Ideal Gases

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Apuntes de la lección

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 and high pressures.
At low temperatures, intermolecular attractions become significant, reducing collision frequency and force, leading to lower pressure than predicted.
At high pressures, the volume of gas particles becomes significant, reducing the available space for movement and causing deviation.

Factors Affecting Gas Volume

The volume a gas occupies depends on pressure (P) and temperature (T).
Gases exert pressure by 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 and increased pressure.
Increasing the temperature (at constant pressure) gives particles more kinetic energy, leading to more frequent collisions; to keep pressure constant, the gas expands, so volume increases.
Increasing the temperature (at constant volume) causes particles to move faster and collide more frequently with the container walls, increasing pressure.

Boyle's Law

Pressure is inversely proportional to volume when temperature is constant: P \propto \frac{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

Volume is directly proportional to temperature in Kelvin at constant pressure: V \propto T.
V/T = a constant (Charles's Law).
A graph of volume against temperature in Kelvin gives a straight line.
When a gas is heated at constant pressure, particles gain kinetic energy, collide more frequently, and the gas expands to keep pressure constant.

Pressure and Temperature Relationship

Pressure is directly proportional to temperature in Kelvin at constant volume: P \propto T.
P/T = a constant.
A graph of temperature in Kelvin against pressure gives a straight line.
Increasing temperature at constant volume increases collision frequency with the container walls, raising pressure.

Combined Gas Law

Combining the three relationships gives: \frac{PV}{T} = \text{a constant}.
For a fixed amount of gas: \frac{P₁V₁}{T₁} = \frac{P₂V₂}{T₂}.
Temperature must be in Kelvin for all gas law calculations.
This equation is used when the amount of gas (moles) is constant.

The Ideal Gas Equation

PV = nRT relates pressure, volume, temperature, and number of moles of an ideal gas.
P = pressure (Pa), V = volume (m³), n = moles (mol), R = gas constant (8.31 J K⁻¹ mol⁻¹), T = temperature (K).
The ideal gas equation can also be used to calculate the molar mass (M) of a gas.
Always convert units: 1 m³ = 1,000,000 cm³ (10⁶ cm³). To convert cm³ to m³, divide by 10⁶; to convert m³ to cm³, multiply by 10⁶.
To convert °C to K, add 273.

Molar Gas Volume

At standard temperature and pressure (STP), one mole of any gas occupies 22.7 dm³ (or 22,700 cm³).
Molar gas volume can be used to convert between moles and volume of gas at STP.
The ideal gas equation can be used to find molar volume under non-standard conditions.

Molar gas volume formula triangle

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Preguntas de práctica

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1.Which of the following is NOT an assumption of the kinetic theory of ideal 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 Boyle's Law, for a fixed amount of gas at constant temperature, the pressure of the gas is:
Easy
- Adirectly proportional to its volume
- Binversely proportional to its volume
- Cdirectly proportional to the square of its volume
- Dindependent of its volume
3.A graph of pressure of a gas against 1/volume gives a straight line through the origin. This graph represents:
Medium
- ACharles' Law
- BBoyle's Law
- Cthe relationship between pressure and temperature at constant volume
- Dthe relationship between volume and temperature at constant pressure
4.Which of the following statements about real gases is correct?
Medium
- AReal gases behave most like ideal gases at low temperatures and high pressures.
- BReal gases behave most like ideal gases at high temperatures and low pressures.
- CReal gases never deviate from ideal gas behaviour.
- DReal gases have no intermolecular forces at any temperature.
5.At high pressures, a real gas deviates from ideal gas behaviour mainly because:
Medium
- Athe volume of the gas particles becomes significant compared to the total volume
- Bintermolecular forces become negligible
- Cthe collisions between particles are no longer elastic
- Dthe temperature of the gas decreases
6.Which of the following statements are true for an ideal gas? (select all that apply)
Medium
- AGas molecules are in constant, rapid, random motion.
- BIntermolecular forces between gas particles are significant.
- CCollisions between gas molecules are perfectly elastic.
- DThe volume of individual gas molecules is negligible compared to the total volume.
- EThe temperature of a gas is directly proportional to the average kinetic energy of its particles.
7.In an elastic collision, kinetic energy is conserved.
Easy
True or false?
8.According to Charles' Law, the volume of a gas is directly proportional to its temperature in degrees Celsius at constant pressure.
Easy
True or false?

