Question

Lithium borohydride $\left(LiB{H}_4\right)$, crystallizes in an orthorhombic system with $4$ molecules per unit cell. The unit cell dimensions are $a=6.22\stackrel{\circ }{\text{A}}$, $b=5\stackrel{\circ }{\text{A}}$, $c=7\stackrel{\circ }{\text{A}}$. If the molar mass of $LiB{H}_4$ is $21.76{\text{g mol}}^{-1}$. The density of the crystal is:
$(N_A=6\times {10}^{23})$

• A. $0.666{\text{g cm}}^{-3}$
  
• B. $0.585{\text{g cm}}^{-3}$
  
• C. $1.23{\text{g cm}}^{-3}$
  
• D. None of these

Answer 1

The correct option is A $0.666{\text{g cm}}^{-3}$


$\text{Volume of the unit cell}=6.22\times 5.00\times 7.00=217.7(\stackrel{\circ }{A}{)}^3$
$\text{Density}=\frac{4\times \text{molar mass}}{\text{volume}\times 6\times {10}^{23}\times ({10}^{-8}{)}^3}$
$=\frac{4\times 21.76}{217.7\times 6\times {10}^{23}\times ({10}^{-8}{)}^3}$
$\approx \frac{4\times 1}{6\times 1}$
$=0.66{\text{g cm}}^{-3}$.