Gas Laws

Chapters 13.1 + 14

Review

TemperatureAverage kinetic energy

PressureCollisions of gas particles between

each other and container walls Volume

Amount of space

Ideal Gas

Don’t exist

Model to explain behavior of all gases

Kinetic Molecular Theory

The particles in a gas are constantly moving in rapid, random, straight-line motion.

Gas particles have no volume compared to the volume of the gas.

No attraction between particles All collisions are completely elastic

Gas Laws

Boyle’s Law Charles’s Law Amontons’s Law Combined Gas Law Avogadro’s Law Dalton’s Law of Partial Pressures Ideal Gas Law

Boyle’s Law

Relationship between pressure and volumeConstant Temperature

Mathematical relationshipsAs pressure is increasing, volume is

decreasingAs pressure is decreasing, volume is

increasing

Boyle’s Law

V

P

Boyle’s Law

PV = constant Temperature remains constant

PV PV1 1 2 2

Example

A 40 L sample of gas at 1atm of pressure is compressed to 10 L. What is the new pressure of the gas?

P1V1 = P2V2

(1atm)*(40L) = P2*(10L)

P2 = 4 atm

Example

The pressure of a 25 L sample is changed from 2 atm to 0.4 atm. What is the new volume of the gas?

P1V1 = P2V2

(2atm)*(25L) = (0.4atm)*V2

V2 = 125 L

Real Life

Charles’s Law

Relationship between volume and temperatureConstant Pressure

Mathematical relationshipsAs temperature is increasing, volume

is increasingAs temperature is decreasing, volume

is decreasing

Charles’s Law

T

V

Charles’s Law

V/T = constantPressure remains constant

Temperature must be in Kelvin

V

T

V

T1

1

2

2

Example

A 4L sample of gas at 300K is heated to 600K. What is the new volume?

K

V

K

L

600300

4 2V

T

V

T1

1

2

2

LV 82

Example

A gas occupying 45L at 27°C is cooled until its volume is 15L. What is the new temperature of the gas?

2

15

300

45

T

L

K

LV

T

V

T1

1

2

2

CKT 1731002

Amontons's Law

In the winter the tire sensors on my wife’s car beep, indicating that there is low pressure in the tires. Why?

What factor is changing with the weather?

What factor is responding to this change?

Which factor(s) remain constant?

Amontons's Law

Mathematical relationshipsAs temperature increases, pressure

increasesAs temperature decreases, pressure

decreases

Amontons's Law

T

P

Amontons's Law

P/T = constant Volume remains constant (rigid

container) Temperature must be in Kelvin

P

T

P

T1

1

2

2

Example

In a pressure cooker, a sample of gas at 1 atm and 300K is heated to 400K. What is the pressure at this temperature?

P

T

P

T1

1

2

2

K

P

K

atm

400300

1 2

atmP 33.12

Example

A sample of gas at 101.3 kPa and 27°C is heated until its pressure is 3.5atm. What is the new temperature?

P

T

P

T1

1

2

2

2

5.3

300

1

T

atm

K

atm

KT 10502

Combined Gas Law

GoalUnderstands how to use the gas laws

to predict the behavior of gases.• Pressure vs. volume (Boyle)• Volume vs. temperature (Charles)• Volume, temperature, and pressure

(Combined)

Review

Boyle’s Law

Charles’s Law

Amontons's Law

PV PV1 1 2 2

V

T

V

T1

1

2

2

P

T

P

T1

1

2

2

Question

How often do only 2 properties of a gas change while the other remains constant?Rarely

Need a gas law that incorporates all three properties (PTV) changing

Combined Gas Law

Combines Boyle’s, Charles’s, and Amontons's Laws together

PV

T

PV

T1 1

1

2 2

2

Example

Example

Worksheet

Combined Gas Law

GoalUnderstands how to use the gas laws

to predict the behavior of gases.• Pressure vs. volume (Boyle)• Volume vs. temperature (Charles)• Volume, temperature, and pressure

(Combined)

Review

1 mole of ANY gas occupies 22.4L of volume at STP

Avogadro’s Law

Relationship between the amount of gas and the volume of the gas

Mathematical relationshipsAs the amount of gas increases,

volume increasesAs the amount of gas decreases,

volume decreases

Avogadro’s Law

n

V

Avogadro’s Law

V/n = constantPressure and Temperature remains

constant

V

n

V

n1

1

2

2

Avogadro’s Law

Equal volumes of gas at the same Temperature and Pressure have the same number of particles

At the same temperature and pressure, which sample contains the same number of moles of particles as 1 liter of O2(g)?

A. 1 L Ne(g) B. 0.5 L SO2(g)

C. 2 L N2(g) D. 4 L H2O(g)

Dalton’s Law

Demonstration Assume each jelly bean represents 1

mole of gas How many moles are in the flask? What fraction is green? Does color make a difference in

pressure when shaken?

Dalton’s Law

Mole Fraction (XA)Moles of one gas divided by total

moles of gas

Partial Pressure (PA)Pressure exerted by one gas in a

sample of gas

Dalton’s Law of Partial Pressures

How does partial pressure relate to total pressure?

Sum of partial pressures equals total pressure

PT = PA + PB + PC…

Dalton’s Law of Partial Pressures How can we relate mole fraction to partial

pressure and total pressure?

XP

PAA

T

ATA PPX *

Example

A container has 1 mol of hydrogen, 1 mol of nitrogen, and 1 mol of oxygen. What is the mole fraction of hydrogen?

3

1Moles of Hydrogen

Total Moles

Example

A container has 1 mol of hydrogen, 1 mol of nitrogen, and 1 mol of oxygen. If the total pressure is 6 atm, what is the partial pressure of nitrogen?

ATA PPX *

APatm6*3

1atmPA 2

Moles of Nitrogen

Total Moles

Review

Boyle’s Law

Charles’s Law

Amontons's Law

Avogadro’s Law

PV PV1 1 2 2

V

T

V

T1

1

2

2

P

T

P

T1

1

2

2

2

2

1

1

n

V

n

V

All Together Now

If we add Avogadro’s Law into the Combined Gas Law:

PV

nT Constant

PV

nTR

22

22

11

11

Tn

VP

Tn

VP

Ideal Gas Law

PV = nRTR = Universal Gas Constant

Ideal Gases follow assumptions of the Kinetic Molecular Theory

Kinetic Theory of Gases

The particles in a gas are constantly moving in rapid, random, straight-line motion.

Gas particles have no volume compared to the volume of the gas.

No attraction between particles All collisions are completely elastic

Ideal Gases

When do real gases act most like an ideal gas? High Temperature Low Pressure

When do real gases act least like an ideal gas? Low Temperature High Pressure

Gas Laws

Boyle’s Law Charles’s Law Amontons's Law Combined Gas Law Avogadro’s Law Dalton’s Law of Partial Pressures Ideal Gas Law