# Lithium borohydrides, LiBH4, crystallizes in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are: a = $6.81 A^{\large\circ}, b = 4.43 A^{\large\circ}$ and $c = 7.17 A^{\large\circ}$. Calculate the density of the crystal. Take atomic mass of Li = 7, B = 11 and H = 1 a.m.u.

Molar mass of LiBH4 = 7 + 11 + 4 =$22 g mol^{−1}$
Mass of the unit cell =$\large\frac{4\times 22gmol^{-1}}{6.02\times 10^{23}mol^{-1}}$$=14.62\times 10^{-23}g$
Volume of the unit cell = $a \times b \times c$
$\Rightarrow (6.81 × 10^{−8 }cm) (4.43 × 10^{−8} cm) (7.17 × 10^{−8} cm)$
$\Rightarrow 21.63 × 10^{−23 }cm^3$
$\therefore$ Density of the unit cell =$\large\frac{\text{Mass}}{\text{Volume}}=\frac{14.62\times 10^{-23}}{21.63\times 10^{-23}cm^3}$
$\Rightarrow 0.676gcm^{-3}$