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

Answer:

8 Silicon atom are present in unit cell.

16 oxygen atoms are present unit cell.

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 = $0.700\times 10^{-7} cm$

$1 nm=10^{-7} cm$

Molar mass of Silica  = $28.09 g/mol+16.00\times 2=60.09 g/mol$

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$

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'.

$2.32 g/cm3=\frac{Z\times 60.09 g/mol}{6.022\times 10^{23} mol^{-1}\times (0.700\times 10^{-7}cm)^{3}}$

$Z = 8$

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