Question

The density of potassium bromide crystal is $2.75gc{m}^{-3}$ and the length of an edge of a unit cell is $654pm$. The unit cell of $KBr$ is one of three types of cubic unit cells. How many formula units of $KBr$ are there in a unit cell? Does the unit cell have a $NaCl$ or $CsCl$ structure?

Answer 1

Given that,

Density of the crystal, $\rho =2.75g.c{m}^{-3}$

Edge length, $a=654pm$

Molar mass, $M=119g/mol$

We know that,

$\rho =\frac{z}{a^3}\times \left[\frac{M}{N_A}\right]$

$z=\frac{\rho \times a^3\times N_A}{M}$

$z=\frac{2.75\times (654\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}}{119}=3.89\approx 4$

Number of mass points per unit cell $=4$

It is $NaCl$ type crystal, i.e., fcc structure.