Question

Ice crystallises in a hexagonal lattice. At the, low temperature, the lattice constants were $a=4.53A^{\circ }$ and $b=7.41A^{\circ }$.

How many $H_{2}O$ molecules are contained in a unit cell? $\left[d\right(ice)=0.92g/c{m}^3]$

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is A $4$

The volume of the unit cell, $V=a^{2}bsin{60}^o$

$V=(4.53\times {10}^{-8}{)}^2\times 7.41\times {10}^{-8}\times 0.866$ $(1\mathring{A}={10}^{-8}cm)$

$V=1.317\times {10}^{-22}c{m}^3$
The density is $0.92g/c{m}^3$
The mass of the unit cell is $0.92g/c{m}^3\times 1.317\times {10}^{-22}c{m}^3=1.21\times {10}^{-22}g$....(1)
The mass of 1 mole of water molecules is 18 g.

1 mole of water molecules $=6.023\times {10}^{23}$ molecules.

The mass of 1 water molecule $=\frac{18}{6.023\times {10}^{23}}=2.98\times {10}^{-23}$ g ......(2)
Divide equation (1) with equation (2).

$\frac{1.21\times {10}^{-22}g}{2.98\times {10}^{-23}}=4$
Thus, four water molecules are contained in a unit cell.