Ice crystallizes in a hexagonal lattice with a unit cell volume of 132 × 10⁻²⁴ cc. If the density at a given temperature is 0.92 g/cc, determine the number of water molecules per unit cell.

A. 1
B. 2
C. 3
D. 4

To find the number of water molecules per unit cell in ice, you can follow these steps:

Calculate the molar mass of water (H2O).
Calculate the number of moles of water in the given density.
Determine the number of water molecules in one mole of water.
Find the number of water molecules per unit cell.
Let's calculate it step by step:

Molar mass of water (H2O):

Hydrogen (H) has an atomic mass of approximately 1 g/mol.
Oxygen (O) has an atomic mass of approximately 16 g/mol.
Molar mass of H2O = 2(H) + 1(O) = 2(1 g/mol) + 16 g/mol = 18 g/mol.
Calculate the number of moles of water in the given density:
Density = Mass/Volume
Mass = Density × Volume
Given density = 0.92 g/cc
Volume of the unit cell = 132 × 10^(-24) cc
Mass of water in one unit cell = 0.92 g/cc × 132 × 10^(-24) cc
Mass of water in one unit cell = 1.2144 × 10^(-24) g

Now, we need to convert this mass into moles using the molar mass of water:
Moles of water in one unit cell = (Mass of water) / (Molar mass of water)
Moles of water in one unit cell = (1.2144 × 10^(-24) g) / (18 g/mol)
Moles of water in one unit cell ≈ 6.74667 × 10^(-26) moles

Determine the number of water molecules in one mole of water:
Avogadro's number tells us that one mole of any substance contains approximately 6.022 × 10^23 molecules.

Find the number of water molecules per unit cell:
Number of water molecules per unit cell = (Moles of water in one unit cell) × (Number of molecules in one mole)
Number of water molecules per unit cell ≈ (6.74667 × 10^(-26) moles) × (6.022 × 10^23 molecules/mole)
Number of water molecules per unit cell ≈ 4.0673 × 10^(-2) molecules

Rounded to the nearest whole number, there are approximately 4 water molecules per unit cell in ice. So, the correct answer is D. 4.