Question

Lithium borohydride crystallizes in an orthorhombic system with $4$ molecules per unit cell. The unit cell dimensions are $a=6.8\mathring{A}$, $b=4.4\mathring{A}$ and $c=7.2\mathring{A}$. If the molar mass is

$21.76$ g mol${}^{-1}$, calculate the density (in g cm${}^{-3}$) of crystal.

• A. $1.34$
• B. $0.87$
• C. $0.94$
• D. $0.67$

Answer 1

The correct option is D $0.67$

The expression for density is as follows:

$\text{Density}=\frac{n\times \text{Molar mass}}{V\times N_a}$
Here,

$n=4$

$M=21.76$ g mol${}^{-1}$

$N_a=6.023\times {10}^{23}$

$V=a\times b\times c$
$\therefore V=6.8\times {10}^{-8}\times 4.4\times {10}^{-8}\times 7.2\times {10}^{-8}$ $=2.154\times {10}^{-22}$ cm${}^3$
$\therefore \text{Density}=\frac{4\times 21.76}{2.154\times {10}^{-22}\times 6.023\times {10}^{23}}$ $=0.6709$ g cm${}^{-3}$