Lithium borohydride, 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 Åand c= 7.17 Å . Calculate the density of the crystal. Take atomic mass of Li= 7, B =11 and H =1 a.m.u

Lithium borohydride, LiBH_(4) , crystallizes in an orthorhombic system

1.	Lithium borohydride, 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 Åand 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» Solution :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)`