Question

The edge of the LiCl unit cell is 514 pm in length. Assuming that the ${\mathbf{Li}}^{+}$ions just fit in the octahedral holes of the closest packed ${\mathbf{Cl}}^{-}$ ions, calculate the ionic radii for the ${\mathbf{Li}}^{+}$and ${\mathbf{Li}}^{+}$ ions. Compare them with the radii given in Fig. 13.8, and discuss the significance of any discrepancies.

Short answer

Radius of ${\mathrm{Li}}^{+}\approx 75.25\mathrm{pm}$

Radius of ${\mathrm{Cl}}^{-}\approx 181.75\mathrm{pm}$

Step-by-step solution

Calculating ionic radius of Cl-

${\mathrm{Cl}}^{-}$has an FCC arrangement

The length of the face diagonal = a√2, where a is the edge length

$$\begin{gathered} 4{\mathrm{r}}^{-}=\mathrm{a}\surd 2 \\ {\mathrm{r}}^{-}=\mathrm{a}/\left(2\surd 2\right) \\ {\mathrm{r}}^{-}=514/2.828 \\ {\mathrm{r}}^{-}\approx 181.75\mathrm{pm} \end{gathered}$$

Calculating ionic radius of Li+

Li⁺is present at edge centers

$$\begin{gathered} 2{\mathrm{r}}^{+}+2{\mathrm{r}}^{-}=\mathrm{a} \\ 2{\mathrm{r}}^{+}=514--2\left(181.75\right) \\ 2{\mathrm{r}}^{+}=150.5 \\ {\mathrm{r}}^{+}\approx 75.25\mathrm{pm} \end{gathered}$$

Comparison with fig 13.8

In the figure, it is given that the ionic radii of Li⁺ and Cl^- are 60 pm and 181 pm, respectively.

The discrepancies found are because the ions are closely packed, and attraction exists between the charges. Moreover, LiCl is slightly covalent in nature which causes vacancy defects.