Dimension and Density: ength for Ag was determined to be 408.6 pm. Ag crystallizes in a fcc lattice with all atoms at the lattice points. Ag has a density of 10.50 g/cm³. Calculate the mass of a single Ag atom. STRATEGY: We can calculate the unit cell volume. Then, from the density, we can find the mass of the unit cell and then the mass of a single Ag atom. The volume of the cell = a³: V = (408.6 x 10-12 m)3 = 6.822 x 10-29 m³ The density of silver (in g/m³) is: d=10.50 g/cm³ x (1 cm/10-2m)3 = 1.050 x 107 g/m³ The mass of a unit cell is: m = d*V m = 1.050 x 107 g/m³ (6.822 x 10-29 m³) m = 7.163 x 10-22 g Ag/cell Because there are 4 atoms in a fcc cell, the mass of a single Ag atom in the cell m = 7.163 x 10-22 g Ag/cell/ (4 atoms/cell) OR: m = 1.791 x 10-22 g Ag/atom M = rho*V*N/Z = (10.50 g/cm³)(6.822 x 10-29 m³)(10°cm³/m³)(6.022x1023)/4 M = 197.84 g/mol Therefore, 197.84 g/mol/6.022x23 atoms/mol = 1.791 x 10-22 g Ag/atom

Dimension and Density: ength for Ag was determined to be 408.6 pm. Ag crystallizes in a fcc lattice with all atoms at the lattice points. Ag has a density of 10.50 g/cm³. Calculate the mass of a single Ag atom. STRATEGY: We can calculate the unit cell volume. Then, from the density, we can find the mass of the unit cell and then the mass of a single Ag atom. The volume of the cell = a³: V = (408.6 x 10-12 m)3 = 6.822 x 10-29 m³ The density of silver (in g/m³) is: d=10.50 g/cm³ x (1 cm/10-2m)3 = 1.050 x 107 g/m³ The mass of a unit cell is: m = dV m = 1.050 x 107 g/m³ (6.822 x 10-29 m³) m = 7.163 x 10-22 g Ag/cell Because there are 4 atoms in a fcc cell, the mass of a single Ag atom in the cell m = 7.163 x 10-22 g Ag/cell/ (4 atoms/cell) OR: m = 1.791 x 10-22 g Ag/atom M = rhoV*N/Z = (10.50 g/cm³)(6.822 x 10-29 m³)(10°cm³/m³)(6.022x1023)/4 M = 197.84 g/mol Therefore, 197.84 g/mol/6.022x23 atoms/mol = 1.791 x 10-22 g Ag/atom

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

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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