Question

One crystalline form of silica (SiO2) has a cubic unit cell, and from X-ray diffraction data it is known that the cell edge length is 0.700 nm. If the measured density is 2.32 g/cm3, how many (a) Si4+ and (b) O2- ions are there per unit cell? The atomic weights of Si and O are, respectively, 28.09 g/mol and 16.00 g/mol.

Answer 1

8 Silicon atom are present in unit cell.

16 oxygen atoms are present unit cell.

Step-by-step explanation:

Number of atoms in unit cell = Z =?

Density of silica = tex]2.32 g/cm^3[/tex]

Edge length of cubic unit cell = a = 0.700 nm =
`0.700* 10^(-7) cm`

`1 nm=10^(-7) cm`

Molar mass of Silica =
`28.09 g/mol+16.00* 2=60.09 g/mol`

Formula used :

`\rho=(Z* M)/(N_(A)* a^(3))`

where,

`\rho` = density

Z = number of atom in unit cell

M = atomic mass

`(N_(A))` = Avogadro's number

a = edge length of unit cell

On substituting all the given values , we will get the value of 'a'.

`2.32 g/cm3=(Z* 60.09 g/mol)/(6.022* 10^(23) mol^(-1)* (0.700* 10^(-7)cm)^(3))`

`Z = 8`

1 silicon is 2 oxygen atoms. then 8 silicon atoms will be 16 oxygen atoms.