21. Kinetic Theory of Ideal Gases

A 20.0-L tank contains 4.86 * 10^-4 kg of helium at 18.0°C. The molar mass of helium is 4.00 g/mol. (b) What is the pressure in the tank, in pascals and in atmospheres?

A 20.0-L tank contains 4.86 * 10^-4 kg of helium at 18.0°C. The molar mass of helium is 4.00 g/mol. (a) How many moles of helium are in the tank?

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?

Meteorology. The vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. The relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water at that same temperature, expressed as a percentage. The air is saturated when the humidity is 100%. (a) The vapor pressure of water at 20.0°C is 2.34 * 10^3 Pa. If the air temperature is 20.0°C and the relative humidity is 60%, what is the partial pressure of water vapor in the atmosphere (that is, the pressure due to water vapor alone)?

How Close Together Are Gas Molecules? 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. (a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

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 * 10^9 people)?

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. (b) How many molecules would be present at the same temperature but at 1.00 atm instead?

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. (a) At a pressure of 9.00 * 10^-14 atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm^3?

A large organic molecule has a mass of 1.41 * 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

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/m^3 . 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.)

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?

Planetary Atmospheres. (a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2 atmosphere), Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2 atmosphere), and Saturn's moon Titan (where the pressure is 1.5 atm and the temperature is -178°C, with a N2 atmosphere).

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m^3 of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m^3. If the temperature remains constant, what is the final value of the pressure?

Helium gas with a volume of 3.20 L, under a pressure of 0.180 atm and at 41.0°C, is warmed until both pressure and volume are doubled. (a) What is the final temperature?