Question

. Metallic iron has a body-centered cubic lattice with all atoms at lattice points and a unit cell whose edge length is 286.6 pm. The density of iron is 7.87 g cm–3 . What is the mass of an iron atom? Compare this value with the value you obtain from the molar mass

Answer 1

Answer:

$\large \boxed{\text{55.8 u}}$

Explanation:

1. Calculate the volume of the unit cell

V = l³ = (2.866 × 10⁻⁸ cm)³ = 2.354 × 10⁻²³ cm³

2. Calculate the mass of a unit cell

$\text{Mass} = 2.866 \times 10^{-23}\text{ cm}^{3} \times \dfrac{\text{7.87 g}}{\text{1 cm}^{3}} = 1.853 \times 10^{-22} \text{ g}$

3. Calculate the mass of one atom

A body-centred unit cell contains two atoms.

$\text{Mass of 1 atom} = \dfrac{1.853 \times 10^{-22} \text{ g}}{\text{2 atoms}} \times \dfrac{\text{1 u}}{1.661 \times 10^{-24}\text{ g}} = \textbf{55.8 u}\\\\\text{The molar mass of Fe from the Periodic Table is \large \boxed{\textbf{55.845 g/mol}} }$