Ideal Gases

邊玩邊學

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Kinetic Theory of Gases

Gas molecules are in constant, rapid, random motion.
The volume of individual gas molecules is negligible compared to the total volume of the gas.
No intermolecular forces exist between gas particles; they do not attract or repel one another.
All collisions between gas molecules are perfectly elastic (no kinetic energy is lost).
The temperature of a gas is directly proportional to the average kinetic energy of its particles.

Gas particles and pressure

Ideal vs. Real Gases

Ideal gases follow all assumptions of the kinetic theory.
Real gases do not perfectly follow this model, but under low pressure and high temperature, they behave similarly to ideal gases.
Real gases deviate from ideal behaviour especially at low temperatures (stronger attractions between particles) and high pressures (particle volume becomes significant).
At high pressure, particles are close together, so their volume becomes significant, reducing available space for movement.
At low temperatures, attractions between molecules become significant, reducing the frequency and force of collisions with container walls, leading to lower pressure than predicted.

Factors Affecting Gas Volume

The volume that a gas occupies depends on pressure (P) and temperature (T).
Gases in a container exert a pressure as the gas molecules are constantly colliding with the walls of the container.
Decreasing the volume (at constant temperature) causes molecules to be squashed together, resulting in more frequent collisions with the container wall.
The pressure of the gas increases when volume decreases at constant temperature.
Increasing the temperature (at constant volume) causes molecules to gain more kinetic energy, move faster, and collide more frequently with the container walls, leading to an increase in pressure.

Boyle's Law

Pressure is inversely proportional to volume (when temperature is constant): P ∝ 1/V.
PV = a constant (Boyle's Law).
A graph of pressure against 1/volume gives a straight line.
A graph of pressure against volume gives a curve.
A graph of PV versus P gives a straight line.

Pressure and volume

Charles's Law

When a gas is heated (at constant pressure), particles gain more kinetic energy, leading to more frequent collisions with container walls.
To keep pressure constant, the gas must expand, so the volume increases.
Volume is directly proportional to the temperature in Kelvin (at constant pressure): V ∝ T.
V/T = a constant (Charles's Law).
A graph of volume against temperature in Kelvin gives a straight line.

Pressure and Temperature Relationship

Increasing the temperature (at constant volume) causes molecules to gain more kinetic energy, move faster, and collide more frequently with container walls.
This leads to an increase in pressure.
Pressure is directly proportional to temperature (in Kelvin) at constant volume: P ∝ T.
P/T = a constant.
A graph of temperature in Kelvin against pressure gives a straight line.

The Ideal Gas Equation

Combining the gas laws gives PV = nRT.
P = pressure (pascals, Pa); V = volume (m³); n = number of moles of gas (mol); R = gas constant (8.31 J K⁻¹ mol⁻¹); T = temperature (Kelvin, K).
The ideal gas equation can also be used to calculate the molar mass (M) of a gas.
When n and R are constant, the ideal gas law simplifies to P₁V₁/T₁ = P₂V₂/T₂.
Temperature must be in Kelvin; add 273 to the Celsius temperature.
To convert m³ to cm³, multiply by 10⁶; to convert cm³ to m³, divide by 10⁶ (or multiply by 10⁻⁶).
Always check units before using the ideal gas equation; it requires volume in m³.

Molar Gas Volume

Gases in a container exert a pressure as the gas molecules are constantly colliding with the walls of the container.
Changing gas volume: decreasing the volume (at constant temperature) of the container causes the molecules to be squashed together which results in more frequent collisions with the container wall.
The pressure of the gas increases.
Gas particles exert a pressure by constantly colliding with the walls of the container.

