Question

A compound formed by elements X and Y crystallizes in a
cubic structure in which the X atoms are at the corners of a
cube and the Y atoms are at the face centres. The formula of
the compound is
(a) XY₃ (b) X₃Y
(c) XY (d) XY₂

Answer 1

1. The correct answer is (a) XY₃

2. The point at the corner of a cube is 1/8th of a point as it is common to 8 such cubes.

3. The point a a face centre is half of a point as it is common to 2 such cubes.

4. As there are 8 corners in a cube, thus X= 1/8*8 = 1

5. As there 6 faces in a cube, thus

Y= 1/2*6=3

6. Hence the formula for the compound is XY3

Answer 2

Formula of the compound is XY3.

Explanation:

• The cubic structure of crystal is very commom in inorganic chemistry.

• The cube has 8 corners, 12 edges and 6 faces.

• If we imagine a ball placed at a corner of a cube, then it's shared by 8 cubes.

• So 1 cube gets 1/8th of a ball.

• Similarly, if we imagine a ball placed at a face of a cube, then its shared by 2 cubes.

• So one cube gets 1/2 of a ball.

• So inside the cube, amount of X = $1/8 \times 8$ = 1.

• Inside the cube amount of Y = $1/2 \times 6$ = 3.

• So the formula of the crystal is XY3.

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