Question

Lithium borohydride $\left(LiB{H}_4\right)$ crystallizes in an orthorhombic system with $4$ molecules per unit cell. The unit cell dimensions are $a=6.8$ $\mathring{A}$, $b=4.4$ $\mathring{A}$ and $c=7.2$ $\mathring{A}$. If the molar mass of the compound is $21.76$ g/mol, the density (in g cm${}^{-3}$) of the compound will be:

• A. $0.67$
• B. $0.33$
• C. $1.72$
• D. none of the above

Answer 1

Answer: (A)

$0.67$

Density $=\frac{zM}{N_A\times (abc\times {10}^{-24})}$

Density $=\frac{4\times 21.76}{6.023\times {10}^{23}\times (6.8\times 4.4\times 7.2\times {10}^{-24})}$

Density $=0.67{\text{gcm}}^{-3}$

Hence, the correct option is $\text{A}$