Chapter 12

Q. 12.3.3

Copper(I) iodide crystallizes with the zinc blende structure. If the edge length of the unit cell is 605 pm, what is the density (in g/cm³) of crystalline CuI?


Verified Solution

You are asked to calculate the density of a solid.
You are given the identity and crystal structure of the solid and the edge length of the unit cell.
Density is calculated from the mass and the volume of the unit cell.
Step 1. Calculate the mass of the unit cell using the fact that there are four formula units per unit cell in the ZnS structure.

\frac{4 \text{ CuI formula units}}{1\text{ unit cell}}\times \frac{1\text{ mol Cul}}{6.022\times 10^{23}\text{ Cil formula units}} \times \frac{190.45\text{ g}}{1\text{ mol Cul}}

= 1.27 \times 10^{-21} g/unit cell

Step 2. Calculate the volume of the unit cell (in cm³) from the edge length.
edge length = 605 pm

605 pm \times\frac{10^{2}\text{ cm}}{10^{12 }\text{ pm}} =6.05\times 10^{-8} cm

volume = a³ = \left(6.05\times 10^{-8}\text{ cm}\right)^{3}=2.21\times 10^{-22} cm³

Step 3. Calculate density from the mass and volume of the unit cell.

density = \frac{\text{mass}}{\text{volume}}=\frac{1.27\times 10^{-21}\text{ g}}{2.21\times 10^{-22}\text{ cm}^{3}} = 5.71 g/cm³