Ice crystallizes in a hexagonal lattice. At a certain low temperature the lattice constants are $\mathrm{a} = 4.53\stackrel{°}{\mathrm{A}}$ and $\mathrm{c}=7.41\stackrel{°}{ \mathrm{A}}$. The number of ${\mathrm{H}}_2\mathrm{O}$molecules contained in a unit cell : ($\mathrm{d}=0.92 \mathrm{g} {\mathrm{cm}}^{-3}$ at the given temperature)

Calculation of Number of H₂O Molecules in Ice Unit Cell

The number of H₂O molecules in the hexagonal unit cell of ice is 12, calculated as follows:

1. Unit Cell Volume

For a hexagonal lattice with constants a = 4.53 Å and c = 7.41 Å:

2. Volume Conversion

Convert volume from cubic angstroms to cubic centimeters (1 Å = 10^-8 cm):

3. Mass of Unit Cell

Using density ρ = 0.92 g/cm³:

4. Number of H₂O Molecules

• Molar mass of H₂O = 18 g/mol
• Avogadro's number, N_A = 6.022 × 10²³ molecules/mol

Rounding to the nearest integer gives 12 molecules per unit cell.

Conclusion

The hexagonal unit cell of ice contains 12 H₂O molecules, consistent with the known structure of ice Ih at low temperatures.

$\begin{array}{l}=\frac{0.92\times 131.6\times {10}^{-24}\times 6.023\times {10}^{23}}{18}\\ =\frac{0.92\times 13.16\times 6.023}{18}=4\end{array}$