Question

BaCl2 crystallizes such that the Ba2+ ions are in a face-centered cubic arrangement and the Cl- ions are in the holes of the lattice (fluorite structure). How many Cl- ions are present in one unit cell of this crystal?

Answer 1

BaCl2 crystallizes such that the Ba2+ ions are in a face-centered cubic arrangement and the Cl- ions are in the holes of the lattice (fluorite structure). The numbers of Cl- ions present in one unit cell of this crystal is 8.

The Cubic system arrangement is one in which the unit cell is shaped like a cube.

A face centered cubic arrangements (FCC) is an atom arrangement located in nature. FCC structural unit cell is made up of atoms organized in a cube with fraction of an atom in each corner and six additional whole atoms in the middle of the cube face.

From the information given;

• Ba2+ is found in the FCC arrangements

The total number of Ba2+ atom present within the unit cell can be computed as:

$\mathbf{(6 \ face \: \: sharing \: atom)( \dfrac{1}{2}) \: + (8 \: edges)( \dfrac{1}{8} \: corner \: sharing \: atoms)}$

$\mathbf{ = 4 \: atoms}$

From the formula for BaCl2; since there is twice number of Cl- present as that of Ba2+;

• Then, the number of Cl- present per unit cell is:
• = 4 × 2
• = 8

Therefore, we can conclude that the numbers of Cl- ions present in one unit cell of this crystal is 8.

Learn more about cubic arrangements here:

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