Gas Laws

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Gas Pressure

Pressure is defined as the force applied per unit area: P = F / A.
Pressure is measured in pascals (Pa), force in newtons (N) and area in square metres (m²).
The equation P = F / A is only relevant when gas molecules exert a force perpendicular to the surface.
A force spread over a large area produces a small pressure; a force spread over a small area produces a large pressure.
Gas molecules bouncing off the walls of a container exert a force at right angles to the walls, creating gas pressure.
When using P = F / A, always use the cross-sectional area of the surface that the force is applied upon.

Diagram showing how increasing the temperature of a gas at constant volume leads to more frequent and energetic collisions with the container walls, thus increasing pressure.

Amount of Substance

The mole is one of the seven SI base units; it measures the amount of substance, not mass.
One mole is the amount of substance that contains as many elementary entities as there are atoms in 12 g of carbon-12.
This number is the Avogadro constant, N_A = 6.02 × 10²³ mol⁻¹ (rounded at IB level).
The number of moles n is calculated using n = N / N_A, where N is the number of particles.
The number of atoms or molecules is found by multiplying the number of moles by N_A.
Molar mass m_r is the mass m of a substance divided by the amount in moles: m_r = m / n, in g mol⁻¹.
One mole of any element equals the relative atomic mass of that element in grams; for a compound, add the relative atomic masses.

Gas Laws

An ideal gas obeys the relation PV ∝ T, which can be written as PV / T = constant.
The empirical gas laws are Boyle's law (constant temperature), Charles's law (constant pressure) and Gay-Lussac's law (constant volume).
Boyle's law: at constant temperature, P ∝ 1/V, so P₁V₁ = P₂V₂.
Charles's law: at constant pressure, V ∝ T, so V₁/T₁ = V₂/T₂.
Gay-Lussac's (pressure) law: at constant volume, P ∝ T, so P₁/T₁ = P₂/T₂.
For all gas law experiments, the mass and number of molecules of the gas are assumed constant.
On a P-V diagram: a horizontal line is constant pressure, a curved isotherm is constant temperature, a vertical line is constant volume.

Gas particles and pressure

Ideal Gas Equation

An ideal gas is defined as a gas which obeys the ideal gas equation at all pressures, volumes and temperatures.
The ideal gas equation is PV = nRT, where P is pressure (Pa), V is volume (m³), n is moles (mol), R is the ideal gas constant and T is temperature (K).
The ideal gas constant R = 8.31 J K⁻¹ mol⁻¹ and is the macroscopic equivalent of the Boltzmann constant k_B.
Another form of the ideal gas equation is PV = Nk_BT, where N is the number of molecules and k_B = 1.38 × 10⁻²³ J K⁻¹.
The Boltzmann constant is defined as k_B = R / N_A.
Always convert temperature to kelvin before substituting into any gas law equation: T(K) = θ(°C) + 273.
The values of R, N_A and k_B are given in the data booklet.

Kinetic Theory of Gases

The kinetic theory models a gas as atoms or molecules moving randomly at high speeds, linking microscopic properties (mass, speed) to macroscopic properties (pressure, volume).
Assumptions include: gas consists of many identical molecules; volume of molecules is negligible compared to the container; molecules are in continuous random motion.
Further assumptions: molecules obey Newton's laws; collisions are elastic; there are no intermolecular forces except during collisions; collision time is negligible.
External forces (e.g. gravity) are ignored, and the number of molecules is very large so average behaviour is considered.
A real gas approximates an ideal gas when pressure is low, density is low, and temperature is sufficiently higher than the boiling point.
At very high pressures and densities, molecules are closer together so attractive forces matter and molecular volume is not negligible.
At low temperatures a gas can change into a liquid, so it no longer behaves like a gas.

Derivation of the Kinetic Theory of Gases Equation

Gas pressure arises from collisions of gas particles with the walls of the container, exerting a force on the walls.
For a molecule of mass m and speed v rebounding elastically, the change in momentum is Δp = −2mv, so the force on the wall is F = 2mv / Δt.
The time between collisions with the same wall is 2l / v, giving a force from one molecule of F = mv² / l.
For N molecules in a cube of side l, pressure is P = Nmv² / (3V), where V = l³.
Using density ρ = Nm / V, this becomes P = ⅓ρv², the kinetic theory of gases equation.
In this equation, P is pressure (Pa), ρ is density (kg m⁻³) and v² is the mean square speed (m² s⁻²).
The 'mean square' speed means an average speed, assuming all molecules travel at the same speed.

