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  4. Ice crystallises in a hexagonal lattice. At the low temperature, the lattice constants were a = 4.53 mathringA and b = 7.41 mathringA. How many H2O molecules are contained in a unit cell? [d(ice) = 0.92 g / cm]

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Q. Ice crystallises in a hexagonal lattice. At the low temperature, the lattice constants were $a = 4.53\, \mathring{A}$ and $b = 7.41\, \mathring{A}$. How many $H_2O$ molecules are contained in a unit cell? $[d(ice) = 0.92 \,g / cm]$Chemistry Question Image

UPSEEUPSEE 2014The Solid State

Solution:

Volume of the unit cell,

$V=$ area of rhombus base $\times b$

$=\left(a^{2} \sin 60^{\circ}\right) \times b$

$=(4.53)^{2} \times \frac{\sqrt{3}}{2} \times 7.41 \times 10^{-24} cm ^{3}$

$=132 \times 10^{-24} cm ^{3}$

Thus, the mass of unit cell

$=V \times d=132 \times 10^{-24} \times 0.92 \times 6.02 \times 10^{23}$

$=73\, g$

This is close to 4 times the molecular weight of $H _{2} O .$ So, there are four molecules of $H _{2} O$ per unit.