January 31, 2008

• Go over homework

• Charles’s Law

• Avogadro’s Law

• Homework -- Page 480 -- 11, 13, 14bc, 15bc, 17, 19, 20

Charles’s Law

Timberlake, Chemistry 7th Edition, page 259

Charles's Law

If n and P are constant, then

V = (nR/P) = kTV = (nR/P) = kT

This means, for example, that Temperature goes up as Pressure goes up.

Jacques Charles(1746 - 1823)

Isolated boron and studied gases.Balloonist.

A hot air balloon is a good example of Charles's law.

VV and TT are directly related.

• Raising the temperature of a gas increases the pressure if the volume is held constant.

• The molecules hit the walls harder.• The only way to increase the temperature at

constant pressure is to increase the volume.

Temperature

• If you start with 1 liter of gas at 1 atm pressure and 300 K

• and heat it to 600 K one of 2 things happens

300 K

• Either the volume will increase to 2 liters at 1 atm

300 K600 K

300 K 600 K

the pressure will increase to 2 atm.

Charles’s Law

Timberlake, Chemistry 7th Edition, page 259

Charles’s Law

The volume and absolute temperature (K) of a gas are directly related

–at constant mass & pressure

kT

VV

T

Charles’ Law

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Volume

(mL)

Temperature

(K)

V / T

(mL / K)

40.0

44.0

47.7

51.3

273.2

298.2

323.2

348.2

0.146

0.148

0.148

0.147

The volume and absolute temperature (K) of a gas are directly related

–at constant mass & pressure

kT

VV

T

Charles’ Law

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Practice Problem – Charles’s Law

A child blows a soap bubble that contains air at 28 °C and has a volume of 23 cm3 at 1 atm. As the bubble rises, it encounters a pocket of cold air (temperature 10 °C). If there is no change in pressure, will the bubble get larger or smaller as the air inside cools to 18 °C? Calculate the new volume of the bubble.

2

2

1

1

T

V

T

V

C18

V

C28

cm23 23

K291

V

K301

cm23 23

V2 = 22 cm2

Practice Problem – Charles’s Law

A sample of gas at 15 °C (at 1 atm) has a volume of 2.58 L. The temperature is then raised to 38 °C. Does the volume of the gas increase or decrease? What is the new volume?

2

2

1

1

T

V

T

V

C38

V

C15

L 2.58 2

K311

V

K288

L 2.58 2

V2 = 2.79 L

Avogadro’s Law

• For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas

2

2

1

1

n

V

n

V

At constant temperature and pressureTemperature must be converted to Kelvin

Avogadro’s Law

nn and VV are directly related.

This means, for example, that As the number of moles goes up volume goes up.

Practice Problem – Avogadro’s LawSuppose we have a 12.2 L sample

containing 0.50 mol of oxygen gas, O2, at a pressure of 1 atm and a temperature of 25 °C. If all of this oxygen is converted to ozone, O3, at the same temperature and pressure, what will be the volume of the ozone formed?

2

2

1

1

n

V

n

V

3 O2 2 O3

32

32 Omol0.33

Omol3

Omol2xOmol0.50

mol0.33

V

mol0.50

12.2L 2

V2 = 8.1 L

Practice Problem – Avogadro’s Law

A 1.5 mol sample of helium at a certain temperature and pressure has a volume of 31.4 L. A second sample of helium at the same temperature and pressure has a volume of 42.4 L. How many moles of helium are in the second sample?

2

2

1

1

n

V

n

V

2n

L42.4

mol1.5

L31.4

n2 = 2.03 mol