A solid metal oxide crystallizes in a cubic unit cell. In the unit cell there are metal (M) ions on every corner and in the center of every face. Oxide ions (O) are found in half of the tetrahedral holes. What is the empirical formula of this metal oxide?

Respuesta :

Answer:

The empirical formula of the solid metal oxide is : [tex]MO[/tex]

Explanation:

M atom is present in the every corner and in the center of every face.

Number of m atoms :

[tex]\frac{1}{8}\times 8+\frac{1}{2}\times 6=4[/tex]

Number of tetrahedral voids in F.C.C = 2n = 2 × 4 = 8

Oxide ion is present in the half of the tetrahedral void

Number oxide ions = [tex]\frac{8}{2}=4[/tex]

The molecular formula of the solid metal oxide is : [tex]M_4O_4=MO[/tex]

The empirical formula represent the lowest number of atoms present in a compound.

The empirical formula of the solid metal oxide is : [tex]MO[/tex]

The empirical formula of this metal oxide is MO.

Calculation of the empirical formula:

Since m atom should be presented in every corner and should be centered for every face.

So here the no of atoms should be

= 1/8 *8 + 1/2 * 6

= 4

Now

Number of tetrahedral voids in F.C.C = 2n = 2 × 4 = 8

And,

Oxide ion should be present in the half of the tetrahedral void

So, the number of oxide ions should be

= 8/2

= 4

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