Average Kinetic Energy of a Molecule

For an ideal gas, molecules collide elastically and have no potential energy, so the internal energy U equals the total kinetic energy.
The average kinetic energy of one molecule is E_k = ½mv² = (3/2)k_BT.
A greater gas temperature means a greater average kinetic energy of the particles.
The internal energy of a gas is U = (3/2)Nk_BT, or equivalently U = (3/2)nRT.
When heat is transferred to a fixed volume of gas, internal energy increases and so does temperature, since U ∝ T.
These equations apply only to monatomic gases such as helium, neon and argon.
A monatomic molecule has only translational energy, while a diatomic molecule has both translational and rotational kinetic energy.

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Übungsfragen

Gratis-Vorschau — 8 von 64 Fragen. Registriere dich, um alle zu sehen.

1.Which of the following is the correct definition of pressure?
Easy
- AThe force applied per unit area
- BThe force applied per unit volume
- CThe energy transferred per unit time
- DThe mass per unit volume
2.What is meant by an ideal gas?
Easy
- AA gas that obeys the equation pV ∝ T at all pressures, volumes and temperatures
- BA gas that has no intermolecular forces at all temperatures
- CA gas that can never be liquefied
- DA gas that has zero volume at absolute zero
3.Which of the following are assumptions of the kinetic model of an ideal gas? (Select all that apply)
Medium
- AThe molecules are in continuous random motion
- BThe molecules collide elastically with each other and the walls
- CThere are strong intermolecular forces between molecules
- DThe volume of the molecules is negligible compared to the volume of the container
- EThe molecules have a range of different masses
4.Boyle's law states that for a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.
Easy
True or false?
5.Which gas law describes the relationship between pressure and temperature at constant volume?
Medium
- ABoyle's law
- BCharles's law
- CGay-Lussac's law (pressure law)
- DAvogadro's law
6.An ideal gas is kept at constant temperature. If its volume is halved, what happens to its pressure?
Medium
- AIt is halved
- BIt is doubled
- CIt remains the same
- DIt is quartered
7.A fixed mass of ideal gas has an initial pressure of 410 Pa at 410 K. It is heated at constant volume to 495 K. What is the final pressure?
Hard
- A495 Pa
- B410 Pa
- C340 Pa
- D500 Pa
8.Match each gas law with its correct relationship.
Medium
- Boyle's law
- Charles's law
- Gay-Lussac's law
- p ∝ 1/V
- V ∝ T
- p ∝ T

