Question

Ice crystallises in a hexagonal lattice. At low temperature at which the structure was determined, the lattice constants were $a=4.53\mathring{A}$ and $c=7.41\mathring{A}$. How many $H_{2}O$ molecules are contained in a unit cell? $\left(d_{\text{ice }}=0.92g/c{m}^3\right)?$

Answer 1

Answer: 4

Density of ice $=0.92g/c{m}^3$

Volume of unit cell $=a\times a\sin 60^{\circ }\times c=a^2\sin 60^{\circ }\times c$

$={\left(4.53\times 10^{-8}\right)}^2\frac{\sqrt{3}}{2}\times 7.41\times 10^{-8}c{m}^3$

$=131.688\times 10^{-24}c{m}^3$

$d=\frac{M}{a^3{N}_0}$

$\therefore M$ (unit cell) $=d{a}^3{N}_0$

Molar mass of $H_{2}O=18gmo{l}^{-1}$

Thus, number of $H_{2}O$ molecules in one unit cell

$=\frac{72.97}{18}\approx 4$