The density of water is 1000 ; kg ; m^{-3}. T | vedclass

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(C) The ratio of the density of liquid water to the density of water vapour is $\frac{1000}{0.6} \approx 1667 \approx 1.67 	imes 10^3$.This means tha

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$40$

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(C) The ratio of the density of liquid water to the density of water vapour is $\frac{1000}{0.6} \approx 1667 \approx 1.67 	imes 10^3$.This means that the volume occupied by a given mass of water in the vapour state is $1.67 	imes 10^3$ times the volume it occupies in the liquid state.Since the volume $V$ is proportional to the cube of the radius $r$ $(V \propto r^3)$,the average distance between molecules scales with the cube root of the volume expansion.Let $r_l$ be the radius in the liquid state and $r_v$ be the radius in the vapour state.Then $\frac{r_v}{r_l} = (1.67 	imes 10^3)^{1/3} \approx 1.67^{1/3} 	imes 10 \approx 1.186 	imes 10 \approx 11.86$.However,the standard approximation used in this context is that the volume increases by $10^3$ times,so the distance increases by a factor of $10$.Given the radius of a molecule is $2 \; \mathring{A}$,the average distance between molecules in the liquid state is $2 	imes 2 = 4 \; \mathring{A}$.In the vapour state,the average distance becomes $10 	imes 4 \; \mathring{A} = 40 \; \mathring{A}$.

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