21. Kinetic Theory of Ideal Gases

The Ideal Gas Law

Ideal Gas Law Practice Problems with Molar Mass

Doubling Pressure & Temperature

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.)

0.00086 moles of an ideal gas undergoes the process shown in the figure. If the initial temperature was <math display="inline"><mrow><mn>340</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">K</mi></mrow></math> and the final pressure is <math display="inline"><mrow><mn>5.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">atm</mi></mrow></math>, what is the final temperature? 
<img src="https://media.pearsoncmg.com/aw/aw_knight_physics_5/msa/content/practice-test/img/CQ18_11_Figure.jpg" alt="A pressure versus volume graph. A process is represented by a vertical line which extends upward from point at p = 2 atmospheres to some point at a higher pressure. ">

3 moles of an ideal gas fill a cubical box with a side length of 30cm. If the temperature of the gas is 20°C, what is the pressure inside the container?

A large cylindrical tank contains 0.750 m^3 of nitrogen gas at 27°C and 7.50 * 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 m^3 and the temperature is increased to 157°C?

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)?

A sample of gas is heated in a closed container with a volume of <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>2</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">L</mi></mrow><mo>,</mo></mrow></math> from an initial temperature and pressure of <math display=“inline”><mrow><mn>20</mn><mo>&#x00B0;</mo><mtext>&#x200B;</mtext><mi mathvariant="normal">C</mi></mrow></math> and <math display=“inline”><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mtext>&#x00A0;</mtext><mtext>atm</mtext></mrow></math> to a final temperature of <math display=“inline”><mrow><mn>238</mn><mo>&#x00B0;</mo><mtext>&#x200B;</mtext><mi mathvariant="normal">C</mi></mrow></math>. What is the final pressure?

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 balloon contains 3900cm3 of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.


An ideal gas is in a sealed container. It has a temperature T when it has volume V at pressure P. What is the temperature of the gas when its volume is quadrupled, and the pressure is halved?


Gases: The Ideal Gas Law

Ideal Gas Law

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?

Ideal Gas Problems: Crash Course Chemistry #13

5 Ideal Gas Law Experiments  - PV=nRT or PV=NkT

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?

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?

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 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?

Solving Ideal Gas Problems With Changing States

Ideal Gas Law Practice Problems & Examples

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?

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

A large organic molecule has a mass of 1.41 * 10^-21 kg. What is the molar mass of this compound?

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?

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

Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm3&nbsp;at 30°C with a pressure of 1 × 105 Pa, calculate how many hydrogen atoms (particles) there are in the sample.

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?

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?

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?

Ideal Gases and the Ideal Gas Law

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)?

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). (a) 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?

Ideal Gas Law Explained

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?

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