Estimate the volume of a water molecule using the data in Example 13.1.

Explanation

In the liquid (or solid) phase, the molecules of water are quite closely packed. The density of water molecule may therefore, be regarded as roughly equal to the density of bulk `"water" = 1000 kgm^(-3)`. To estimate the volume of a water molecule, we need to know the mass of a single water molecule. We know that 1 mole of water has a mass approximately equal to
(2 + 16)g = 18 g = 0.018 kg.
Since 1 mole contains about `6 xx 10^(23)` molecules (Avogadro.s number), the mass of a molecule of water is `(0.018)//(6 xx 10^(23)) "kg" = 3 xx 10^(-26)` kg. Therefore, a rough estimate of the volume of a water molecule is as follows:
`"Volume of a water molecule" = (3 xx 10^(-26) "kg")// (1000 "kg" m^(-3) )`
`= 3 xx 10^(-29) m^(3)`
` = (4//3) pi (Radius)^(3)`
Hence, `"Radius" ~~ 2 xx 10^(-10) m = 2 Å`