Gas LawsUnit 4 - IB Notes

Real vs. Ideal Gas

• KMT describes IDEAL gases. • This works for most gases … mostly • REAL gases are different:

Electrostatic Attractions

Volume

Avogadro’s Law

Equal volumes of different gases at the same temperature and pressure contain the same number of moles of particles!

Ideal Gas Law…

1 mole of a gas = 22.4 L

P = pressure (atm, kPa, mm Hg) V = volume (L or dm3) n = # of moles of gas R = ideal gas constant T = temperature (K)

Ideal Gas Law…

PV = nRT

R = 0.0821 L atm mol-1 K-1 R = 8.314 dm3 kPa mol-1 K-1 R = 62.4 L mm Hg mol-1 K-1

Example Problems

Calculate the volume of 10.0 moles of He gas at a pressure of 300 kPa and 50.0 ˚C.

Example Problems

Calculate the volume of 1.00 mol of H2 at STP*.

*STP = 0.00 ˚C and 1.00 atm

Gas Law History

P

V

V1P1 = V2P2

Boyle’s Law

Gas Law History

Charles’s Law

V

T

V1 = V2 T1 T2

Temperature is ALWAYS in Kelvin!

Gas Law History

Guy-Lussac’s Law

P1 = P2 T1 T2

Temperature is ALWAYS in Kelvin!

P

T

Combined Gas Law…From your Reference Tables

P1V1 P2V2

T1 T2=

Combined Gas Law…From your Reference Tables

P1V1 P2V2

T1 T2=

Constant Temperature = Boyle’s Law Example: heat is not added to the system and system is not insulated.

Combined Gas Law…From your Reference Tables

P1V1 P2V2

T1 T2=

Constant Temperature = Boyle’s Law Example: heat is not added to the system and system is not insulated.

Constant Pressure = Charles’s Law Example: system is open to air

Combined Gas Law…From your Reference Tables

P1V1 P2V2

T1 T2=

Constant Temperature = Boyle’s Law Example: heat is not added to the system and system is not insulated.

Constant Pressure = Charles’s Law Example: system is open to air

Constant Volume = Gay-Lussac’s Law Example: system is enclosed in a non-expandable container (glass jar).

Dalton’s Law of Partial Pressures

The total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture.

1. number of moles of gas 2. size of container 3. temperature of mixture

Combined Gas Law

Combining the above three laws allows us to

calculate changes for systems in which volume,

pressure, and temperature are changing.

*again, temperature must be expressed in Kelvin

* Notice that when

• Temperature is constant, the equation becomes Boyle’s Law

o Example: heat is not added to the system and system is not insulated

• Pressure is constant, the equation becomes Charles’ Law

o Example: system is open to air

• Volume is constant, the equation becomes Gay-Lussac’s Law

o Example: system in enclosed in a non-expandable container such as a glass

jar

Dalton’s Law of Partial Pressures

Dalton’s Law states that: The total pressure of a mixture of gases is equal to the

sum of the pressures of all the gases in the mixture.

Ptotal = P1 + P2 + P3 + …

The partial pressure of the gas depends on

1. the number of moles of gas,

2. The size of the container

3. the temperature of the mixture

Example 1:

A mixture of oxygen, carbon dioxide, and nitrogen has a total pressure 0.97 atm.

What is the partial pressure of O2, if the partial pressure of CO2 is 0.70 atm and the

partial pressure of N2 is 0.12 atm?

Ptotal = P1 + P2 + P3 + …

Ptotal = Pnitrogen + P carbon dioxide + Poxygen

0.97 atm = 0.12 atm + 0.70 atm + X

X= 0.15 atm

Dalton - Examples

A mixture of oxygen, carbon dioxide, and nitrogen has a total pressure of 0.97 atm. What is the partial pressure of O2 if the partial pressure of CO2 is 0.70 atm and the partial pressure of N2 is 0.12 atm?

Combined Gas Law

Combining the above three laws allows us to

calculate changes for systems in which volume,

pressure, and temperature are changing.

*again, temperature must be expressed in Kelvin

* Notice that when

• Temperature is constant, the equation becomes Boyle’s Law

o Example: heat is not added to the system and system is not insulated

• Pressure is constant, the equation becomes Charles’ Law

o Example: system is open to air

• Volume is constant, the equation becomes Gay-Lussac’s Law

o Example: system in enclosed in a non-expandable container such as a glass

jar

Dalton’s Law of Partial Pressures

Dalton’s Law states that: The total pressure of a mixture of gases is equal to the

sum of the pressures of all the gases in the mixture.

Ptotal = P1 + P2 + P3 + …

The partial pressure of the gas depends on

1. the number of moles of gas,

2. The size of the container

3. the temperature of the mixture

Example 1:

A mixture of oxygen, carbon dioxide, and nitrogen has a total pressure 0.97 atm.

