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?

At an altitude of $11,000$ m (a typical cruising altitude for a jet airliner), the air temperature is $-56.5$°C and the air density is $0.364$ kg/m³ . What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the earth, so the calculation of Example $18.4$ in Section $18.1$ doesn't apply.)

A large organic molecule has a mass of $1.41\times {10}^{-21}$ kg. What is the molar mass of this compound?

How many moles are in a $1.00$-kg bottle of water? How many molecules? The molar mass of water is $18.0$ g/mol.

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?

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)?