Chemistry Q61 – NEET-UG 2023

Home Chemistry Basic ChemistryQuestion #59

A compound is formed by two elements A and B. The element B forms cubic close packed structure and atoms of A occupy

1 / 3

of tetrahedral voids. If the formula of the compound is

A_{x} B_{y}

, then the value of

x + y

is in option

Clue 1 of 3: Crystal Structure Basics

Understand the number of atoms and voids in a cubic close-packed (ccp) structure.

🧠 Full Solution Path

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

Element B forms a cubic close-packed (ccp) structure. A ccp structure is equivalent to a face-centered cubic (FCC) lattice. In an FCC unit cell, the effective number of atoms ( $Z$ ) is 4. Therefore, the number of B atoms per unit cell is 4.

The number of tetrahedral voids in a ccp structure is twice the number of effective atoms ( $2 Z$ ). So, the number of tetrahedral voids = $2 \times 4 = 8$ .

Step 2: Calculate the number of atoms of element A○ Expand

Atoms of A occupy $1 / 3$ of the tetrahedral voids. Therefore, the number of A atoms per unit cell is:

Number of A atoms = \frac{1}{3} \times Number of tetrahedral voids = \frac{1}{3} \times 8 = \frac{8}{3}

Step 3: Determine the empirical formula and sum of subscripts○ Expand

The ratio of A atoms to B atoms is $A : B = \frac{8}{3} : 4$ . To obtain whole numbers, multiply both sides by 3:

A : B = 8 : 12

Simplify the ratio by dividing both numbers by their greatest common divisor, which is 4:

A : B = 2 : 3

Thus, the formula of the compound is $A_{2} B_{3}$ . Comparing this to $A_{x} B_{y}$ , we have $x = 2$ and $y = 3$ . The value of $x + y$ is:

x + y = 2 + 3 = 5

💡 Teacher's Secret Hint

Always simplify the ratio of atoms to the smallest whole numbers to get the empirical formula.

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Chemistry Question 61 – NEET-UG 2023

Clue 1 of 3: Crystal Structure Basics

🧠 Full Solution Path