21. Kinetic Theory of Ideal Gases

A 1.0-mol sample of helium gas has a temperature of 18°C. How fast would a 65-kg person have to run to have the same kinetic energy?

A 0.40-kg trash-can lid is suspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 15 m/s?

Oxygen diffuses from the surface of insects to the interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectional area of 2 x 10^-9 m². Assume the concentration of oxygen inside is half what it is outside in the atmosphere. Calculate the diffusion rate J. Assume the diffusion constant is 1 x 10^-5 m²/s.

In the van der Waals equation of state, the constant b represents the amount of “unavailable volume” (per mole) occupied by the molecules themselves. Thus V is replaced by (V-nb), where n is the number of moles. For oxygen, b is about 3.2 x 10^-5 m³ /mol. Estimate the diameter of an oxygen molecule.

For oxygen gas, the van der Waals equation of state achieves its best fit for a = 0.14 N·m⁴ /mol² and b = 3.2 x 10^-5 m³/ mol. Determine the pressure in 1.0 mol of the gas at 0°C if its volume is 0.70 L, calculated using the van der Waals equation.

A scuba tank has a volume of 3100 cm³. For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium. What is the ratio of the average kinetic energies of the two types of molecule?

For oxygen gas the van der Waals constants are a = 0.14 N·m⁴/mol² and b = 3.2 x 10^-5 m³/mol. Using these values, graph six curves of pressure vs. volume between V = 2 x 10^-5 m³ and 2.0 x 10^-4 m³, for 1 mol of oxygen gas at temperatures of 80 K, 100 K, 120 K, 130 K, 150 K, and 170 K. From the graphs determine approximately the critical temperature for oxygen.