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Assume X has a body- centered cubic lattice with all atoms at the lattice points. The edge length of the unit cell is 316.0 pm. The atomic weight of X is 154.0 amu. Calculate its density. Density = 3 g/cm'

Assume X has a body- centered cubic lattice with all atoms at the lattice points. The edge length of the unit cell is 316.0 pm. The atomic weight of X is 154.0 amu. Calculate its density. Density = 3 g/cm'

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Assume X has a body- centered cubic lattice with all atoms at the lattice points. The edge length of the unit cell is 316.0 pm. The atomic weight of X is 154.0 amu. Calculate its density. Density = 3 g/cm
Transcribed Image Text:Assume X has a body- centered cubic lattice with all atoms at the lattice points. The edge length of the unit cell is 316.0 pm. The atomic weight of X is 154.0 amu. Calculate its density. Density = 3 g/cm
Expert Solution
Step 1

In a body centered unit cell one atom exist in the center and eight 1/8 atom lies in the corner of the unit cell.

Therefore total number of atoms in a body centered unit cell, n = 1 + (8 x 1/8) = 1+ 1 =2 atoms

Knowing the unit cell dimension, the theoretical density can be calculated using the relation,

                                           Chemistry homework question answer, step 1, image 1

where,  ρ is the density of the crystal

              n  is the number of atoms in the unit cell = 2

             M is the atomic weight of element X = 154.0 amu = 154.0 g/mol

             NA is the Avogadro’s number = 6.022 x 1023 mol-1

              a is the edge length of the unit cell  =316.0 pm = 3.16 x 10-8 cm

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