Molar gas volume formula triangle

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1.Which of the following is NOT an assumption of the kinetic theory of gases?
Easy
- AGas molecules are in constant, rapid, random motion
- BThe volume of individual gas molecules is negligible compared to the total volume of the gas
- CIntermolecular forces between gas particles are significant
- DAll collisions between gas molecules are perfectly elastic
2.According to the kinetic theory, the temperature of a gas is directly proportional to:
Easy
- AThe average kinetic energy of its particles
- BThe volume of the gas
- CThe pressure of the gas
- DThe number of moles of gas
3.Which of the following statements about real gases is correct?
Easy
- AReal gases behave most like ideal gases at high pressure and low temperature
- BReal gases behave most like ideal gases at low pressure and high temperature
- CReal gases always behave exactly like ideal gases
- DReal gases never deviate from ideal gas behaviour
4.A gas is heated at constant volume. Which statement best explains the increase in pressure?
Medium
- AThe gas particles expand and occupy more space
- BThe gas particles gain kinetic energy and collide more frequently with the container walls
- CThe gas particles become larger and hit the walls harder
- DThe number of gas particles increases
5.A sample of gas is compressed at constant temperature. Which of the following graphs would be a straight line through the origin?
Medium
- APressure against volume
- BPressure against 1/volume
- CVolume against pressure
- DPV against 1/volume
6.Which of the following is the correct expression of Charles's Law?
Medium
- AV ∝ 1/T
- BV ∝ T
- CV ∝ P
- DV ∝ 1/P
7.A fixed amount of gas undergoes a change where pressure and temperature both change. Which equation correctly relates the initial and final states?
Medium
- AP1V1 = P2V2
- BV1/T1 = V2/T2
- CP1V1/T1 = P2V2/T2
- DP1T1 = P2T2
8.Which of the following is the correct unit for the gas constant R in the ideal gas equation?
Medium
- AJ K mol
- BJ K⁻¹ mol⁻¹
- CPa m³ K⁻¹ mol⁻¹
- Ddm³ kPa K⁻¹ mol⁻¹

