Question

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:

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

Given:

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

Density $=0.92$ g cm${}^{-3}$

Mass of the unit cell $=$ Volume $\times$ Density $=132\times {10}^{-24}\times 0.92$ $=121.44\times {10}^{-24}$ g

Molar mass of water $=18.02$ g mol${}^{-1}$

Number of moles of water $=\frac{121.44\times {10}^{-24}}{18.02}$ $=6.739\times {10}^{-24}$ mol

Number of molecules $=6.739\times {10}^{-24}\times 6.023\times {10}^{23}$ molecules per mole $=4.05$ molecules $=4$ molecules approximately