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Lithium borohydride (LiBH)(4) crystalliz...

Lithium borohydride `(LiBH)_(4)` crystallizes in an orthorohombic system having 4 molecules per unit cell. The unit cell dimensions are : `a = 6.81 Å and c = 7.17 Å`. Calculate the density of the crystal (At. Mass of `Li = 7, B = 11, H = 1u)`.

Text Solution

Verified by Experts

Molar mass of `LiBH_4`=7+11+4=22 g `mol^(-1)`
Mass of the unit cell =`(4xx22 "g mol"^(-1))/(6.02xx10^23 "mol"^(-1))=14.62xx10^(-23)g`
Volume of the unit cell = a x b x c =`(6.81xx10^(-8) cm)(4.43xx10^(-8)cm) (7.17xx10^(-8)cm) =21.63xx10^(-23) cm^3`
`therefore` Density of the unit cell =`"Mass"/"Volume"=(14.62xx10^(-23)g)/(21.63xx10^(-23) cm^2)=0.676 g cm^(-3)`
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