更多題目

9.In the ideal gas equation PV = nRT, what does the symbol n represent?
Medium
- ANumber of molecules
- BNumber of moles of gas
- CNumber of atoms
- DAvogadro's number
10.Under which conditions does a real gas deviate most from ideal gas behaviour?
Hard
- AHigh temperature and low pressure
- BLow temperature and high pressure
- CHigh temperature and high pressure
- DLow temperature and low pressure
11.Which of the following statements about the volume of gas particles is correct for an ideal gas?
Medium
- AThe volume of the particles is negligible compared to the total volume
- BThe volume of the particles is a significant fraction of the total volume
- CThe volume of the particles is exactly half the total volume
- DThe volume of the particles is equal to the total volume
12.Which of the following graphs represents Boyle's Law?
Medium
- APressure against volume (a curve)
- BPressure against 1/volume (a straight line through origin)
- CVolume against temperature (a straight line through origin)
- DPressure against temperature (a straight line through origin)
13.Which of the following are assumptions of the kinetic theory of gases? (select all that apply)
Medium
- AGas molecules are in constant, rapid, random motion
- BThe volume of individual gas molecules is negligible compared to the total volume
- CIntermolecular forces between gas particles are significant
- DAll collisions between gas molecules are perfectly elastic
- EThe temperature of a gas is directly proportional to the average kinetic energy of its particles
14.Which of the following statements about real gases are correct? (select all that apply)
Medium
- AReal gases deviate from ideal behaviour at low temperatures
- BReal gases deviate from ideal behaviour at high pressures
- CReal gases have no intermolecular forces
- DAt high pressure, the volume of gas particles becomes significant
- EAt low temperature, attractions between molecules become significant
15.In an elastic collision, kinetic energy is conserved.
Easy
True or false?
16.The pressure of a gas is inversely proportional to its volume at constant temperature.
Easy
True or false?
17.At constant pressure, the volume of a gas is directly proportional to its temperature in degrees Celsius.
Easy
True or false?
18.Real gases behave more like ideal gases at high temperatures and low pressures.
Medium
True or false?
19.Match each gas law with its correct relationship.
Medium
- Boyle's Law
- Charles's Law
- Pressure-Temperature Law (constant volume)
- P ∝ 1/V
- V ∝ T
- P ∝ T
20.Arrange the steps to calculate the volume of gas using the ideal gas equation in the correct order.
Medium
- Rearrange the ideal gas equation to find volume: V = nRT/P
- Convert all units to SI: pressure in Pa, volume in m³, temperature in K
- Substitute the values into the rearranged equation
- Calculate the volume and convert to the required unit if necessary
21.Which of the following statements about the kinetic theory of gases are correct? (select all that apply)
Medium
- AGas molecules are in constant, rapid, random motion.
- BThe volume of individual gas molecules is negligible compared to the total volume of the gas.
- CIntermolecular forces between gas particles are significant.
- DAll collisions between gas molecules are perfectly elastic.
- EThe temperature of a gas is inversely proportional to the average kinetic energy of its particles.
22.Match each gas law with the correct relationship it describes.
Medium
- Boyle's Law
- Charles's Law
- Pressure law (at constant volume)
- P ∝ 1/V at constant temperature
- V ∝ T at constant pressure
- P ∝ T at constant volume
23.Arrange the steps to calculate the volume of a gas using the ideal gas equation in the correct order.
Medium
- Rearrange the ideal gas equation to make volume the subject: V = nRT/P.
- Convert the given temperature from °C to Kelvin by adding 273.
- Convert the pressure from kPa to Pa by multiplying by 1000.
- Substitute the values into the rearranged equation and calculate the volume in m³.
- Convert the volume from m³ to dm³ by multiplying by 1000.
24.Which of the following graphs would be a straight line through the origin for a fixed amount of ideal gas at constant temperature?
Medium
- APressure against volume
- BPressure against 1/volume
- CVolume against temperature in °C
- DPressure against temperature at constant volume
25.Which graph best represents Boyle's Law for a fixed amount of ideal gas at constant temperature?
Medium
- APressure against 1/volume gives a straight line through the origin
- BPressure against volume gives a straight line through the origin
- CPressure against volume gives a straight line with a positive y-intercept
- DPressure against temperature gives a curve
26.Which equation correctly relates the initial and final states of a fixed amount of gas when pressure, volume and temperature all change?
Medium
- AP₁V₁/T₁ = P₂V₂/T₂
- BP₁V₁T₁ = P₂V₂T₂
- CP₁T₁/V₁ = P₂T₂/V₂
- DP₁V₁ = P₂V₂
27.In the ideal gas equation PV = nRT, what does n represent?
Easy
- ANumber of moles of gas
- BNumber of gas particles
- CMolar mass of the gas
- DNumber of collisions per second
28.Which of the following is an assumption of the kinetic theory of gases?
Easy
- AThe volume of individual gas molecules is negligible compared to the total volume of the gas
- BGas molecules attract each other with weak forces
- CCollisions between gas molecules are inelastic
- DThe temperature of a gas is inversely proportional to the average kinetic energy of its particles
29.At constant temperature, the pressure of a fixed amount of ideal gas is inversely proportional to its volume.
Easy
True or false?
30.At constant pressure, the volume of a fixed amount of ideal gas is directly proportional to its temperature in degrees Celsius.
Easy
True or false?
31.Which pair of variables must be measured to determine the number of moles of gas in the container using PV = nRT?
Medium
- APressure, volume and temperature
- BPressure, volume and molar mass
- CMass, volume and temperature
- DPressure, temperature and density
