# Ice crystallises in a hexagonal lattice having the volume of unit cell as 132 × 10–24 cm3. If density is 0.92 g cm–3 at a given temperature, then what is the number of H2O molecules per unit cell?

Jun 5, 2018

There are four water molecules per unit cell.

#### Explanation:

Step 1. Calculate the mass of a unit cell

$\text{Mass" = 132 ×10^"-24" color(red)(cancel(color(black)("cm"^3))) × "0.92 g"/(1 color(red)(cancel(color(black)("cm"^3)))) = 1.21 × 10^"-21" color(white)(l)"g}$

Step 2. Calculate the mass of a water molecule

$\text{Mass of 1 molecule " = 1 color(red)(cancel(color(black)("molecule"))) × (1 color(red)(cancel(color(black)("mol"))))/(6.022 × 10^23 color(red)(cancel(color(black)("molecules")))) × "18.02 g"/(1 color(red)(cancel(color(black)("mol")))) = 2.992 × 10^"-23"color(white)(l) "g}$

Step 3. Calculate the number of water molecules per unit cell

n = (1.21 × 10^"-21" color(red)(cancel(color(black)("g"))))/"1 unit cell" × "1 molecule"/(2.992 × 10^"-23"color(red)(cancel(color(black)("g")))) = "4.06 molecules/unit cell"

$\text{≈ 4 molecules/unit cell}$