Iron metall crystallizes in a body-centered cubic unit cell with an edge length

Question

Iron metall crystallizes in a body-centered cubic unit cell with an edge length of 287 pm. The molar mass of iron is 55.85 g/mol, and its density is 7.86 g/cm^3. Use this data to calculate a value for Avogadro%u2019s number in atoms/mol. I have tried 6.011 x 10^17 but is wrong. Iron metall crystallizes in a body-centered cubic unit cell with an edge length of 287 pm. The molar mass of iron is 55.85 g/mol, and its density is 7.86 g/cm^3. Use this data to calculate a value for Avogadro%u2019s number in atoms/mol. I have tried 6.011 x 10^17 but is wrong.

Explanation / Answer

since structure is bcc

r = sqrt(3)*a/4

a = edge length

r = 124.2746 pm

volime of 1 atom = 4/3 *pi*r^3 = 8038731.152 pm^3

molar mass of iron = 55.85gm

so volume = mass/density = 55.85/7.86 = 7.1055 cm^3

V = 7.1055* (10^10)^3 pm^3

so no of atoms = avagadros no = V/volume of 1 atom = 8.839*10^23

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