21. Kinetic Theory of Ideal Gases

A constant-volume gas thermometer registers an absolute pressure corresponding to $325$ mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?

The pressure of a gas at the triple point of water is $1.35$ atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO₂ solidifies?

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?

You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds $0.900$ L. The pressure of the gas inside the balloon equals air pressure ($1.00$ atm). If the air inside the balloon is at a constant $22.0$°C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?

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. How many grams of helium are there? The molar mass of helium is $4.00$ g/mol.

A $20.0$-L tank contains $4.86\times10^{-4}$ kg of helium at $18.0$°C. The molar mass of helium is $4.00$ g/mol. What is the pressure in the tank, in pascals and in atmospheres?

A $20.0$-L tank contains $4.86\times {10}^{-4}$ kg of helium at $18.0$°C. The molar mass of helium is $4.00$ g/mol. 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?

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 $100\%$. The vapor pressure of water at $20.0$°C is $2.34\times {10}^3$ 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)?

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?

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)?

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?

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?

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