Más preguntas

9.Match each gas law statement to its correct proportionality relationship.
Medium
- Boyle's Law (constant T)
- Charles' Law (constant P)
- Pressure–temperature law (constant V)
- P ∝ 1/V
- V ∝ T
- P ∝ T
10.Place the steps for calculating the molar mass of a gas from experimental pressure, volume, temperature and mass data into the correct order.
Medium
- Rearrange PV = nRT to make n the subject
- Convert all quantities to SI units (Pa, m³, K)
- Substitute values and calculate the number of moles, n
- Calculate molar mass using M = mass / n
11.Which of the following statements correctly describe the assumptions of the kinetic theory of ideal 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 of the gas.
- 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.
12.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.
- CAt low temperatures, intermolecular attractions cause the pressure to be lower than predicted by the ideal gas equation.
- DAt high pressures, the volume of gas particles becomes significant, causing deviation.
- EReal gases follow the ideal gas equation exactly under all conditions.
13.According to Charles' Law, a graph of volume against temperature in Kelvin for a fixed amount of gas at constant pressure is a straight line passing through the origin.
Easy
True or false?
14.At high pressures, real gases behave more like ideal gases because the particles are closer together.
Easy
True or false?
15.Which graph correctly represents Boyle's Law?
Easy
- AA graph of pressure against volume gives a straight line through the origin.
- BA graph of pressure against 1/volume gives a straight line through the origin.
- CA graph of volume against temperature in Kelvin gives a straight line through the origin.
- DA graph of pressure against temperature in Kelvin gives a straight line through the origin.
16.A gas cylinder contains helium at 20,000 kPa. It is used to fill 160 balloons, each of volume 14.1 dm³, at 298 K and 108 kPa. What is the total volume of helium inside the cylinder in dm³?
Medium
- A12.2 dm³
- B1.22 dm³
- C122 dm³
- D1220 dm³
17.A fixed mass of gas at constant temperature has its volume halved. Which statement best explains what happens to the pressure?
Medium
- AThe molecules collide with the walls twice as frequently, so the pressure doubles
- BThe molecules move twice as fast, so the pressure doubles
- CThe molecules become larger, so the pressure doubles
- DThe molecules attract each other more strongly, so the pressure doubles
18.A graph of PV (y-axis) against P (x-axis) is plotted for a fixed mass of ideal gas at constant temperature. Which description of the graph is correct?
Medium
- AA horizontal straight line
- BA straight line through the origin
- CA curve that rises as P increases
- DA curve that falls as P increases
19.A gas in a sealed rigid container is cooled from 300 K to 150 K. What happens to the pressure of the gas?
Medium
- AIt halves
- BIt doubles
- CIt stays the same
- DIt quarters
20.Two sealed flasks of equal volume are at the same temperature. Flask A contains 1 mol of helium and flask B contains 1 mol of carbon dioxide. Which statement is correct?
Medium
- AThe pressures in A and B are equal because both contain the same number of moles at the same volume and temperature
- BThe pressure in B is greater because CO2 molecules are heavier
- CThe pressure in A is greater because helium atoms are smaller
- DThe pressure in B is greater because CO2 molecules move faster
21.A 2.0 dm3 flask contains 10.84 g of a gaseous alkane X. The pressure in the flask is 300 kPa and the temperature is 20 °C. (R = 8.31 J K-1 mol-1) Which alkane is X?
Hard
- AC3H8 (Mr = 44)
- BC2H6 (Mr = 30)
- CC4H10 (Mr = 58)
- DCH4 (Mr = 16)
22.A sample of O2(g) at 303 kPa and 28 °C occupies 95.0 cm3. Which statements about this sample are correct? (select all that apply)
Medium
- AThe amount of oxygen present is approximately 0.0114 mol
- BThe mass of oxygen formed is approximately 0.36 g
- CO2 behaves less ideally at very high pressures because the volume of the molecules becomes significant
- DO2 behaves less ideally at very low temperatures because intermolecular attractions become significant
- EThe volume must be converted to dm3 before substituting into PV = nRT
23.Which changes would increase the frequency of collisions of gas molecules with the walls of a fixed-volume container? (select all that apply)
Medium
- AIncreasing the temperature of the gas
- BAdding more gas molecules to the container
- CReducing the volume of the container at constant temperature
- DCooling the gas
