Answer
See the detailed answer below.
Work Step by Step
We know that the mean free path is inversely proportional to the density.
$$\lambda_{ }\propto \dfrac{1}{\rho_{ }}$$
Thus,
$$\dfrac{\lambda_{ air}}{\lambda_{ water}}=\dfrac{\rho_{water}}{\rho_{air}}$$
$$\dfrac{\lambda_{ air}}{\lambda_{ water}}=\dfrac{\rho_{water}}{\frac{1}{1000}\rho_{water}}=1000$$
Hence,
$$\lambda_{ air}=1000\lambda_{ water}$$
Therefore, the average distance between air molecules is 1000 times greater than the average distance between water molecules.
