On a Hot Summer Day, the Temperature Is 40

On a hot summer day, the temperature is 40.0°C and the pressure is 1.01 × 10⁵ Pa. Let us model the air as all nitrogen of molecular mass 28.0 g/mol having molecules of diameter 0.500 nm that are moving at their root-mean-square speed. Avogadro's number is 6.02 × 10²³ molecules/mol, the ideal gas constant is 8.31 J/mol•K, and the Boltzmann constant is 1.38 × 10^-23 J/K. Calculate reasonable estimates for
(a) the root-mean-square speed of the nitrogen molecules.
(b) the average distance a typical molecule travels between collisions.
(c) the average time a molecule travels between collisions, assuming that the molecules are moving at their root-mean-square speeds.
(d) the number of collisions an average molecule undergoes per second.