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 cylindrical tank contains $0.750$ m³ of nitrogen gas at $27$°C and $7.50\times {10}^3$ Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to $0.410$ m³ and the temperature is increased to $157$°C?

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?

Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.0°C in summer to -100°C in winter. Over the course of a Martian year, what are the ranges of (b) the density (in mol/m^3) of the atmosphere?

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.

If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is $1003$°C and the pressure is $92$ atm?