Mehr Fragen

9.Match each gas law with the quantity that is held constant in that law.
Medium
- Boyle's law
- Charles's law
- Gay-Lussac's (pressure) law
- Temperature
- Pressure
- Volume
10.Which of the following statements about real gases are correct? (Select all that apply)
Medium
- AAt very high pressures, attractive forces between molecules become significant
- BAt low temperatures, a gas may liquefy and no longer behave as an ideal gas
- CReal gases obey the ideal gas equation at all pressures and temperatures
- DAt low densities, the volume of the molecules becomes negligible compared to the container volume
- EReal gases have strong intermolecular forces at all temperatures and pressures
11.Place the following steps of the kinetic theory derivation of gas pressure in the correct order, from first to last.
Easy
- Find the change in momentum when a molecule hits a wall
- Calculate the number of collisions per second on a wall
- Find the change in momentum per second (force)
- Calculate the total pressure from N molecules
- Consider the effect of the molecule moving in 3D space
12.What is the SI unit of pressure?
Easy
- APascal (Pa)
- BNewton (N)
- CJoule (J)
- DKelvin (K)
13.Which of the following are assumptions of the kinetic theory of gases? (Select all that apply)
Medium
- AGas molecules are in continuous random motion
- BCollisions between gas molecules are elastic
- CIntermolecular forces are significant except during collisions
- DThe volume of the molecules is negligible compared to the volume of the container
- EThe time of a collision is long compared to the time between collisions
14.A fixed mass of gas at constant temperature occupies a volume of 2.0 m³ at a pressure of 300 Pa. The volume is reduced to 0.50 m³. What is the new pressure?
Medium
- A75 Pa
- B600 Pa
- C1200 Pa
- D150 Pa
15.A gas in a cylinder with a movable piston is heated from 300 K to 600 K while the pressure remains constant. What happens to the volume?
Medium
- AIt halves
- BIt stays the same
- CIt doubles
- DIt quadruples
16.A gas at 200 K has a pressure of 100 kPa. It is heated at constant volume to 400 K. What is the new pressure?
Medium
- A50 kPa
- B100 kPa
- C200 kPa
- D400 kPa
17.A sample of gas has a volume of 1.5 × 10⁻³ m³ at a pressure of 2.0 × 10⁵ Pa and a temperature of 300 K. How many moles of gas are present? (R = 8.31 J K⁻¹ mol⁻¹)
Medium
- A0.12 mol
- B0.24 mol
- C0.48 mol
- D0.06 mol
18.A fixed mass of gas at 27 °C is heated at constant pressure until its volume doubles. What is the final temperature in °C?
Medium
- A54 °C
- B327 °C
- C600 °C
- D300 °C
19.A gas cylinder contains 4.0 × 10²³ molecules of an ideal gas at 300 K in a volume of 0.02 m³. What is the pressure? (k_B = 1.38 × 10⁻²³ J K⁻¹)
Hard
- A8.3 × 10⁴ Pa
- B1.7 × 10⁵ Pa
- C4.1 × 10⁴ Pa
- D2.8 × 10⁵ Pa
20.The graph of pressure against volume for a fixed mass of gas at constant temperature is:
Medium
- AA straight line through the origin
- BA straight line with a positive intercept
- CA curve that gets steeper as volume increases
- DA curve that gets less steep as volume increases
21.A gas is trapped in a container of fixed volume. The temperature is increased from 300 K to 450 K. What is the ratio of the new pressure to the original pressure?
Medium
- A2:3
- B3:2
- C1:1
- D9:4
22.A 0.5 m³ container holds an ideal gas at 2.0 × 10⁵ Pa and 400 K. If the gas is allowed to expand to 1.0 m³ while the temperature is kept constant, what is the final pressure?
Medium
- A4.0 × 10⁵ Pa
- B2.0 × 10⁵ Pa
- C1.0 × 10⁵ Pa
- D0.5 × 10⁵ Pa
23.Which graph correctly represents the relationship between the pressure and absolute temperature of a fixed mass of gas at constant volume?
Medium
- APressure vs. temperature is a straight line through the origin
- BPressure vs. temperature is a horizontal line
- CPressure vs. temperature is a curve that flattens as temperature increases
- DPressure vs. temperature is a straight line with a negative intercept on the temperature axis
24.A gas at 300 K has an average molecular kinetic energy of 6.21 × 10⁻²¹ J. What is the average kinetic energy at 600 K?
Medium
- A3.11 × 10⁻²¹ J
- B6.21 × 10⁻²¹ J
- C1.24 × 10⁻²⁰ J
- D2.48 × 10⁻²⁰ J
25.The density of an ideal gas is 1.2 kg m⁻³ at a pressure of 1.0 × 10⁵ Pa. What is the mean square speed of the molecules?
Hard
- A2.5 × 10⁵ m² s⁻²
- B5.0 × 10⁵ m² s⁻²
- C1.7 × 10⁵ m² s⁻²
- D8.3 × 10⁴ m² s⁻²
26.Which of the following statements about the graph of pressure against volume for a fixed mass of gas at constant temperature are correct? (Select all that apply)
