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

0.6708 gm/cm³

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0.7608 gm/cm³

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0.8808 gm/cm³

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0.5608 gm/cm³

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Solution

The correct option is A
0.6708 gm/cm³

Since,
Density, $ρ = \frac{n \times M}{V o l u m e \times A v . N o}$
Where n = 4, Av. No = $6.023 \times 10^{23}$ , and Volume = V = $(a \times b \times c) c m^{3}$
$= 6.8 \times 10^{- 8} \times 4.4 \times 10^{- 8} \times 7.2 \times 10^{- 8} c m^{3} = 2.154 \times 10^{- 22} c m^{3} ∴ d e n s i t y, ρ = \frac{4 \times 21.76}{2.154 \times 10^{- 22} \times 6.023 \times 10^{23}} = 0.6708 g c m^{- 3}$

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