Density is mass per unit volume. Mathematically, `D = M/V`
Where, `D_w` is the density of boiling water, and `D_v` , that of the vapour.
Assuming no loss of vapour to the surroundings (i.e. constant mass),
`rArr (M/V_v)/(M/V_w) = 1/1600`
Volume has the dimension of` L^3` . Assuming the mean distance of separation between water molecules in any given phase (liquid or vapour) to be l, volume (at that phase) will be given by `l^3` .
In other words, mean distance of separation between water molecules in any given phase will be obtained from cube root of its volume at that phase. Hence we can write,
`rArr (l_v)/(l_w)=root(3)(1600) = 11.7.`
Therefore, the ratio of the mean separation of water molecules at 100°C in the vapour to that in the liquid = 11.7.