21. Kinetic Theory of Ideal Gases

The Ideal Gas Law

21. Kinetic Theory of Ideal Gases

# The Ideal Gas Law - Video Tutorials & Practice Problems

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concept

### Ideal Gases and the Ideal Gas Law

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Problem

Problem3 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

2.7 × 10

^{5}PaB

0.27 Pa

C

1.85 × 10

^{4}PaD

8.12 × 10

^{3}Pa3

Problem

ProblemHydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm^{3 }at 30°C with a pressure of 1 × 10^{5} Pa, calculate how many hydrogen atoms (particles) there are in the sample.

A

2.42 × 10

^{22}B

2.39 × 10

^{22}C

2.39 × 10

^{28}4

concept

### Solving Ideal Gas Problems With Changing States

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Problem

ProblemA balloon contains 3900cm^{3} 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.

A

0.012 m

^{3}B

0.0041 m

^{3}C

0.39 m

^{3}D

0.0044 m

^{3}6

example

### Doubling Pressure & Temperature

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PRACTICE PROBLEMS AND ACTIVITIES (70)

- A constant-volume gas thermometer registers an absolute pressure corresponding to 325 mm of mercury when in co...
- The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its...
- A large cylindrical tank contains 0.750 m^3 of nitrogen gas at 27°C and 7.50 * 10^3 Pa (absolute pressure). Th...
- You have several identical balloons. You experimentally determine that a balloon will break if its volume exce...
- 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...
- 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 i...
- 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 ma...
- Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, whic...
- Meteorology. The vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium wi...
- How Close Together Are Gas Molecules? Consider an ideal gas at 27°C and 1.00 atm. To get some idea how close t...
- In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules ...
- Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a ...
- Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a ...
- 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 an...
- If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V)...
- Planetary Atmospheres. (a) Calculate the density of the atmosphere at the surface of Mars (where the pressure ...
- A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank origi...
- 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...
- The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the...
- The total lung capacity of a typical adult is 5.0 L. Approximately 20% of the air is oxygen. At sea level and ...
- The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0...
- An inflated bicycle inner tube is 2.2 cm in diameter and 200 cm in circumference. A small leak causes the gaug...
- In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you a...
- The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0...
- In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you a...
- In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you a...
- Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until t...
- Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until t...
- A container of gas at 2.0 atm pressure and 127°C is compressed at constant temperature until the volume is hal...
- 10 g of dry ice (solid CO₂) is placed in a 10,000 cm^3 container, then all the air is quickly pumped out and t...
- A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. c. How many moles o...
- A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. a. What type of pro...
- A diver 50 m deep in 10°C fresh water exhales a 1.0-cm-diameter bubble. What is the bubble's diameter just as ...
- A sealed container holds 3.2 g of oxygen at 1 atm pressure and 20°C. The gas first undergoes an isobaric proce...
- 0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are and (c) volume V₃?
- 0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are (b) pressure p₂,
- 0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are (a) temperature T₁,
- 0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochor...
- 0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochor...
- A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm ab...
- A gas with initial state variables p₁, V₁ , and T₁ expands isothermally until V₂=2V₁. What are and (b) p₂?
- A gas with initial state variables p₁, V₁, and T₁ expands isothermally until V₂=2V₁. What are (a) T₂
- A gas with initial state variables p₁, V₁, and T₁ is cooled in an isochoric process until p₂=1/3p₁. What are ...
- A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. d. What is the reading of a...
- A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. c. What is the number densi...
- A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if (b) the Kelvin tempe...
- A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if (a) the Celsius temp...
- A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, a. Has t...
- A 6.0-cm-diameter, 10-cm-long cylinder contains 100 mg of oxygen (O₂) at a pressure less than 1 atm. The cap o...
- The interior of a Boeing 737-800 can be modeled as a 32-m-long, 3.7-m-diameter cylinder. The air inside, at cr...
- The 50 kg circular piston shown in FIGURE P18.57 floats on 0.12 mol of compressed air. a. What is the piston ...
- The 50 kg circular piston shown in FIGURE P18.57 floats on 0.12 mol of compressed air. b. How far does the pi...
- The cylinder in FIGURE CP18.73 has a moveable piston attached to a spring. The cylinder's cross-section area i...
- The closed cylinder of FIGURE CP18.74 has a tight-fitting but frictionless piston of mass M. The piston is in ...
- On average, each person in the industrialized world is responsible for the emission of 10,000 kg of carbon dio...
- The 3.0-m-long pipe in FIGURE P18.49 is closed at the top end. It is slowly pushed straight down into the wate...
- A diving bell is a 3.0-m-tall cylinder closed at the upper end but open at the lower end. The temperature of t...
- An electric generating plant boils water to produce high-pressure steam. The steam spins a turbine that is con...
- On a cool morning, when the temperature is 15°C, you measure the pressure in your car tires to be 30 psi. Afte...
- A 10-cm-diameter, 40-cm-tall gas cylinder, sealed at the top by a frictionless 50 kg piston, is surrounded by ...
- A 6.0-cm-diameter cylinder of nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented ...
- A 6.0-cm-diameter cylinder of nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented ...
- 14 g of nitrogen gas at STP are pressurized in an isochoric process to a pressure of 20 atm. What are (a) the...
- A 1.0 m ✕ 1.0 m ✕ 1.0 m cube of nitrogen gas is at 20℃ and 1.0 atm. Estimate the number of molecules in the cu...
- Photons of light scatter off molecules, and the distance you can see through a gas is proportional to the mean...
- Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H₂). The n...
- Equation 20.3 is the mean free path of a particle through a gas of identical particles of equal radius. An ele...
- (II) What is the pressure inside a 41.0-L container holding 105.0 kg of argon gas at 21.6°C?