- ERemoving gas molecules from the container
24.The temperature of a gas is directly proportional to the average kinetic energy of its particles.
Easy
True or false?
25.Real gases behave most like ideal gases at low temperatures and high pressures.
Easy
True or false?
26.In an experiment to measure the molar mass of a gas, the gas is collected in a pre-weighed gas syringe. Which of the following is the most important reason for measuring the mass of the gas by difference?
Medium
- ATo account for the mass of the syringe
- BTo ensure the gas is pure
- CTo prevent the gas from escaping
- DTo correct for changes in temperature
27.A student calculates the molar mass of a gas using the ideal gas equation. They measure the volume in cm³ but forget to convert it to m³ before substituting into PV = nRT. How will this error affect the calculated value of the molar mass?
Medium
- AThe calculated molar mass will be 10⁶ times too small
- BThe calculated molar mass will be 10⁶ times too large
- CThe calculated molar mass will be 10³ times too small
- DThe calculated molar mass will be 10³ times too large
28.Which piece of apparatus is most suitable for measuring the volume of gas evolved in a reaction where the gas is soluble in water?
Medium
- AGas syringe
- BMeasuring cylinder
- CBurette
- DVolumetric flask
29.A 0.245 g sample of a volatile liquid is vaporised in a 250 cm³ flask at 100 °C and 101 kPa. What is the molar mass of the liquid? (R = 8.31 J K⁻¹ mol⁻¹)
Hard
- A30 g mol⁻¹
- B58 g mol⁻¹
- C87 g mol⁻¹
- D116 g mol⁻¹
30.Which of the following procedures would improve the accuracy of an experiment to determine the molar mass of a gas using the ideal gas equation? (select all that apply)
Medium
- AMeasuring the volume of gas at room temperature and pressure rather than at elevated temperature
- BEnsuring the gas syringe is airtight
- CUsing a larger mass of gas
- DMeasuring the pressure using a barometer
- EIgnoring the mass of the gas when weighing
31.In an elastic collision between gas molecules, kinetic energy is conserved.
Easy
True or false?
32.Match each experimental procedure with its purpose when determining the molar mass of a gas.
Medium
- Weighing the gas syringe before and after filling
- Using a water bath to control temperature
- Measuring pressure with a barometer
- Checking the syringe for leaks
- To find the mass of gas collected
- To keep temperature constant
- To obtain accurate pressure reading
- To ensure no gas escapes
33.Place the steps for calculating the molar mass of a gas from experimental data into the correct order.
Medium
- Calculate the number of moles using n = PV/RT
- Measure the mass of the gas
- Calculate molar mass using M = mass/n
- Convert volume to m³ and temperature to K
34.Which of the following graphs would produce a straight line through the origin?
Medium
- APressure against volume
- BPressure against 1/volume
- CVolume against pressure
- D1/pressure against volume
35.A gas cylinder contains 20.0 dm³ of helium at 15 000 kPa and 25 °C. It is used to fill balloons each of volume 12.0 dm³ at 100 kPa and 25 °C. What is the maximum number of balloons that can be filled?
Hard
- A25
- B250
- C2.5
- D2500
36.A sample of gas occupies 500 cm³ at 25 °C and 100 kPa. What volume will it occupy at 50 °C and 200 kPa?
Hard
- A250 cm³
- B273 cm³
- C500 cm³
- D1000 cm³
37.Which of the following statements about the kinetic theory of ideal gases is correct?
Medium
- AGas molecules attract each other strongly
- BThe volume of gas molecules is negligible compared to the container volume
- CCollisions between gas molecules are inelastic
- DThe temperature of a gas is inversely proportional to the average kinetic energy of its particles
38.Which of the following is the correct value of the gas constant R used in the ideal gas equation PV = nRT?
Easy
- A8.31 J K⁻¹ mol⁻¹
- B0.0821 J K⁻¹ mol⁻¹
- C6.02 × 10²³ J K⁻¹ mol⁻¹
- D1.38 × 10⁻²³ J K⁻¹ mol⁻¹
39.A graph of pressure (y-axis) against 1/volume (x-axis) for a fixed mass of gas at constant temperature is:
Easy
- Aa straight line through the origin
- Ba curve that slopes downwards
- Ca horizontal straight line
- Da straight line with a negative gradient
40.In the kinetic theory of ideal gases, gas molecules are assumed to be in constant, rapid, random motion.
Easy
True or false?
41.Complete the statement of Boyle's Law.
Easy
At constant temperature, the pressure of a fixed amount of gas is ____ proportional to its volume, so PV = ____.
42.Complete the ideal gas equation and identify the units of each variable.
Easy
PV = nRT, where P is in ____, V is in ____, n is in mol, R is in J K⁻¹ mol⁻¹, and T is in ____.
