Kinetic Theory (Gas Laws)

1
Kinetic Theory (Gas Laws)

• Chapter 16

2
Atomic Mass Unit

• Uses Carbon-12 as standard
• 1 atom of 12C masses 12.000 u
• 1 u 1.66 X 10-27 kg

3
Review of Moles

• 1 mole 6.022 X 1023 atoms/molecules
• GMA
• GMMA
• What is the molar mass of nitrogen, N2?
• What is the molar mass of BaCl2?
• How many moles are in 132 grams of CO2?
• How many atoms are in a 200 gram sample of iron?

4
States of Matter
They wander in random patterns quite close to one
another.
Can wiggle in place (these are the wiggle lines)
5
Plasma

• 4th state of matter
• Ionized gases
• Electrons are removed from the atoms
• Positive ions remain
• Present in
• Stars
• Lightning
• Arc welding
• Most common state of matter in the universe

6
Plasma

• A hydrogen and helium plasma such as you would
  find in the sun

e
He
e
He
e
H
H
e
He
e
He
e
e
H
H
e
7
Temperature

• Measure of the average molecular motion of a
  group of atoms/molecules
• Conversion Formulas
• F 1.8 (oC) 32
• K C 273
• C K 273

8
Temperature
9
(No Transcript)
10

• Absolute Zero
• All atomic and molecular motion stops
• Coldest possible temperature
• Never reached absolute zero
• Liquid Nitrogen 77 K (-196 oC)
• Dry Ice 216 K (-56.6 oC)

11

• 102 oF ? oC
• -10.0 oC ? oF
• 25 oC ? K
• 177 K ? oC
• 310 oC ? K

12

• 102 oF ? 39oC
• -10.0 oC ? 14.0 oF
• 25 oC ? 298 K
• 177 K ? -96 oC
• 310 oC ? 583 K

13
Kinetic Molecular Theory

• A gas is composed of small particles (molecules)
  that are spaced widely apart.
• Compressible
• Low density - about a 1000 times less dense than
  a liquid
• The molecules of a gas are in rapid, constant
  motion
• Pressure the force of the molecules hitting the
  side of a container

14
(No Transcript)
15

• All collisions are elastic
• Molecules dont lose any energy when they
  collide.
• Gas molecules have little/no attractive force on
  one another.
• Too far apart
• Mix thoroughly unlike oil and water (too far
  apart for polar/non-polar forces to matter)

16

• The temperature of a gas is directly proportional
  to average kinetic energy of the molecules.
• KE 3kT
• 2
• k Boltzmanns constant 1.38 X 10-23 J/K

17
Kinetic Molecular Theory Ex 1

• What is the average KE of molecules in a gas at
  37oC?
• T 273 37 310 K
• KE 3kT
• 2
• KE (3/2)(1.38 X 10-23 J/K)(310 K) 6.42 X
  10-21J
• (this is per molecule)

18
Kinetic Molecular Theory Ex 2

• What is the average KE of molecules in a gas at
  100 oC?
• ANS 7.72 X 10-21J

19

• P1V1 n1RT1 P2V2 n2RT2
• Solve both equations for R
• R P1V1 R P2V2
• n1T1 n2T2
• P1V1 P2V2
• n1T1 n2T2

20

• See what you can cross out (what you are not
  told)
• Remember to convert to Kelvin and moles if needed.

21
Boyles Law

• Boyles Law The pressure and volume of a gas
  are inversely related
• Bicycle pump example
• Piston down low volume, high pressure
• Piston up high volume, low pressure

22

• Example
• The volume of a cars cylinder is 475 mL at 1.05
  atm. What is the volume when the cylinder is
  compressed and the pressure is 5.65 atm?
• P1V1 P2V2
• n1T1 n2T2

23

• Collapses to
• P1V1 P2V2
• (Answer 88.3 mL)

24

• Example
• A weather balloon has a volume of 40.0 liters on
  the surface of the earth at 1.00 atm. What will
  be the volume at 0.400 atm as it rises?
• P1V1 P2V2
• n1T1 n2T2

25
Barometer

• Torricelli (1643)
• Height of column stayed about 760 mm (760 torr)
• The higher the elevation, the lower the mercury
• Weather
• Rising pressure calm weather
• Dropping pressure storm (fast moving air)

26
Charles Law

• Charles Law The temperature and volume of a gas
  are directly related
• HOTTER BIGGER
• Can be used to find absolute zero
• Temperature must be in Kelvin

27
(No Transcript)
28
(No Transcript)
29

• A basketball has a volume of 12.0 L when blown up
  at 25.00 oC. What will be the volume if it is
  taken outside on a day when it is only 5.00 oC?
• P1V1 P2V2
• n1T1 n2T2

30

• Collapses to
• V1 V2
• T1 T2

31

• 2. If a tire contains 30.0 L of air at 10.0 oC,
  what volume will it occupy when it is driven and
  warms up to 50.0 oC?

32
Guy-Lussacs Law

• Gay-Lussacs Law The temperature and pressure
  of a gas are directly related.
• Temperature must be in Kelvin
• Gas in a spray can has a pressure of 5.00 atm at
  25.0 oC. What will be the pressure at 400.0 oC?
• P1V1 P2V2
• n1T1 n2T2

33
Avagadros Law

• Avagadros Law The volume of a gas is directly
  proportional to the moles present
• MORE BIGGER
• A balloon has a volume of 1.00 L when 50.0 grams
  of N2 are in the balloon. What is the volume if
  an additional 25.0 grams of N2 are added?

