Concept explainers
Iron crystallizes in a body-centered cubic lattice. The cell length as determined by X-ray diffraction is 286.7 pm. Given that the density of iron is 7.874 g/cm3, calculate Avogadro’s number.
Interpretation:
The Avogadro’s number of Iron atom in its body centered cubic lattice has to be calculated.
Concept Introduction:
In packing of atoms in a crystal structure, the atoms are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing forms two types of lattices – body – centered lattice and face – centered lattice.
In body-centered cubic unit cell, each of the six corners is occupied by every single atom. Center of the cube is occupied by one atom. Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared. Thus the number of atoms per unit cell in BCC unit cell is,
Answer to Problem 12.123QP
The Avogadro’s number of Barium atom in its body centered cubic lattice is calculated as
Explanation of Solution
One mole of Iron has mass of
Edge length of the cubic unit cell is given. The cubic value of edge length gives the volume of the unit cell. In each cell of unit cell of body centered cubic lattice, 2 Iron atoms are occupied.
The Avogadro’s number of Iron atom in one mole of Iron is,
Dividing the volume of one mole Iron atoms by volume of one mole of Iron atoms in its unit cell gives the Avogadro’s number of Iron atoms in one mole of Iron.
The Avogadro’s number of Iron atom in its body centered cubic lattice has been calculated.
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Chapter 12 Solutions
CHEMISTRY:ATOMS FIRST-2 YEAR CONNECT
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