A compound is formed by 2 elements P and Q. Atoms of element Q (as anions) makes ccp and those of P (as cations) fill all tertrahedral voids and also occupy half of the octahedral voids. What is the correct formula of this compound?
Answer & explanation
Correct answer: option 2
The correct answer is option 2. \(P_5Q_2\).
Let us break down the process of determining the formula of the compound where elements \( P \) and \( Q \) form a cubic close-packed (ccp) structure:
Cubic Close-Packed (CCP) Structure:
In a cubic close-packed lattice (also known as face-centered cubic or FCC), the atoms are packed in a repeating pattern with each atom surrounded by 12 others.
Tetrahedral Voids: For every atom in a ccp lattice, there are 2 tetrahedral voids.
Octahedral Voids: For every atom in a ccp lattice, there is 1 octahedral void.
Counting Atoms and Voids:
The unit cell of a ccp lattice effectively contains 4 atoms.
In this structure:
Tetrahedral voids: Each unit cell contains \( 2 \times 4 = 8 \) tetrahedral voids.
Octahedral voids: Each unit cell contains 4 octahedral voids.
Given Conditions
Atoms of Q form ccp lattice:
The atoms of Q are arranged in the ccp structure, meaning there are 4 Q atoms per unit cell
Atoms of P fill all tetrahedral voids and half of the octahedral voids:
All the tetrahedral voids are filled by P atoms. Half of the octahedral voids are also filled by P atoms
Detailed Calculation
In a ccp unit cell, there are:
8 tetrahedral voids
4 octahedral voids
Tetrahedral Voids: All 8 tetrahedral voids are filled by P atoms. So, there are 8 P atoms filling tetrahedral voids.
Octahedral Voids: Half of the 4 octahedral voids are filled by P atoms, which means 2 P atoms are filling octahedral voids.
Total P atoms = 8 (from tetrahedral voids) + 2 (from octahedral voids) = 10 P atoms.
Total Q atoms in the unit cell = 4 (as Q forms the ccp lattice)
Total P atoms = 10
The empirical formula would be:
\(\text{Empirical Formula} = P_{10}Q_{4}\)
To simplify this formula, divide the subscripts by their greatest common divisor, which is 2:
\(\frac{P_{10}Q_{4}}{2} = P_{5}Q_{2}\)
Conclusion
The formula of the compound, where the atoms of \( P \) and \( Q \) are arranged according to the given structure and conditions, simplifies to \( P_5Q_2 \). Thus, the correct formula for the compound is (2) \( P_5Q_2 \)