Question

Lithium borohydride crystallizes in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are a = 6.8 $\stackrel{\circ }{A}$ , b = 4.4 $\stackrel{\circ }{A}$ and c = 7.2 $\stackrel{\circ }{A}$. If the molar mass is 21.76 g, calculate density of the crystal.

• A. 0.6708 gm/cm³
• B. 0.7608 gm/cm³
• C. 0.8808 gm/cm³
• D. 0.5608 gm/cm³

Answer 1

The correct option is A

0.6708 gm/cm³

Since,
Density, $\rho =\frac{n\times M}{Volume\times Av.No}$
Where n = 4, Av. No = $6.023\times {10}^{23}$ , and Volume = V = $(a\times b\times c)c{m}^3$

$=6.8\times {10}^{-8}\times 4.4\times {10}^{-8}\times 7.2\times {10}^{-8}c{m}^3=2.154\times {10}^{-22}c{m}^3\therefore density,\rho =\frac{4\times 21.76}{2.154\times {10}^{-22}\times 6.023\times {10}^{23}}=0.6708gc{m}^{-3}$