The diameter of an atom is about 1 angstrom (10-10 m). In order todevelop some intuition for the molecular scale of a gas, assumethat you are considering 1 liter of air (mostly N2 and O2, withmolar masses of 28 g/mol and 32 g/mol respectively) at roomtemperature and atmospheric pressure (about 105 Pa). As always, besure to show your work and explain your reasoning.
a) Calculate the number of molecules in this sample of air.
b) Estimate the average spacing between the molecules.
c) Estimate the average speed of a molecule based on theMaxwell-Boltzmann distribution.
d) Suppose that we scale up the gas so that each atom is the sizeof a tennis ball. We also scale up the spaces between the atomsproportionally. Now what would be the average spacing betweenmolecules? What would be the average speed of a molecule in milesper hour?
The diameter of an atom is about 1 angstrom (10-10 m). In order todevelop some intuition for the molecular scale of a gas, assumethat you are considering 1 liter of air (mostly N2 and O2, withmolar masses of 28 g/mol and 32 g/mol respectively) at roomtemperature and atmospheric pressure (about 105 Pa). As always, besure to show your work and explain your reasoning.
a) Calculate the number of molecules in this sample of air.
b) Estimate the average spacing between the molecules.
c) Estimate the average speed of a molecule based on theMaxwell-Boltzmann distribution.
d) Suppose that we scale up the gas so that each atom is the sizeof a tennis ball. We also scale up the spaces between the atomsproportionally. Now what would be the average spacing betweenmolecules? What would be the average speed of a molecule in milesper hour?