32.The gas constant R has units J K⁻¹ mol⁻¹.
Easy
True or false?
33.A gas syringe contains 100 cm³ of gas at 20 °C. The syringe is heated to 40 °C at constant pressure. Which volume would be expected if the gas behaves ideally?
Medium
- A107 cm³
- B200 cm³
- C50 cm³
- D100 cm³
34.Which of the following precautions improve the accuracy of a gas volume measurement in a syringe? (select all that apply)
Medium
- AReading the volume at eye level
- BAllowing the syringe to reach room temperature before reading
- CUsing a syringe with a larger volume scale
- DChecking for leaks in the apparatus
- EReading the volume immediately after adding the reactant
35.Match each experimental observation with the correct gas law explanation.
Medium
- A balloon expands when warmed in a hot room
- A sealed syringe plunger is harder to push when the volume is halved
- A sealed rigid container's pressure increases when heated
- Charles's Law: V ∝ T at constant P
- Boyle's Law: P ∝ 1/V at constant T
- Pressure Law: P ∝ T at constant V
36.Place the steps for determining the molar mass of an unknown gas using the ideal gas equation in the correct order.
Medium
- Measure the mass of the gas in a known volume flask
- Measure the pressure and temperature of the gas
- Calculate moles using n = PV/RT
- Calculate molar mass using M = mass/n
37.A gas is collected in a eudiometer tube over water. The total pressure is 101 kPa and the water vapour pressure at the experimental temperature is 3 kPa. Which correction should be applied to find the pressure of the dry gas?
Medium
- ASubtract 3 kPa from 101 kPa
- BAdd 3 kPa to 101 kPa
- CMultiply 101 kPa by 3
- DDivide 101 kPa by 3
38.When using a gas syringe, the volume reading should be taken after the plunger has stopped moving and the apparatus has reached thermal equilibrium.
Easy
True or false?
39.A student calculates the volume of 0.50 mol of an ideal gas at 100 kPa and 300 K using V = nRT/P and obtains 0.0125 m³. Which of the following statements about this calculation are correct? (select all that apply)
Hard
- AThe volume is equivalent to 12.5 dm³
- BThe pressure must be converted to 100 000 Pa before substitution
- CThe temperature should be converted to 27 °C
- DThe gas constant R = 8.31 J K⁻¹ mol⁻¹ is used
- EThe volume should be reported in cm³ without conversion
40.Which graph correctly represents the relationship between pressure and volume for a fixed amount of ideal gas at constant temperature?
Medium
- AA curve that decreases as volume increases
- BA straight line through the origin
- CA straight line with a positive intercept on the pressure axis
- DA curve that increases as volume increases
41.Convert 25 °C to Kelvin. Give your answer to the nearest whole number.
Medium
42.A gas occupies a volume of 2.0 dm³ at a pressure of 100 kPa. Calculate the new volume in dm³ when the pressure is increased to 200 kPa at constant temperature.
Medium
43.Calculate the volume occupied by 0.50 mol of an ideal gas at 100 kPa and 300 K. Use R = 8.31 J K⁻¹ mol⁻¹. Give your answer in dm³ to 3 significant figures.
Medium
44.Complete the statement about the kinetic theory of gases.
Easy
The temperature of a gas is directly proportional to the average ____ energy of its particles.
45.Complete the statement about Boyle's Law.
Medium
Boyle's Law states that the pressure of a fixed amount of gas is ____ proportional to its volume at constant temperature.
46.Complete the statement about Charles's Law.
Medium
Charles's Law states that the volume of a fixed amount of gas is directly proportional to its temperature in ____ at constant pressure.
47.What is the name of the gas law that states P ∝ 1/V at constant temperature?
Easy
48.What is the name of the gas law that states V ∝ T at constant pressure?
Easy
49.Convert 25 °C to Kelvin.
Medium
50.A sample of gas occupies 2.0 dm³ at 100 kPa. Calculate the new volume in dm³ when the pressure is increased to 200 kPa at constant temperature.
Medium
51.A 500 cm³ sample of gas exerts a pressure of 120 kPa at 27 °C. Calculate the amount of gas in moles. Use R = 8.31 J K⁻¹ mol⁻¹.
Medium
52.Calculate the volume of hydrogen gas, in dm³, produced at 25 °C and 100 kPa. Use R = 8.31 J K⁻¹ mol⁻¹ and Ar(Mg) = 24.3.
Hard
53.Explain what is meant by the term ideal gas and state the conditions under which carbon dioxide shows deviation from ideal gas behaviour.
Hard
54.Explain why O₂(g) behaves even less ideally at very high pressures and very low temperatures.
Medium
55.Describe how the student should set up the apparatus to collect and measure the volume of hydrogen gas produced.
Medium
56.Explain why a real gas such as carbon dioxide deviates more from ideal behaviour at high pressure than at low pressure.
Hard
57.Explain why gas volume calculations in a reaction are likely to be more accurate at 150 °C than at room temperature.
Hard
58.Convert 25 °C to Kelvin. Give your answer to the nearest whole number.
Medium
- A358 K
- B328 K
- C268 K
- D298 K
59.A gas occupies a volume of 2.0 dm³ at a pressure of 100 kPa. Calculate the new volume in dm³ when the pressure is increased to 200 kPa at constant temperature.
Medium
- A0 dm³
- B3 dm³
- C1 dm³
- D2 dm³
60.Calculate the volume occupied by 0.50 mol of an ideal gas at 100 kPa and 300 K. Use R = 8.31 J K⁻¹ mol⁻¹. Give your answer in dm³ to 3 significant figures.
Medium
- A14.5 dm³
- B11.5 dm³
- C12.5 dm³
- D13.5 dm³
61.Convert 25 °C to Kelvin.
Medium
- A298 K
- B268 K
- C328 K
- D358 K
62.A sample of gas occupies 2.0 dm³ at 100 kPa. Calculate the new volume in dm³ when the pressure is increased to 200 kPa at constant temperature.
Medium
- A2 dm³
- B1 dm³
- C0 dm³
- D3 dm³
63.A 500 cm³ sample of gas exerts a pressure of 120 kPa at 27 °C. Calculate the amount of gas in moles. Use R = 8.31 J K⁻¹ mol⁻¹.
Medium
- A0.024 mol
- B1.024 mol
- C-0.976 mol
- D2.024 mol
64.Calculate the volume of hydrogen gas, in dm³, produced at 25 °C and 100 kPa. Use R = 8.31 J K⁻¹ mol⁻¹ and Ar(Mg) = 24.3.
Hard
- A3.44 dm³
- B1.44 dm³
- C2.44 dm³
- D4.44 dm³

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