Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure was determined, the lattice constants were $a = 34 ˚ A$ and $c = 7.41 ˚ A$ . How many $H_{2} O$ molecules are contained in a unit cell? (The density of ice is $0.92 g / c c$ at $0^{o} C$ A unit cell of $H_{2} O$ is shown.)

Open in App

Solution

Volume of unit cell, $V =$ Area of Base $\times$ Height
$= 2 \times \frac{\sqrt{3}}{4} a^{2} \times c$
$= 2 \times \frac{\sqrt{3}}{4} \times 1156 \times 10^{- 16} \times 7.41 \times 10^{- 8}$ $c m^{3}$
Mass of unit cell $= V \times S$
$= 7.409 \times 10^{- 21} \times 0.92$
$= 6.816 \times 10^{- 21}$ $g m$
Let there be $N$ water molecules in the given cell
$⟹ 6.816 \times 10^{- 21} = n \times \frac{18}{6.023 \times 10^{23}}$
$⟹ n = 227.9 \approx 228$ $H_{2} O$ molecules

Suggest Corrections

Similar questions

Q. Ice crystallises in a hexagonal lattice. At the, low temperature, the lattice constants were

a = 4.53 A^{\circ}

and

b = 7.41 A^{\circ}

How many

H_{2} O

molecules are contained in a unit cell?

[d (i c e) = 0.92 g / c m^{3}]

Q. Ice crystallizes in a hexagonal lattice. At low temperature, at which the structure was determined, the lattice constants were

a = 4.53 ˚ A

and

b = 7.60 ˚ A

(see figure). How many molecules of water are contained in a given unit cell? [Density of ice is

0.92

g cm

^{- 3}

ice crystallises in a hexagonal lattice.at the low temperatures at which the structure was determined, the lattice constants were a= 4.53 Angstroms ; b=7.41 Angstorms .How many H molecules are contained in a unit cell

ans =4 ?

Q. 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

0.92 g c 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)

Q. Ice crystallises in a hexagonal lattice having volume of the unit cell as

132 \times 10^{- 24}

cc. If density is

0.92

g/cc at a given temperature, then the number of water molecules per unit cell is:

Join BYJU'S Learning Program

Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure was determined, the lattice constants were a=34˚A and c=7.41˚A. How many H2O molecules are contained in a unit cell? (The density of ice is 0.92g/cc at 0oC A unit cell of H2O is shown.)

Volume of unit cell, V= Area of Base × Height=2×√34a2×c=2×√34×1156×10−16×7.41×10−8 cm3Mass of unit cell =V×S=7.409×10−21×0.92=6.816×10−21 gmLet there be N water molecules in the given cell⟹6.816×10−21=n×186.023×1023⟹n=227.9≈228 H2O molecules