NH 4 Br has a face-centered cubic unit cell in which the Br - anions occupy corn
ID: 834529 • Letter: N
Question
NH4Br has a face-centered cubic unit cell in which the Br- anions occupy corners and face centers, while the cations fit into the hole between adjacent anions. What is the radius of NH4+ if the ionic radius of Br- is 195.0 pm and the density of NH4Br is 2.429 g/cm3? Hint: notice that the cation and anion touch each other and together make up the side of the cube.
NH4Br has a face-centered cubic unit cell in which the Br- anions occupy corners and face centers, while the cations fit into the hole between adjacent anions. What is the radius of NH4+ if the ionic radius of Br- is 195.0 pm and the density of NH4Br is 2.429 g/cm3? Hint: notice that the cation and anion touch each other and together make up the side of the cube.
Explanation / Answer
Start with the density and convert it to molecules/cm3:
(2.429 g/cm3) x [(6.022x10^23 NH4Br molecules)/(97.95 g NH4Br)] = 1.493x10^22 molecules/cm3
Since a fcc has a total of four molecules per unit cell, we can determine the volume of the unit cell:
[(4 molecules)/(1 unit cell)] x [(1 cm3)/(1.493x10^22 molecules)] = 2.679x10^-22 cm3/unit cell
from this we can determine the edge of the unit cell:
(2.679x10^-22 cm3)^1/3 = 6.446x10^-8 cm or 644.6 pm
Finally, since the edge of the unit cell equals 2ra + 2rc, where ra is the radius of the anion and rc is the radius of the cation, then you know:
644.6 = 2(195.0) + 2rc
rc = 127.3 pm
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