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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 = `( 4 xx 22 " g mol"^(-1))/(6.022 xx 10^(23)"mol"^(-1)) = 14.62 xx 10^(-23) g`
Volume fo the unit cell = ` a xx b xx c `
` ( 6.81 xx 10^(-8) cm) ( 4.43 xx 10^(-8) cm) ( 7.17 xx 10^(-8) cm) = 21. 63 xx 10^(-23) "cm"^(3)`
Density of the unit cell = `("Mass")/("Volume") = ( 14.62 xx 10^(-23)g)/(21.63 xx 10^(-23) cm^(2)) = 0.676 g cm^(-3)`
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