Example

Question:

Estimate the volume of a water molecule using the data in Example 12.1.

Solution:

In the liquid phase, molecules of water are closely packed. The density of a water molecule is approximately the same as bulk water, \(1000\,\mathrm{kg\,m^{-3}}\).
The mass of one mole of water is: \[ (2 + 16)\mathrm{g} = 18\,\mathrm{g} = 0.018\,\mathrm{kg} \]
Since one mole contains about \(6 \times 10^{23}\) molecules, the mass of a water molecule is: \[ \frac{0.018}{6 \times 10^{23}}\,\mathrm{kg} = 3 \times 10^{-26}\,\mathrm{kg} \]
Volume of a water molecule: \[ = \frac{3 \times 10^{-26}\,\mathrm{kg}}{1000\,\mathrm{kg\,m^{-3}}} = 3 \times 10^{-29}\,\mathrm{m}^3 \]
Assuming spherical shape, \[ V = \frac{4}{3} \pi r^3 \] So, \[ r \approx 2 \times 10^{-10}\,\mathrm{m} = 2\,\angstrom \]