Chapter 3 Solutions - Chapter 3 Homework Solutions 3.3....

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Chapter 3 Homework Solutions 3.3. Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight of 95.94 g/mol. Compute its theoretical density and compare it with the experimental value found inside the front cover. This problem calls for a computation of the density of molybdenum. According to Equation 3.5 ρ = nA Mo V C N A For BCC, n = 2 atoms/unit cell, and realizing that V C = a 3 , and using Equation 3.3 V C = 4 R 3 3 Thus, ρ = nA Mo 4 R 3 3 N A (2 atoms/unit cell)(95.94 g/mol) (4) ( 0.1363 × 10 -7 cm ) /3 [] 3 /(unit cell) ( 6.02 × 10 23 atoms/mol ) = 10.22 g/cm 3 The value given inside the front cover is 10.22 g/cm 3 . 3.11. Demonstrate that the minimum cation-to-anion radius ratio for a coordination number of 8 is 0.732. This problem asks us to show that the minimum cation-to-anion radius ratio for a coordination number of 8 is 0.732. From the cubic unit cell shown below
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the unit cell edge length is 2r A , and from the base of the unit cell x 2 = (2 r A ) 2 + (2 r A ) 2 = 8 r A 2 or x = 2 r A 2 Now from the triangle that involves x, y, and the unit cell edge x 2 + (2 r A ) 2 = y 2 r A +2 r C ) 2 ( 2 r A 2 ) 2 + 4 r A 2 r A + 2 r C ) 2 which reduces to 2 r A ( 3 1 ) r C or r C r A = 3 1 = 0.732 3.22. We are asked list point coordinates for both sodium and chlorine ions for a unit cell of the sodium chloride crystal structure, which is shown in Figure 3.5.
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This note was uploaded on 07/12/2010 for the course CHE 253 taught by Professor Carrion during the Spring '08 term at University of Louisville.

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Chapter 3 Solutions - Chapter 3 Homework Solutions 3.3....

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