Medium
- AThe graph is a curve that never touches the axes
- BThe product of pressure and volume is constant at all points on the curve
- CThe graph is a straight line passing through the origin
- DThe graph is further from the origin at higher temperatures
- EThe graph is closer to the origin at higher temperatures
27.A fixed mass of ideal gas undergoes a change. Which of the following statements are always true? (Select all that apply)
Medium
- AIf the temperature is constant, the pressure is inversely proportional to the volume
- BIf the pressure is constant, the volume is directly proportional to the absolute temperature
- CIf the volume is constant, the pressure is directly proportional to the absolute temperature
- DIf the volume is constant, the pressure is inversely proportional to the absolute temperature
- EIf the temperature is constant, the pressure is directly proportional to the volume
28.For a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute temperature.
Easy
True or false?
29.The pressure of a fixed mass of gas at constant volume is directly proportional to its temperature in degrees Celsius.
Medium
True or false?
30.Real gases behave most like an ideal gas at low pressure and high temperature.
Medium
True or false?
31.In the kinetic theory model, gas pressure arises from the force exerted by gas molecules when they collide elastically with the walls of the container.
Medium
True or false?
32.Match each gas law to the quantity that is held constant.
Medium
- Boyle's law
- Charles's law
- Gay-Lussac's law
- Temperature
- Pressure
- Volume
33.Match each equation to the gas law it represents.
Medium
- P₁V₁ = P₂V₂
- V₁/T₁ = V₂/T₂
- P₁/T₁ = P₂/T₂
- Boyle's law
- Charles's law
- Gay-Lussac's law
34.The gas is heated to 600 K at constant volume. What happens to the pressure?
Medium
- AIt halves
- BIt stays the same
- CIt doubles
- DIt quadruples
35.A gas is trapped in a cylindrical tube above a column of oil. The tube has a radius of 0.5 cm and the height of the gas column is 1.0 cm. What is the volume of the trapped gas?
Medium
- A7.9 × 10⁻⁷ m³
- B1.6 × 10⁻⁶ m³
- C7.9 × 10⁻⁵ m³
- D3.1 × 10⁻⁶ m³
36.A fixed mass of gas is trapped in a container with a movable piston. The gas is compressed at constant temperature. Which statement correctly describes the change in pressure and the reason for it?
Medium
- APressure increases because the molecules collide with the walls more frequently.
- BPressure increases because the average kinetic energy of the molecules increases.
- CPressure decreases because the volume decreases.
- DPressure stays the same because the temperature is constant.
37.A fixed mass of gas undergoes a change. Which of the following statements is always true?
Medium
- AThe product of pressure and volume is proportional to the absolute temperature.
- BThe pressure is inversely proportional to the volume.
- CThe volume is directly proportional to the temperature in degrees Celsius.
- DThe pressure is directly proportional to the temperature in degrees Celsius.
38.A fixed mass of gas in a container with a movable piston is heated at constant pressure. The volume doubles. What happens to the average kinetic energy of the gas molecules?
Hard
- AIt doubles.
- BIt halves.
- CIt remains the same.
- DIt increases by a factor of √2.
39.A fixed mass of an ideal gas is taken through a cycle of changes: it is first compressed at constant temperature, then heated at constant volume, then expanded at constant temperature back to its original volume, and finally cooled at constant volume back to its original pressure. Which of the following statements are correct? (Select all that apply)
Hard
- ADuring the first compression, the pressure increases and the average kinetic energy of the molecules remains constant.
- BDuring the heating at constant volume, the pressure increases and the average kinetic energy of the molecules increases.
- CDuring the expansion at constant temperature, the pressure decreases and the average kinetic energy of the molecules decreases.
- DDuring the cooling at constant volume, the pressure decreases and the average kinetic energy of the molecules decreases.
- EThroughout the cycle, the total internal energy of the gas returns to its original value.
40.A gas is trapped in a container of fixed volume. The pressure is measured at different temperatures. A graph of pressure against temperature in degrees Celsius is plotted. What is the significance of the intercept on the temperature axis?
Medium
- AIt gives the temperature at which the pressure would be zero, which is 0 °C.
