Calculation of Volume Occupied by One Molecule of Water

Density of Water:
The given density of water is 1 g/cm³.

Avogadro's Number:
Avogadro's number (N_A) is the number of atoms or molecules present in one mole of a substance. It is approximately equal to 6.022 × 10²³ mol⁻¹.

Molar Mass of Water:
The molar mass of water (H₂O) can be calculated by summing up the atomic masses of its constituent elements. The atomic masses of hydrogen (H) and oxygen (O) are approximately 1 g/mol and 16 g/mol, respectively. Therefore, the molar mass of water is:

Molar mass of water (H₂O) = 2 × (atomic mass of hydrogen) + atomic mass of oxygen
= 2 × 1 g/mol + 16 g/mol
= 18 g/mol

Number of Water Molecules in One Mole:
Since the molar mass of water is 18 g/mol, one mole of water contains 6.022 × 10²³ water molecules. This is equal to Avogadro's number (N_A).

Mass of One Water Molecule:
To determine the mass of one water molecule, we divide the molar mass of water by Avogadro's number. Therefore,

Mass of one water molecule = Molar mass of water / Avogadro's number
= 18 g/mol / 6.022 × 10²³ mol⁻¹

Volume Occupied by One Water Molecule:
To calculate the volume occupied by one water molecule, we need to convert the mass of one molecule to grams. Given that the density of water is 1 g/cm³, the volume occupied by one water molecule can be calculated using the formula:

Volume = Mass / Density

Therefore,

Volume occupied by one water molecule = (Mass of one water molecule) / (Density of water)
= (18 g/mol / 6.022 × 10²³ mol⁻¹) / 1 g/cm³
≈ 2.99 × 10⁻²³ cm³

Conclusion:
The volume occupied by one molecule of water is approximately 2.99 × 10⁻²³ cm³.