A compound consists of atoms A and B. The atoms of B form hcp lattice. The atoms of A occupy 1/3rd of octahedral voids and 1/3rd of tetrahedral voids. What is the molecular formula of the compound ?

The correct answer is Option 4. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Chemistry Q140 – AP-EAMCET 2025

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Home Chemistry Basic ChemistryQuestion #30

A compound consists of atoms A and B. The atoms of B form hcp lattice. The atoms of A occupy

\frac{1}{3}

rd of octahedral voids and

\frac{1}{3}

rd of tetrahedral voids. What is the molecular formula of the compound ?

Clue 1 of 3: Crystal Lattice Voids

Understand the relationship between the number of atoms in a close-packed structure (like hcp) and the number of octahedral and tetrahedral voids it generates.

🧠 Full Solution Path

Step 1: Determine the number of B atoms and associated voids✦ Active

Let the number of B atoms in the hcp lattice be $N$ . In an hcp (hexagonal close-packed) lattice, the number of octahedral voids is equal to the number of atoms, and the number of tetrahedral voids is twice the number of atoms.

Number of B atoms = N

Number of octahedral voids = N

Number of tetrahedral voids = 2 N

💡 Teacher's Secret Hint

Remember that hcp and ccp (fcc) structures have the same number of octahedral and tetrahedral voids relative to the number of atoms.

Step 2: Calculate the number of A atoms occupying the voids○ Expand

Atoms of A occupy $\frac{1}{3}$ rd of the octahedral voids and $\frac{1}{3}$ rd of the tetrahedral voids. We calculate the number of A atoms from each type of void.

Number of A atoms from octahedral voids = \frac{1}{3} \times N = \frac{N}{3}

Number of A atoms from tetrahedral voids = \frac{1}{3} \times 2 N = \frac{2 N}{3}

💡 Teacher's Secret Hint

Pay close attention to the fractions of voids occupied. A common mistake is to use the total number of voids instead of the fraction occupied.

Step 3: Find the total number of A atoms○ Expand

The total number of A atoms is the sum of A atoms occupying octahedral voids and tetrahedral voids.

Total number of A atoms = \frac{N}{3} + \frac{2 N}{3} = \frac{3 N}{3} = N

Step 4: Determine the simplest whole-number ratio and molecular formula○ Expand

Now, we have the number of A atoms and B atoms. We find their simplest whole-number ratio to determine the molecular formula.

Ratio of A : B = N : N = 1 : 1

Molecular formula = A B

💡 Teacher's Secret Hint

The molecular formula represents the simplest whole-number ratio of atoms in the compound.

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Chemistry Question 140 – AP-EAMCET 2025

Clue 1 of 3: Crystal Lattice Voids

🧠 Full Solution Path