Copper Iodide (CuI) can form in either a table-salt like cubic lattice structure
ID: 897915 • Letter: C
Question
Copper Iodide (CuI) can form in either a table-salt like cubic lattice structure, or the complex structure shown below. In the salt-like structure, CuI is a good iodine supplement for the plant goats, who keep the grass on the hillside cut short (an important safety function credited in the FSAR to prevent loss of offsite power through grass fires). However, in the complex structure at right, the material can be fatal to your safety-related goats. Calculate the density of each phase, so that the purchasing department can verify that they are obtaining the correct form of CuI. Note: you would have to make some assumption in order to calculate the edge length of the unit cell at right, but let’s say that it is a cube and that the two interior atoms are at the bcc center position and the center of the bottom face, which is close enough for a rough density value.
Explanation / Answer
(i) Rock-salt structure of CuI(alpha-CuI):
FCC arrangement of I- ions
Ionic radius of I-, rI- = 206 pm
Edge length for fcc:
a = 2^(3/2)*r = 2*1.414*206 = 582.66 pm
volume of cell, V = a^3 = 1.97E8 pm3 = 1.97E-22cm3
no of I- ions, Zeff(I-) = 4
Cu+ occupy octahedral(Oh) voids:
No of Cu+ ions, Zeff(Cu+) = 4
No of formula units CuI = 4
Molar mass of CuI, MW = 190.45 g/mol
Mass of unit cell, W = 4*190.45/(6.02E23)=0.126E-20 gm
Volume of unit cell, V = 1.97E-22 cm3
Density = 0.126E-20/1.97E-22=6.4 gm/cm3
(ii)Wurtzite structure of CuI(beta-CuI):
FCC arrangement of I- ions
Ionic radius of I-, rI- = 206 pm
Edge length for fcc:
a = 2^(3/2)*r = 2*1.414*206 = 582.66 pm
volume of cell, V = a^3 = 1.97E8 pm3 = 1.97E-22cm3
no of I- ions, Zeff(I-) = 4
Cu+ occupy half of tetrahedral(Th) voids:
No of Cu+ ions, Zeff(Cu+) = 4
No of formula units CuI = 4
Molar mass of CuI, MW = 190.45 g/mol
Mass of unit cell, W = 4*190.45/(6.02E23)=0.126E-20 gm
Volume of unit cell, V = 1.97E-22 cm3
Density = 0.126E-20/1.97E-22=6.4 gm/cm3
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