Question

Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure was determined, the lattice constants were $a=34\mathring{A}$ and $c=7.41\mathring{A}$. How many $H_{2}O$ molecules are contained in a unit cell? (The density of ice is $0.92g/cc$ at $0^{o}C$ A unit cell of $H_{2}O$ is shown.)

Answer 1

Volume of unit cell, $V=$ Area of Base $\times$ Height

$=2\times \frac{\sqrt{3}}{4}{a}^2\times c$

$=2\times \frac{\sqrt{3}}{4}\times 1156\times {10}^{-16}\times 7.41\times {10}^{-8}$ $c{m}^3$

Mass of unit cell $=V\times S$

$=7.409\times {10}^{-21}\times 0.92$

$=6.816\times {10}^{-21}$ $gm$

Let there be $N$ water molecules in the given cell

$⟹6.816\times {10}^{-21}=n\times \frac{18}{6.023\times {10}^{23}}$

$⟹n=227.9\approx 228$ $H_{2}O$ molecules