34
Putting it all together

• Often you change more than one thing at a time.
• Ex In a car, volume, temperature, and pressure
  may change.
• 1. The volume of 0.0400 mol of a gas is 500.0 mL
  at 1.00 atm and 20.0 oC. What is the volume at
  2.00 atm and 30.0oC?

35

• 2. The gauge pressure in a tire is 200 kPa at
  10oC. After driving, the temperature rises to
  40oC. What will be the new gauge pressure?
  (Remember to add 101.3 kPa to the gauge pressure
  to get absolute pressure)

36
The Ideal Gas Law

• Works very well in situations close to Earths
  pressures and temperatures
• Does not work for extreme situations (Jupiters
  atmosphere is too cold and too dense)

37

• PV nRT
• P pressure in atmosphere
• V volume in Liters
• n number of moles
• T Temperature in Kelvin
• R gas constant
• R 8.31 J/ mol-K

38
STP

• Standard Temperature Pressure
• Standard Temperature 0oC (273 K)
• Standard Pressure 1.013 X 105 N/m2 (101.3 kPa,
  1 atm)

39
The Ideal Gas Law

• Examples
• What is the volume of 1.00 mole of a gas at STP?
• What is the mass of oxygen in a container at STP
  that has a volume of 10.0 m3?
• A helium balloon has a radius of 18.0 cm. How
  many moles and grams of helium are needed to fill
  the balloon at 20oC and 1.05 atm? (V 4/3pr3)

40
The Ideal Gas Law

• 4. Estimate the number of molecules you exhale
  in one breath at STP.

41
Three Processes

1. Constant Volume (isochoric)
2. Vertical Line on PV diagram
3. No work done
4. Pressure cooker
5. Constant Pressure (isobaric)
6. Horizontal line on PV graph
7. Work done
8. Constant Temperature (isothermal)
9. Hyperbola curve on PV graph

42
(No Transcript)
43

• Stop here in Knights Text

44
Grahams Law of Diffusion

• Gases mix to fill their volume evenly
• Grahams Law of Diffusion the speed of a gas is
  inversely proportional to its molar mass
• The larger the molar mass, the slower the gas
  molecule

45
(No Transcript)
46
Grahams Law Example

• At the same temperature, which moves faster, an
  He atom or an N2 molecule?

47
Calculating Average Speed

• Root-mean-square velocity
• vrms 3kT
• m
• Heavier molecules are slower
• Temperature increases speed

Molar mass
48
Average Speed Example 1

• What is the rms speed of one O2 molecule at 20oC?
• First we need the mass of one O2 in kilograms
• (32 u)(1.67 X 10-27kg) 5.3 X 10-26 kg
• vrms (3)(1.38 X 10-23 J/K)(293 K) ½
• (5.3 X 10-26 kg)
• vrms 480 m/s (about 1000 mph)

49
Average Speed Example 2

• What is the rms speed of one N2 molecule at 20oC?
• ANS 510 m/s (about 1100 mph)

50
Relative Humidity

• Vapor exists above all liquids
• Even solids have a vapor pressure
• Saturated vapor pressure depends on temperature
• When saturated vapor pressure exceeds atmospheric
  pressure, boiling occurs

51
Vapor pressure at 100 oC is now the same as
atmospheric pressure
52
Our Atmosphere

• 99 N2 and O2
• 78 N2
• 21 O2
• 1 CO2 and the Noble Gases

53
Relative Humidity

• Partial Pressure - Pressure caused by one
  component of the atmosphere
• Rel Humidity partial pressureH2O X 100
• saturated vapor pressure H2O

54
Relative Humidity Example 1

• On a hot day, the temperature is 30oC and the
  partial pressure of water vapor is 21.0 torr.
  What is the relative humidity?
• 21 torr X 100 66
• 31.8 torr

55
Relative Humidity Example 2

• What is the air pressure at a place where the
  water boils at 95 oC?
• ANS About 643 torr

56
Relative Humidity Example 3

• On a given day, the relative humidity is 73.
  What is the temperature if you assume that the
  air pressure is normal?
• ANS Above 90 oC

57
Thermal Expansion

• Most substances expand when heated
• Do not all expand to the same degree
• Bimetallic strips often used in thermometers

58

• DL aLoDT
• DL - Change in length
• a - Coefficient of linear expansion
• Lo - Original Length
• DT - Change in temperature (oC or K)

59
Thermal Expansion Example 1

• Why does running hot water sometimes help you
  open a glass jar with a metal lid?

60
Thermal Expansion Example 2

• A circular hole is cut in a cookie sheet. When
  the sheet is baked, will the hole expand or
  contract?
• (ANS Expands)

61
Thermal Expansion Example 3

• A steel (a12 X 10-6) bridge is 200 m long at 20
  oC. How long will it be at 40 oC? At -30 oC?
• (ANS 4.8 cm longer, 12 cm shorter)

62
Thermal Expansion Example 4

• An iron ring must fit snugly on an iron rod. The
  ring starts with a diameter of 6.420 cm at 20 oC,
  and must expand to 6.453 cm. To what temperature
  should the rod be heated?
• (ANS 450 oC)