Consider an ideal gas at $27$°C and $1.00$ atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare the average kinetic energies of the three types of atoms.

Modern vacuum pumps make it easy to attain pressures of the order of ${10}^{-13}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. At a pressure of $9.00\times {10}^{-14}$ atm and an ordinary temperature of $300.0$ K, how many molecules are present in a volume of $1.00$ cm³?

What is the total translational kinetic energy of the air in an empty room that has dimensions $8.00$ m$\times 12.00$ m$\times 4.00$ m if the air is treated as an ideal gas at $1.00$ atm?

Modern vacuum pumps make it easy to attain pressures of the order of $10^{-13}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. How many molecules would be present at the same temperature but at $1.00$ atm instead?

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about $7\times {10}^9$ people)?