1.5 Ideal Gases

Question 1

What assumptions are made in the kinetic theory of gases?

Answer 1

The assumptions made in the kinetic theory of gases are:

The gas molecules are moving very fast and randomly

The molecules hardly have any volume

The gas molecules do not attract or repel each other (no intermolecular forces)

No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)

The temperature of the gas is directly proportional to the average kinetic energy of the molecules

Question 2

True or False?

Ideal gas molecules have significant volume.

Answer 2

False.

Ideal gas molecules are assumed to have negligible volume.

Question 3

Define elastic collision.

Answer 3

An elastic collision is when no kinetic energy is lost when gas molecules collide with each other.

Question 4

What is the relationship between temperature and average kinetic energy of gas molecules?

Answer 4

The temperature of the gas is directly proportional to the average kinetic energy of the molecules, i.e. as temperature increases, the average kinetic energy increases.

Question 5

What is an ideal gas?

Answer 5

An ideal gas is a gas that follows the kinetic theory of gases.

Question 6

True or False?

Real gases exactly fit the description of ideal gases.

Answer 6

False.

Real gases do not exactly fit the description of ideal gases but may come very close.

Question 7

What factors does the volume of a gas depend on?

Answer 7

The volume that a gas occupies depends on its pressure and temperature.

Question 8

What is the difference between elastic and inelastic collisions?

Answer 8

In an elastic collision, energy is conserved and particles move away in opposite directions.

In an inelastic collision, kinetic energy is not conserved and particles usually stick together

Question 9

True or False?

The kinetic theory assumes gas molecules attract each other.

Answer 9

False.

The kinetic theory assumes gas molecules do not attract or repel each other (no intermolecular forces).

Question 10

How do gases exert pressure in a container?

Answer 10

Gases exert pressure as the gas molecules are constantly colliding with the walls of the container.

Question 11

State Boyle’s Law.

Answer 11

Boyle’s Law states that pressure is inversely proportional to volume at constant temperature.

Question 12

What is the mathematical expression of Boyle’s Law?

Answer 12

The mathematical expression of Boyle’s Law is P ∝ 1/V or PV = constant.

Question 13

True or False?

Decreasing the volume of a gas at constant temperature increases its pressure.

Answer 13

True.

Decreasing the volume of a gas at constant temperature increases its pressure.

Question 14

Define Charles’ Law.

Answer 14

Charles’ Law states that volume is directly proportional to temperature in Kelvin at constant pressure.

Question 15

What is the mathematical expression of Charles’ Law?

Answer 15

The mathematical expression of Charles’ Law is V ∝ T or V/T = constant.

Question 16

How does increasing temperature affect gas pressure at constant volume?

Answer 16

Increasing temperature at constant volume increases the pressure of the gas.

Question 17

True or False?

Pressure is inversely proportional to temperature at constant volume.

Answer 17

False.

Pressure is directly proportional to temperature at constant volume.

Question 18

State the ideal gas equation.

Answer 18

The ideal gas equation is PV = nRT.

Question 19

What does P represent in the ideal gas equation?

Answer 19

P represents pressure (in pascals, Pa) in the ideal gas equation.

Question 20

What does V represent in the ideal gas equation?

Answer 20

V represents volume (in m³) in the ideal gas equation.

Question 21

What does n represent in the ideal gas equation?

Answer 21

n represents the number of moles of gas (mol) in the ideal gas equation.

Question 22

What does R represent in the ideal gas equation?

Answer 22

R represents the gas constant (8.31 J K⁻¹ mol⁻¹) in the ideal gas equation.

Question 23

What does T represent in the ideal gas equation?

Answer 23

T represents temperature (in Kelvin, K) in the ideal gas equation.

Question 24

True or False?

The ideal gas equation can be used to calculate the molar mass of a gas.

Answer 24

True.

The ideal gas equation can be used to calculate the molar mass of a gas.

Question 25

How do you convert temperature from Celsius to Kelvin?

Answer 25

To convert temperature from Celsius to Kelvin, add 273 to the Celsius temperature.

Question 26

How do you convert pressure from kilopascals to pascals?

Answer 26

To convert pressure from kilopascals to pascals, multiply by 1000.

Question 27

How do you convert volume from dm3 to m3?

Answer 27

To convert volume from dm3 to m3, divide by 1000.

