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Question: Ice crystallises in a hexagonal lattice at lower temperature, the lattice constants are a = 4.5 Å an...

Ice crystallises in a hexagonal lattice at lower temperature, the lattice constants are a = 4.5 Å and c = 7.5 Å. The density of ice = 0.9 gm/cm3 . How many H2O molecules are present in one unit cell ?

A

6

B

4

C

3

D

2

Answer

4

Explanation

Solution

vol. of unit cell = a2c sin 600 = (4.5)2 × 7.5 ×32\frac{\sqrt{3}}{2}

× 10–24 cm3 = 131. 5 × 10–24 cm3

Mass of unit cell = 131.5 × 10–24 × 0.9 gm.

= 118.37 × 10–24 gm

Mass of one H2O molecule = 18 amu

= 18 × 106\frac{10}{6} × 10–24 g

No. of H2O molecules present in one unit cell

= 118.37×10–2418×106×10−24\frac{118.37 \times 10^{–24}}{18 \times \frac{10}{6} \times 10^{- 24}} = 118.3730\frac{118.37}{30} = 3.945 ~ 4