Question

Calculate the radius ratio for CaO if the ionic radii of Ca2 and O2– are 100 pm and 140 pm, respectively.

Based on the radius ratio above, what is the expected coordination number of CaO? The range of radius ratios for each coordination number is given in parentheses.

If the density of solid iron is 7.87 g/cm3, what is the packing efficiency of Fe if it adopts a body-centered cubic unit cell? The molar mass of Fe is 55.847 g/mol.

Determine the empirical formula of the compound with a crystal structure where beryllium ions occupy all of the tetrahedral holes in a cubic close-packed (ccp) array of carbon anions.

Determine the empirical formula of the compound with a crystal structure where boron ions occupy one-half of the tetrahedral holes in a cubic close-packed (ccp) array of nitrogen anions.

Determine the empirical formula of the compound with a crystal structure where silver ions occupy all of the octahedral holes in a cubic close-packed array of chlorine anions.

Answer 1

1 ) radius ratio = Rcation / R anion = 100 / 140

= 0.714

this is the range in between 0.414 -0.732 . so geometry is octahedral .

coordination number = 6

2)

for BCC , Z =2 ,

M = 55.847 g /mol given

d = 7.87 g /cm^3

d = Z M / N a^3

7.87 = 2 x 55.847 / (6.023 x 10^23) x a^3

a^3 = 2.4 x 10^-23 cm^3

for Fe atom radius = 126 pm = 126 x 10^-12 m = 1.26 x 10^-8 cm

packing efficiency = { 2 x (4/3) r^3 / a^3 } x 100

= {2 x (4/3 ) x 3.14 x (1.26 x10^-8) / 2.4 x 10^-23 } x 100

= 68 %

3)   

for each tetrahedral hole 2 atoms are occupied.

carbon at cubic that means corner .

Carbon atoms per unit cell = 8 x 1/8 = 1

so empirical formula : Be2C

4 )

for half tetrahedral hole = B atoms = 1

for cubic arry N aroms =1

empirical formula = BN

5)

each octahedral holes takes one atom . so number of silver atoms = 1

chlorine atoms occupy cubic pack so number of atoms of Cl = 1

empirical formual = AgCl