Question 28

How do you convert volume from cm3 to m3?

Answer 28

To convert volume from dm3 to m3, divide by 1,000,000.

Question 29

True or False? Pressure in the ideal gas equation should be in pascals (Pa).

Answer 29

True. Pressure in the ideal gas equation should be in pascals (Pa).

Question 30

Calculate the volume, in dm3, occupied by 0.5 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.

Answer 30

The volume is 5.55 dm3. P = 220 kPa = 220 000 Pa n = 0.5 mol R = 8.31 J K-1 mol-1 T = 21 oC = 294 K V = n R T / P = 0.5 x 8.31 x 294 / 220,000 = 0.00555 = 5.55 dm3

Question 31

Calculate the pressure of a gas, in kPa, given that 0.10 moles of the gas occupy 10.0 dm3 at a temperature of 25 oC.

Answer 31

The pressure is 24.5 kPa. n = 0.10 mol V = 10.0 dm3 = 0.0100 m3 = 10.0 x 10-3 m3 R = 8.31 J K-1 mol-1 T = 25 oC = 298 K P = n R T / V = 0.10 x 8.31 x 298 / 10.1x10- 3 = 24 519 Pa = 24.5 kPa

Question 32

Calculate the temperature of a gas, in oC, if 0.05 moles of the gas occupy 1.0 dm3 at a pressure of 100 kPa.

Answer 32

The remperature is -32.3 oC. n = 0.05 mol V = 1.0 dm3 = 0.001 m3 = 1.0 x 10-3 m3 R = 8.31 J K-1 mol-1 P = 100 kPa = 100 000 Pa T = P V / n R = 100,000 x 1.0x10-3 / 0.05 x 8.31 = 240.67 K = -32.3 oC

Question 33

A flask of volume 1000 cm3 contains 6.0 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C. Calculate the molar mass of the gas.

Answer 33

The molar mass of the gas is 54.2 g mol-1. P = 300 kPa = 300 000 Pa V = 1000 cm3 = 0.001 m3 = 1.0 x 10-3 m3 R = 8.31 J K-1 mol-1 T = 23 oC = 296 K n =P V / R T = 300,000 x 1.0x10-3 / 8.31 x 296 = 0.12 mol M = 6.5 / 0.12 = 54.2 g mol-1

Question 34

Under what conditions do real gases show significant deviation from the ideal gas equation?

Answer 34

Real gases show significant deviation from the ideal gas equation when the temperature is very low or the pressure is very high.

Question 35

What is a key assumption of the kinetic theory about gas molecule volume?

Answer 35

The kinetic theory assumes that the volume the actual gas molecules themselves take up is tiny compared to the volume the gas occupies in a container.

Question 36

True or False? The kinetic theory assumes no interaction between gas molecules.

Answer 36

True. The kinetic theory assumes that when gas molecules are far apart there is very little interaction between the molecules.

Question 37

How do intermolecular forces affect gas pressure at high pressures?

Answer 37

At high pressures, intermolecular forces cause attraction between molecules, reducing the number of collisions with the container walls and resulting in less pressure than expected by the ideal gas equation.

Question 38

What happens to the fraction of space occupied by gas molecules at low temperatures and high pressures?

Answer 38

At low temperatures and high pressures, the fraction of space taken up by the molecules becomes substantial compared to the total volume.

Question 39

True or False? Real gases always behave exactly like ideal gases.

Answer 39

False. Real gases deviate from ideal gas behavior, especially at low temperatures and high pressures.

Question 40

How does the volume of gas molecules affect the accuracy of the ideal gas equation?

Answer 40

The ideal gas equation becomes increasingly inaccurate at low temperatures and high pressures because the volume of gas molecules becomes significant compared to the total volume.

Question 41

What causes the pressure of real gases to be less than expected by the ideal gas equation at high pressures?

Answer 41

At high pressures, intermolecular attractions reduce collisions with container walls, causing the pressure to be less than expected by the ideal gas equation.

Question 42

True or False? The ideal gas equation is always accurate for all gases under all conditions.

Answer 42

False. The ideal gas equation shows significant deviations for real gases, especially at low temperatures and high pressures.

Question 43

How do low temperatures affect the behavior of real gases compared to ideal gases?

Answer 43

At low temperatures, real gases deviate significantly from ideal gas behavior because the gas molecules are closer together, making intermolecular forces more significant.