43.Calculate the volume, in dm³, occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C. (R = 8.31 J K⁻¹ mol⁻¹)
Medium
44.A 2.00 dm³ container of oxygen at a pressure of 80 kPa was heated from 20 °C to 70 °C. The volume expanded to 2.25 dm³. Calculate the final pressure of the gas in kPa. Give your answer to 2 significant figures.
Medium
45.A 1.5 dm³ container at 5 °C is allowed to warm to 21 °C at constant pressure. Calculate the volume of gas, in cm³, that escapes from the container. Give your answer to 3 significant figures.
Medium
46.Complete the statements about gas laws by filling in the blanks.
Medium
Boyle's Law states that pressure is ____ proportional to volume at constant temperature. Charles' Law states that volume is ____ proportional to temperature in Kelvin at constant pressure.
47.The ideal gas equation is PV = nRT. Identify the units of each variable as used in this equation.
Medium
P is measured in ____; V in ____; n in ____; R in J K⁻¹ mol⁻¹; T in ____.
48.A 1.5 dm3 container of gas at 5 °C is allowed to warm to 21 °C at constant pressure. Calculate the volume of gas, in cm3, that escapes from the container. Give your answer to 3 significant figures.
Hard
49.A balloon contains 2500 mL of helium gas at 75 °C. Determine the new volume in mL of the gas when the temperature changes to 55 °C, assuming the pressure is constant. Give your answer to three significant figures.
Medium
50.A 10.0 L container of helium gas with a pressure of 33 000 Pa at 0 °C is heated until the new pressure is 200 000 Pa. Determine the new temperature of the gas in K, assuming the volume remains constant.
Hard
51.A bubble of gas escapes from a scuba tank at 60 m depth where the pressure is 588 kPa and the temperature is 8 °C. Determine the factor by which the volume of the bubble increases by the time it reaches the surface where the pressure is 100 kPa and the temperature is 20 °C. Give your answer to 2 significant figures.
Hard
52.Complete the statements about real gases by filling in the blanks.
Medium
Real gases deviate from ideal behaviour at ____ temperatures and ____ pressures. At high pressure, the ____ of the gas particles becomes significant. At low temperature, ____ between particles become significant.
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.Under what conditions does a real gas behave most like an ideal gas?
Medium
55.Explain why calculating gas volumes in a reaction is likely to be more accurate at 150 °C than at room temperature.
Hard
56.Explain why a gas deviates more from ideal behaviour at high pressures.
Hard
57.Explain what is meant by the term 'ideal gas' and state the conditions under which carbon dioxide shows deviation from ideal gas behaviour.
Medium
58.Calculate the volume, in dm³, occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C. (R = 8.31 J K⁻¹ mol⁻¹)
Medium
- A10.67 dm³
- B8.67 dm³
- C7.67 dm³
- D9.67 dm³
59.A 2.00 dm³ container of oxygen at a pressure of 80 kPa was heated from 20 °C to 70 °C. The volume expanded to 2.25 dm³. Calculate the final pressure of the gas in kPa. Give your answer to 2 significant figures.
Medium
- A75 kPa
- B83 kPa
- C91 kPa
- D99 kPa
60.A 1.5 dm³ container at 5 °C is allowed to warm to 21 °C at constant pressure. Calculate the volume of gas, in cm³, that escapes from the container. Give your answer to 3 significant figures.
Medium
- A86.3 cm³
- B103.5 cm³
- C77.7 cm³
- D94.9 cm³
61.A 1.5 dm3 container of gas at 5 °C is allowed to warm to 21 °C at constant pressure. Calculate the volume of gas, in cm3, that escapes from the container. Give your answer to 3 significant figures.
Hard
- A77 cm3
- B104 cm3
- C95 cm3
- D86 cm3
62.A balloon contains 2500 mL of helium gas at 75 °C. Determine the new volume in mL of the gas when the temperature changes to 55 °C, assuming the pressure is constant. Give your answer to three significant figures.
Medium
- A2360 mL
- B2124 mL
- C2832 mL
- D2596 mL
63.A 10.0 L container of helium gas with a pressure of 33 000 Pa at 0 °C is heated until the new pressure is 200 000 Pa. Determine the new temperature of the gas in K, assuming the volume remains constant.
Hard
- A1489 K
- B1821 K
- C1655 K
- D1987 K
64.A bubble of gas escapes from a scuba tank at 60 m depth where the pressure is 588 kPa and the temperature is 8 °C. Determine the factor by which the volume of the bubble increases by the time it reaches the surface where the pressure is 100 kPa and the temperature is 20 °C. Give your answer to 2 significant figures.
Hard
- A6
- B8
- C5
- D7

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