Question

Argon has a cubic closest packed structure as a solid. Assuming that argon has a radius of 190 pm. Calculate the density of solid argon.

Short answer

The density of solid argon is$1.71g/c{m}^3$ .

Step-by-step solution

The density

The density of a substance can be determined by using the formula:

$Density = \frac{mass}{volume}$

Determining the face diagonal

The compound Ar is cubic closest packed solid. There are four Ar atoms per unit cell, and the atoms touch along the face diagonal with a face-centered unit cell.

$Let l = length of cube edge$

$$\begin{gathered} Face diagonal = 4r = l\sqrt{2}, \\ l = 4(190 pm)/\sqrt{2} \\ = 537pm \\ = 5.37 \times {10}^{-8} cm \end{gathered}$$

$$\begin{gathered} Density = \frac{mass}{volume} \\ = \frac{4atoms \times \frac{1 mol}{6.022 \times {10}^{23} atoms}\times \frac{39.95 g}{mol}}{{(5.37 \times {10}^{-8} cm)}^3} \\ = 1.71 g/c{m}^3 \end{gathered}$$