Question

he density of potassium bromide crystal is $\,2.75g/c{m^3}\,$ and the length of an edge of the unit cell is $654pm$ .The unit cell of $KBr$ is one of the three types of cubic unit cell. How many formula units of $KBr$ are there in a unit cell? $[KBr = 119]$
A.$2$
B.$4$
C.$6$
D.$8$

Answer 1

The answer for this question can be obtained by using the formula to calculate density of the unit cell. A unit cell's density is given as the ratio of the unit cell's mass and volume. The mass of a unit cell is proportional to the product of a unit cell's number of atoms and a unit cell's mass of each atom.
Formula used:
$\rho = \dfrac{{Z \times M}}{{{N_A} \times {a^3}}}$
Where $Z$= Number of formula units
$M$= Molar mass of $KBr$
${N_A}$= Avogadro number
$a$ = Edge length

Complete step by step answer:
Let us analyze the given data;
Density $\rho = 2.75g/c{m^3}$
Edge length $a = 654pm$ which is equal to $654 \times {10^{ - 10}}cm$
Molar mass of $KBr$ $= 119g/mol$
We Know that formula for calculating the density of unit cell is,
$\rho = \dfrac{{Z \times M}}{{{N_A} \times {a^3}}}$
From this we can arrange the formula for calculating the number of formula units $Z$, that is,
$Z = \dfrac{{\rho \times {N_A} \times {a^3}}}{M}$
$= \dfrac{{2.75 \times 6.022 \times {{10}^{23}} \times {{(654 \times {{10}^{ - 10}})}^3}}}{{119}}$
$= 3.9$ which is approximately equal to $4$.
So, the right answer is option B that is $4$.

Additional information:
Formula unit is the simplest ratio at which an ionic compound exists. Or simply we can say its empirical formula. The number of formula units is the number of atoms per unit cell which is denoted by $Z$.

Note:
Note that while doing the calculations $654pm$ should be changed to $cm$ since the value of density in question is given in $g/c{m^3}$, Otherwise the answer would be incorrect. $\,1\,centimetre\,$ is equal to $\,10000000000\,picometre\,$ . In addition, note that not all the particles in the shape of the unit cell are complete. Its corner particles will still add up to one whole particle for the fractional particles in the unit cell, its face particles (for face-centered lattices) add up to three whole particles, and one for the base particles.