Question

Ice crystallizes in hexagonal lattice having a volume of the unit cell is $132\times {10}^{-23}c{m}^3$. If the density of ice is $0.92gc{m}^{-3}$ at a given temperature, then a number of $H_{2}O$ molecules per unit cell is:

(Write your answer to the nearest integer)

Answer 1

Volume $=132\times {10}^{-23}c{m}^3$
Density $=0.92g/c{m}^3$
Mass $=\text{Density}\times \text{volume}=0.92g/c{m}^3\times 132\times {10}^{-23}c{m}^3=1.21\times {10}^{-21}g$
1 mole $=$ 18 g $=6.023\times {10}^{23}$ water molecules.
Mass of one water molecule $=\frac{18g/mole}{6.023\times {10}^{23}molecules/mole}=2.99\times {10}^{-23}g$
The number of water molecules per unit cell $=\frac{1.21\times {10}^{-21}g}{2.99\times {10}^{-23}g}=40.6\simeq 41$