Question

Lithium boron hydride crystallizes in an orthorhombic system with 4 molecules per unit cell. Dimensions of the unit cell are:
$a=6\stackrel{\circ }{A},\text{b}=4\stackrel{\circ }{A}$ and $c=7\stackrel{\circ }{A}$.
If the molar mass is $21g$, calculate the density of crystal.

• A. $0.99g/c{m}^3$
• B. $0.83g/c{m}^3$
• C. $1.25g/c{m}^3$
• D. $1.50g/c{m}^3$

Answer 1

The correct option is B $0.83g/c{m}^3$

Density $=\frac{Zm}{N_{A}v}$

Given $Z=4$
$m=21g$
$v=a\times b\times c$
$=6\times {10}^{-8}\times 4\times {10}^{-8}\times 7\times {10}^{-8}$
$=1.68\times {10}^{-22}c{m}^3$

Density$=\frac{4\times 21}{6.02\times {10}^{23}\times 1.68\times {10}^{-22}}=0.83g/c{m}^3$