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love history [14]
4 years ago
11

One crystalline form of silica (SiO2) has a cubic unit cell, and from X-ray diffraction data it is known that the cell edge leng

th 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.
Chemistry
1 answer:
Sav [38]4 years ago
5 0

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.

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