Lithium borohydride (LiBH4), crystallises in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are: a = 6.81 Ao, b = 4.43 Ao, C = 7.17 Ao. If the molar mass of LiBH4 is 21.76 g mol-1. The density of the crystal is

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Lithium borohydride (LiBH₄), crystallises in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are: a = 6.81 $\overset{o}{A}$ , b = 4.43 $\overset{o}{A}$ , C = 7.17 $\overset{o}{A}$ . If the molar mass of LiBH₄ is 21.76 g mol^-1. The density of the crystal is

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1.23 g cm^-3

None of these

0.585 g cm²

0.668 g cm^-3

answer is A.

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Detailed Solution

$We know that, ρ = \frac{ZM}{NV}$ $= \frac{4 \times (21.76 g {mol}^{- 1})}{(6.023 \times 10^{23} {mol}^{- 1}) (6.81 \times 4.43 \times 7.17 \times 10^{- 24} {cm}^{3})} = 0.668 {cm}^{- 3}$