Q12.141CP - Chemistry: Molecular Nature Of Matter And Change

Question

The crystal structure of sodium is based on the body-centered cubic unit cell. What is the mass of one unit cell of Na?

Step-by-Step Solution

Answer

Mass of one unit cell of Na is $46 \mathrm{g}/\mathrm{mol}$.

Definition of crystal structure

In a crystal, the constituent particles form a structure by repeating a symmetric pattern along three dimensions. This symmetric structure of the particles in a crystal is named as crystal structure.

Calculation of mass of one unit cell

$\begin{array}{rcl}\mathrm{Mass} \mathrm{of} \mathrm{a} \mathrm{unit} \mathrm{cell}& =& \mathrm{Number} \mathrm{of} \mathrm{ions} \mathrm{in} \mathrm{the} \mathrm{unit} \mathrm{cell}\\ & & \times \mathrm{mass} \mathrm{of} \mathrm{an} \mathrm{atom} \mathrm{in} \mathrm{the} \mathrm{unit} \mathrm{cell} \mathrm{Number} \mathrm{of} \mathrm{ions} \mathrm{in} \mathrm{body}\\ & & -\mathrm{centered} \mathrm{cubic} \mathrm{unit} \mathrm{cell}\\ & =& \left(\frac{1}{8}\times 8\right)+1\\ & =& 2\end{array}$

Mass of one Na atom $=23 \mathrm{g}/\mathrm{mol}$.

Therefore, the mass of the unit cell of Na is $2\times 23 \mathrm{g}/\mathrm{mol}=46 \mathrm{g}/\mathrm{mol}$.