- BIt gives the temperature at which the pressure would be zero, which is -273 °C.
- CIt gives the temperature at which the volume would be zero, which is 0 K.
- DIt gives the temperature at which the gas would become ideal.
41.Complete the equation for an ideal gas using the Boltzmann constant.
Easy
pV = N ____ T
42.Calculate the number of moles of neon gas in a cylinder containing 4.7 × 10²³ molecules. Give your answer to 2 significant figures.
Medium
43.A container holds 2.0 mol of argon gas. Calculate the number of argon atoms in the container. Use Avogadro's constant N_A = 6.02 × 10²³ mol⁻¹. Give your answer to 2 significant figures.
Medium
44.A container is filled with 2.6 × 10²⁰ molecules of argon gas. The molar mass of argon is 40 g mol⁻¹. Calculate the total mass of argon in the container in grams. Give your answer to 3 significant figures.
Medium
45.What name is given to the constant with value 6.02 × 10²³ mol⁻¹?
Easy
46.Complete the equation for the average kinetic energy of a single molecule of an ideal gas.
Easy
E____k = ____ k____B T
47.Calculate the average kinetic energy of a single molecule of an ideal gas at a temperature of 300 K. Use Boltzmann constant k_B = 1.38 × 10⁻²³ J K⁻¹. Give your answer to 3 significant figures.
Medium
48.A gas occupies a volume of 3.0 m³ at a pressure of 150 Pa. It is compressed at constant temperature to a volume of 1.0 m³. Calculate the new pressure in Pa.
Medium
49.Calculate the average kinetic energy of a single molecule of an ideal gas at 400 K. Use k_B = 1.38 × 10⁻²³ J K⁻¹. Give your answer in joules to 2 significant figures.
Medium
50.A sample of gas has a volume of 2.0 × 10⁻³ m³ at a pressure of 1.5 × 10⁵ Pa and a temperature of 350 K. Calculate the number of moles of gas. Use R = 8.31 J K⁻¹ mol⁻¹. Give your answer to 2 significant figures.
Hard
51.Complete the equation relating the mean square speed of gas molecules to pressure and density.
Medium
P = (1/3) × ____ × v²
52.A fixed mass of gas is at 27 °C. It is heated at constant pressure until its volume doubles. Complete the sentence to find the final temperature.
Medium
The initial absolute temperature is ____ K, so the final absolute temperature is ____ K.
53.Define the mole.
Easy
54.State the conditions for a real gas to approximate to an ideal gas.
Medium
55.Describe how the ideal gas constant, R, is defined.
Hard
56.When there are a large number of particles in a container, their collisions with the walls of the container give rise to gas pressure. Explain how the pressure exerted by an ideal gas on the walls of its container arises in terms of molecular motion.
Hard
57.A fixed mass of gas is held in a container with a movable piston. The gas is compressed at constant temperature. Explain, in terms of molecular motion, why the pressure of the gas increases.
Hard
58.Calculate the number of moles of neon gas in a cylinder containing 4.7 × 10²³ molecules. Give your answer to 2 significant figures.
Medium
- A-0.22 mol
- B0.78 mol
- C2.78 mol
- D1.78 mol
59.A container holds 2.0 mol of argon gas. Calculate the number of argon atoms in the container. Use Avogadro's constant N_A = 6.02 × 10²³ mol⁻¹. Give your answer to 2 significant figures.
Medium
- A1.44e+24 atoms
- B1.32e+24 atoms
- C1.2e+24 atoms
- D1.08e+24 atoms
60.A container is filled with 2.6 × 10²⁰ molecules of argon gas. The molar mass of argon is 40 g mol⁻¹. Calculate the total mass of argon in the container in grams. Give your answer to 3 significant figures.
Medium
- A2.0172 g
- B-0.9828 g
- C1.0172 g
- D0.0172 g
61.Calculate the average kinetic energy of a single molecule of an ideal gas at a temperature of 300 K. Use Boltzmann constant k_B = 1.38 × 10⁻²³ J K⁻¹. Give your answer to 3 significant figures.
Medium
- A-1 J
- B1 J
- C2 J
- D6.21e-21 J
62.A gas occupies a volume of 3.0 m³ at a pressure of 150 Pa. It is compressed at constant temperature to a volume of 1.0 m³. Calculate the new pressure in Pa.
Medium
- A405 Pa
- B540 Pa
- C450 Pa
- D495 Pa
63.Calculate the average kinetic energy of a single molecule of an ideal gas at 400 K. Use k_B = 1.38 × 10⁻²³ J K⁻¹. Give your answer in joules to 2 significant figures.
Medium
- A2 J
- B8.3e-21 J
- C-1 J
- D1 J
64.A sample of gas has a volume of 2.0 × 10⁻³ m³ at a pressure of 1.5 × 10⁵ Pa and a temperature of 350 K. Calculate the number of moles of gas. Use R = 8.31 J K⁻¹ mol⁻¹. Give your answer to 2 significant figures.
Hard
- A1.1 mol
- B0.1 mol
- C2.1 mol
- D-0.9 mol

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