text { Number of } P \text { atoms }}{\text { Number of } Q \text { atoms }}$
$=\frac{2 \cdot x}{3 x}=\frac{2}{3}$
Therefore, the formula of the compound is $P_{2} Q_{3}$.