Lithium borohydride, , crystallizes in an orthorhombic system with four molecules per unit cell. The — Solid State Chemistry Question
Question
Lithium borohydride, $LiBH_4$, crystallizes in an orthorhombic system with four molecules per unit cell. The unit cell dimensions are: $a = 6.0$ Å, $b = 4.4$ Å and $c = 7.5$ Å. The density of crystals is (Li = 7, B = 11, $N_A = 6 \times 10^{23}$)
💡 Solution & Explanation
Molar mass of $LiBH_4 = 7 + 11 + 4(1) = 22$ g/mol. Volume $V = a \times b \times c = 6.0 \times 4.4 \times 7.5 \times 10^{-24}$ cm$^3 = 198 \times 10^{-24}$ cm$^3$. Density = $\frac{Z \times M}{N_A \times V} = \frac{4 \times 22}{6 \times 10^{23} \times 198 \times 10^{-24}} = \frac{88}{118.8} \approx 0.74$ g/cm$^3$. Therefore, correct answer is A.