Chemistry Q140 – AP-EAMCET 2026

Home Chemistry Basic ChemistryQuestion #28

A compound is formed by elements A and B. Element B forms ccp structure. Atoms of A occupy

x %

of tetrahedral voids. All the octahedral voids are vacant. Compound formula is

A_{2} B_{3}

. What is

x %

Clue 1 of 3: Crystal Structure Voids

Understand the relationship between the number of atoms in a close-packed structure and the number of tetrahedral and octahedral voids.

🧠 Full Solution Path

Step 1: Determine the number of atoms and voids in the ccp structure✦ Active

In a cubic close-packed (ccp) structure, the number of atoms per unit cell is 4. Let element B form the ccp lattice, so the number of B atoms per unit cell, $N_{B}$ , is 4.

For a ccp structure, the number of tetrahedral voids is twice the number of atoms, and the number of octahedral voids is equal to the number of atoms.

Number of B atoms (N_{B}) = 4

Number of tetrahedral voids = 2 \times N_{B} = 2 \times 4 = 8

Number of octahedral voids = N_{B} = 4

💡 Teacher's Secret Hint

Remember that ccp is equivalent to FCC (Face-Centered Cubic) structure, where the number of atoms per unit cell is 4.

Step 2: Calculate the number of A atoms based on void occupancy○ Expand

It is given that all octahedral voids are vacant. Atoms of A occupy $x %$ of the tetrahedral voids.

So, the number of A atoms, $N_{A}$ , can be expressed as:

N_{A} = \frac{x}{100} \times (Number of tetrahedral voids)

N_{A} = \frac{x}{100} \times 8

💡 Teacher's Secret Hint

Ensure you use the correct type of void (tetrahedral) for element A's occupancy, as specified in the problem.

Step 3: Use the compound formula to find the value of x○ Expand

The compound formula is given as $A_{2} B_{3}$ . This means the ratio of A atoms to B atoms in the compound is $2 : 3$ .

\frac{N_{A}}{N_{B}} = \frac{2}{3}

Substitute the expressions for $N_{A}$ and $N_{B}$ from the previous steps:

\frac{\frac{x}{100} \times 8}{4} = \frac{2}{3}

Now, simplify and solve for $x$ :

\frac{8 x}{400} = \frac{2}{3}

\frac{2 x}{100} = \frac{2}{3}

\frac{x}{50} = \frac{2}{3}

x = \frac{2 \times 50}{3}

x = \frac{100}{3}

x \approx 33.33

Therefore, $x %$ is approximately $33.3 %$ .

💡 Teacher's Secret Hint

Be careful with algebraic manipulation. Double-check your simplification steps to avoid errors.

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Chemistry Question 140 – AP-EAMCET 2026

Clue 1 of 3: Crystal Structure Voids

🧠 Full Solution Path