Intermolecular distances!

Let $d_{L}$ and $d_{V}$ represent the average distances between molecules in the liquid phase and in the vapour phase, respectively. Assume that both phases are at 100°C and atmospheric pressure and the vapour behaves like an ideal gas. Calculate the ratio $\dfrac{d_{V}}{d_{L}}$ .

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Use the following data:

Density is waste in liquid phase: $10^3$ kg per cubic metre

Molar mass of water: $1.8 \times 10^{-2}$ kg per mole

Atmospheric pressure: $10^5$ newton per square metre

Gas constant: 8.3 joule per mole kelvin

Avogadro's Number: $6 \times 10^{23}$