Calcium carbide crystallizes as a cube with 1 calcium ion on each corner and one calcium...

Calcium carbide crystallizes as a cube with 1 calcium ion on each corner and one calcium ion in the center of the cell. There are 8 carbon atoms located along edges of the cell and there are two carbons internal to the cell. What is the formula of calcium carbide?

Ca₂C₃

CaC₄

CaC₃

CaC₂

CaC

Expert Solution

A cube has 8 corners and 12 edges. In a cubic unit cell, 8 atoms at the corners are shared by the 8 neighbouring cells and atom at each edge is shared by 4 neighbouring atoms.
Therefore, Calcium atoms at corners that belong to one unit cell =

1 Ca atom is at centre that completely belongs to that one unit cell.
Total number of Ca atoms in a unit cell = 1+ 1 = 2
Now there are 8 carbon atoms along edges of the cell. Thus, C atoms that belongs to one unit cell is

Additionally, there are two carbon atoms present in the cell. Therefore, total number of C atoms in a unit cell = 4
Hence, the formula for calcium carbide is Ca₂C₄ or CaC₂.
Therefore, the correct option is CaC₂.

queen_honey_blossom answered 2 years ago

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