What is the partial pressure of O2, if the partial pressure of CO2 is 0.70 atm and the

partial pressure of N2 is 0.12 atm?

Ptotal = P1 + P2 + P3 + …

Ptotal = Pnitrogen + P carbon dioxide + Poxygen

0.97 atm = 0.12 atm + 0.70 atm + X

X= 0.15 atm

Dalton - Water Vapor

Particularly useful when working in the lab, collecting gas over water. There is always some water vapor in the air. Must take into consideration the pressure that water vapor exerts on the total pressure.

• The total pressure equals the pressure of the water vapor + the pressure of the gas.

Dalton’s Law is particularly useful when you are working in the lab and have

collected gas over water. Because there is always some water vapor in the air, you

must take into consideration the pressure that water vapor exerts on the total pressure.

the total pressure equals the pressure of the water vapor + the pressure of the gas.

Ptotal = Pgas + P water vapor

Because water vapor pressure varies with temperature, you must make sure to take

that into consideration. Many sources have tables of water vapor pressure at various

temperatures.

Temperature

(°C)

Vapour

pressure

(kPa)

0 0.6

3 0.8

5 0.9

8 1.1

10 1.2

12 1.4

14 1.6

16 1.8

18 2.1

19 2.2

20 2.3

21 2.5

22 2.6

23 2.8

24 3.0

25 3.2

26 3.4

27 3.6

28 3.8

29 4.0

30 4.2

32 4.8

35 5.6

40 7.4

50 12.3

60 19.9

70 31.2

80 47.3

90 70.1

100 101.3

Example:

Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature

of 25 °C. What is the partial pressure of hydrogen gas?

According to the table the vapor pressure of water at 25°C is 3.2 kPa.

Ptotal = Pgas + P water vapor

95.0 kPa = X + 3.2 kPa

X = 91.8 kPa

Dalton - Water Vapor

Dalton’s Law is particularly useful when you are working in the lab and have

collected gas over water. Because there is always some water vapor in the air, you

must take into consideration the pressure that water vapor exerts on the total pressure.

the total pressure equals the pressure of the water vapor + the pressure of the gas.

Ptotal = Pgas + P water vapor

Because water vapor pressure varies with temperature, you must make sure to take

that into consideration. Many sources have tables of water vapor pressure at various

temperatures.

Temperature

(°C)

Vapour

pressure

(kPa)

0 0.6

3 0.8

5 0.9

8 1.1

10 1.2

12 1.4

14 1.6

16 1.8

18 2.1

19 2.2

20 2.3

21 2.5

22 2.6

23 2.8

24 3.0

25 3.2

26 3.4

27 3.6

28 3.8

29 4.0

30 4.2

32 4.8

35 5.6

40 7.4

50 12.3

60 19.9

70 31.2

80 47.3

90 70.1

100 101.3

Example:

Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature

of 25 °C. What is the partial pressure of hydrogen gas?

According to the table the vapor pressure of water at 25°C is 3.2 kPa.

Ptotal = Pgas + P water vapor

95.0 kPa = X + 3.2 kPa

X = 91.8 kPa

Tables provided for VP @ various temperatures.

Dalton - Water Vapor

Dalton’s Law is particularly useful when you are working in the lab and have

collected gas over water. Because there is always some water vapor in the air, you

must take into consideration the pressure that water vapor exerts on the total pressure.

the total pressure equals the pressure of the water vapor + the pressure of the gas.

Ptotal = Pgas + P water vapor

Because water vapor pressure varies with temperature, you must make sure to take

that into consideration. Many sources have tables of water vapor pressure at various

temperatures.

Temperature

(°C)

Vapour

pressure

(kPa)

0 0.6

3 0.8

5 0.9

8 1.1

10 1.2

12 1.4

14 1.6

16 1.8

18 2.1

19 2.2

20 2.3

21 2.5

22 2.6

23 2.8

24 3.0

25 3.2

26 3.4

27 3.6

28 3.8

29 4.0

30 4.2

32 4.8

35 5.6

40 7.4

50 12.3

60 19.9

70 31.2

80 47.3

90 70.1

100 101.3

Example:

Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature

of 25 °C. What is the partial pressure of hydrogen gas?

According to the table the vapor pressure of water at 25°C is 3.2 kPa.

Ptotal = Pgas + P water vapor

95.0 kPa = X + 3.2 kPa

X = 91.8 kPa

Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature of 25˚C. What is the partial pressure of the hydrogen gas?

Ptotal = Pgas + Pwater vapor

95 kPa = X + 3.2 kPa

X = 91.8 kPa

Maxwell-Boltzmann Distribution• Distribution of the kinetic energy of particles. • # of particles = constant • Higher temperature = higher kinetic energy of particles

Maxwell-Boltzmann Simulation

Maxwell-Boltzmann Video Explanation