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 Gay-Lussac’s Law Combined Gas Law Avogadro’s Law Ideal Gas Law

Boyle’s Law

Relationship between pressure and volumeConstant Temperature and amount of

gas Mathematical relationships

As pressure is increasing, volume is decreasing

As 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

Charles’s Law

Relationship between volume and temperatureConstant Pressure and amount of gas

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

VT

VT

1

1

2

2

Example

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

KV

KL

6003004 2

VT

VT

1

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

1530045

TL

KL

VT

VT

1

1

2

2

CKT 1731002

Gay-Lussac'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?

Gay-Lussac's Law

Mathematical relationshipsAs temperature increases, pressure

increasesAs temperature decreases, pressure

decreases

Gay-Lussac's Law

T

P

Gay-Lussac's Law

P/T = constant Volume remains constant (rigid

container) and amount of gas Temperature must be in Kelvin

PT

PT

1

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?

PT

PT

1

1

2

2

K

PK

atm400300

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?

PT

PT

1

1

2

2

2

5.33001

Tatm

Katm

KT 10502

Review

Boyle’s Law

Charles’s Law

Gay-Lussac's Law

PV PV1 1 2 2

VT

VT

1

1

2

2

PT

PT

1

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 Gay-Lussac's Laws together

PVT

PVT

1 1

1

2 2

2

Example

A gas at 5atm is heated and compressed from 10L at 100K to 5L at 200K. What is the new pressure?

PVT

PVT

1 1

1

2 2

2

KLP

KLatm

200)5)((

100)10)(5( 2

atmP 202

Example

A gas at 2atm and 27°C occupies 10L of space. What is the new volume when it is cooled to STP?

PVT

PVT

1 1

1

2 2

2

KVatm

KLatm

273))(1(

300)10)(2( 2

LV 2.182

Real Life

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

Vn

Vn

1

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)

Review

Boyle’s Law

Charles’s Law

Gay-Lussac’s Law

Avogadro’s Law

PV PV1 1 2 2

VT

VT

1

1

2

2

PT

PT

1

1

2

2

2

2

1

1

nV

nV

All Together Now

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

PVnT

Constant

PVnT

R

22

22

11

11

TnVP

TnVP

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