Question

Silver crystallizes in a face centred cubic system, 0.408 nm along each edge. The density of silver is 10.6 $g/cm^{3}$ and the atomic mass is 107.9$g/mol.$ Calculate Avogadro's number.

• A. $6.00 \times 10^{23}$atom/mol
• B. $9.31 \times 10^{23}$atom/mol
• C. $6.23 \times 10^{23}$atom/mol
• D. $9.61 \times 10^{23}$atom/mol

Answer 1

Answer: (A)

$6.00 \times 10^{23}$atom/mol

Answer 2

The unit cell has a volume of (0.408

$\times 10^{- 9}m)^{3} = 6.79 \times 10^{- 29}m^{3}$ per unit cell and contains four atoms. The volume of 1 mole of silver is,

$107.9g/mol\left\lbrack \frac{(1 \times 10^{- 2}m)^{3}}{10.6g} \right\rbrack = 1.02 \times 10^{- 5}m^{3}/mol$; where 107.9 g/mol is the molecular mass of the silver

The number of unit cells per mol. is,

$1.02 \times 10^{- 5}m^{3}/mol\left( \frac{1\text{unit cell}}{6.79 \times 10^{- 29}m^{3}} \right) = 1.50 \times 10^{23}$unit cells per mol.

and the number of atoms per mol. is,

$\left( \frac{4\text{atoms}}{\text{unit cell}} \right)\left( \frac{1.50 \times 10^{23}\text{unit cell}}{\text{mol}} \right) = 6.00 \times 10^{23}$ atom/mol.