Question

Lithium borohydribe, `LiBH_4`, crystallizes in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are : a=6.81 Å, b=4.43 Å and c=7.17 Å.Calculate the density of the crystal. Take atomic mass of Li=7, B=11 and H=1 a.m.u.

Answer 1

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)`