Chapter 3, Problem 3H.5AST

Interpretation Introduction

Interpretation:

Density of sodium chloride has to be determined.

Concept Introduction:

Radius ratio of smaller ion to larger ion in solid state is used to represent relative size of larger ion. This radius ratio is used to predict structure of unit cell from crystal lattice as follows:

$\begin{array}{ccc}\text{Radius ratio}& \text{Crystal structure}& \text{Coordination number}\\ <0.4& \text{zinc-blende structure}& 4\\ 0.4-0.7& \text{rock-salt structure}& 6\\ >0.7& \text{cesium-chloride structure}& 8\end{array}$

Expression to calculate radius ratio $\left(\rho \right)$ is as follows:

  $\rho =\frac{r_{\text{smaller}}}{r_{\text{larger}}}$        (1)

Density of unit cell is as follows:

  $d=\frac{ZM}{a^3{N}_{\text{A}}}$

Here,

$Z$ is atoms in unit cell.

$M$ is molar mass.

$a$ is edge length of unit cell.

$N_{\text{A}}$ is Avogadro number.