Announcements•First project presentations will be next time

•Second Exam is two weeks from today on Wednesday October 28

•The third exam and second project presentations will be during the final exam period: Wednesday December 9 @ 4:00pm.

•Homework: Chapter 9 # 51, 52, 53 & 55 +

Supplemental Problems

Atmospheres and Gas Laws

On a microscopic level, T is the average kinetic energy of the

gas molecules kTmvKE aveave 2

3221

For a constant temperature and quantity of gas, the product of

the volume and pressure is constant

2211 VPVP

For a fixed pressure and quantity of gas, the volume and temperature are related

2

2

1

1

TV

TV

Combining the two gives the Ideal Gas Law

nRTPV n is the quantity of gas (moles or

number of molecules) and R is the Universal Gas Constant whose value

depends on the units used in the other quantities

(8.31 J/(mole-K), 0.0821 L-atm/(mole-K)

ExampleA cylinder contains 20L of oxygen at 20°C and 15atm. The temperature is raised to 35°C and the volume is reduced to 8.5L. What is the final pressure of the gas?

Example Solution 1The first thing to do is some algebra: put the Gas Law into a ratio form with the constant on one side and everything else on the other side

22

22

11

11

TnVP

TnVPR

nTPVnRTPV

Example Solution 2Cancel anything that stays the same and then solve for what you are wanting to find. In this case, only the amount of gas (n) stays the same.

1 1 2 2 1 1 2 2 1 22 1

1 1 2 2 1 2 2 1

PV PV PV PV VTP PnT n T T T V T

Example Solution

1 22 1

2 1

20 35 27315

8.5 20 273

37.1 37

VTP PV T

Latm

L

atm atm

The temperature must be in Kelvin so add 273° to the temperatures

Example for you•The best laboratory vacuum is about 1.00x10-18 atm. How many gas molecules are there per cubic centimeter at 293K?

1 mole = 6.022 x 1023 molecules

Example SolutionSince we want the number of atoms in a cubic centimeter, the volume is 1.00 cm3 = 1.00 mL.Use R = 0.0821(L-atm)/(mole-Kelvin)

18 323

23 23

1.00 10 1.00 104.157 10

0.0821 293

4.157 10 6.022 10 25.03

L atmmole K

atomsmole

PVPV nRT nRT

atm Ln moles

K

moles atoms

Since you can’t have a fraction of an atom, truncate to 25 atoms per cubic centimeter.

How much does air weigh?

The pressure of any fluid is related to the density of the fluid, the height of the column and the acceleration due to gravity

Pressure equals density times gravity times height

ghP is the density of the fluid, g is the acceleration due to gravity and h is the height of the column of fluid above.If the density isn’t constant such as in an atmosphere, then the pressure becomes an integral

( ) ( )bottom

topP h g h dh

Example for you•A scuba diver dives to a depth of 50 m in water with a density of 1000 kg/m3. What pressure does he experience in Pa?•Same problem except the diver is in a water tank on Mars. gMars = 3.69 m/s2

Example SolutionThe density of water is 1000 kg/m3 on Earth and Mars. If we find the gauge pressure (the pressure above atmospheric pressure) the only difference between Earth and Mars will be the acceleration due to gravity (“g”). On Mars g = 0.377gEarth so the pressure on Mars will be 37.7% that on Earth

3 2

5

5 5

1000 9.8 50

4.9 10

0.377 1.847 10 1.8 10

kg mEarth m s

Mars Earth

P gh m

Pa

P P Pa Pa