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Question: Lithium borohydride\((LiBH_{4}),\) crystallises in an orthorhombic system with 4 molecules per unit ...

Lithium borohydride(LiBH4),(LiBH_{4}), crystallises in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are :a = 6.81Å, b= 4.43Å, c=717Å. If the molar mass of LiBH4LiBH_{4} is 21.76 gmol−1gmol^{- 1}. The density of the crystal is –

A

0.668 gcm−3gcm^{- 3}

B

0.585gcm20.585gcm^{2}

C

1.23gcm−31.23gcm^{- 3}

D

None

Answer

0.668 gcm−3gcm^{- 3}

Explanation

Solution

We know that,

ρ=ZMN0V=4×(21.76gmol−1)(6.023×1023mol−1)(6.81×4.43×7.17×10−24cm3)=0.668gcm−3\rho = \frac{ZM}{N_{0}V} = \frac{4 \times (21.76gmol^{- 1})}{(6.023 \times 10^{23}mol^{- 1})(6.81 \times 4.43 \times 7.17 \times 10^{- 24}cm^{3})} = 0.668gcm^{- 3}