Gas Laws

1
Gas Laws
2
Gas Pressure

• Pressure is defined as force per unit area
• Gas pressure is defined as collisions with the
  walls of a container
• Internal collisions between molecules don't count
• As molecules move faster more collisions, hence
  greater pressure
• Measured using a barometer
• Pressure can also be changed by changing the area
  struck by the particles

3
Daltons Law of Partial Pressure
4

• When Dalton studied the properties of gases, he
  found that each gas in a mixture exerts pressure
  independently of the other gases present

5
Daltons Law of Partial Pressures

• States that the total pressure of a mixture of
  gases is equal to the sum of the pressures of all
  the gases in the mixture

6
Daltons Law of Partial Pressures

• the pressure contributed by a single gas is
  called its partial pressure
• Partial pressure depends on the of moles of
  gas, size of the container, and temperature of
  the mixture
• At a given temperature and pressure, the partial
  pressure of 1 mole of any gas is the same

7
Daltons Law of Partial Pressures

• Ptotal P1 P2 P3 Pn
• Ptotal represents the total pressure of the
  mixture of gases, P1, P2, P3represents the
  partial pressures

8
Example

• What is the partial pressure of hydrogen gas in a
  mixture of hydrogen and helium if the total
  pressure is 600 mmHg and the partial pressure of
  helium is 439 mmHg?
• Ptotal P1 P2 P3 Pn
• 600 mmHg 439 mmHg PHydrogen
• PHydrogen 161 mmHg

9
Practice Problems
10
Practice 1

• Find the total pressure for a mixture that
  contains four gases with partial pressures of
  5.00 kPa, 4.56 kPa, 3.02 kPa, and 1.20 kPa.
• 13.78 kPa

11
Practice 2

• Find the partial pressure of carbon dioxide in a
  gas mixture with a total pressure of 30.4 kPa if
  the partial pressures of the other two gases in
  the mixture are 16.5 kPa, and 3.7 kPa.
• 10.2 kPa

12
Boyles Law
13
Robert Boyle

• Performed experiments to study the relationship
  between pressure and the volume of a gas
• Displayed that under constant temperature,
  doubling of the pressure would result in the
  volume being cut in half and vice versa
• Discovered that pressure and volume are inversely
  proportional

14
Boyles Law

• States that volume of a given amount of gas held
  at constant temperature varies inversely with the
  pressure
• P1V1 P2V2
• P1 V1 represent the initial set of conditions
  for the gas and P2 V2 represent the new set of
  conditions for the gas

15
Boyles Law

• If you know any 3 of the 4 values for a gas at
  constant temperature, you can solve for the 4th
  by rearranging the equation
• Example
• P2 P1V1
• V2
• which can be done for any of the values in the
  equation

16
Example

• The volume of a gas at 99.0 kPa is 300.0 mL. If
  the pressure is increased to 188 kPa, what will
  be the new volume?
• P1V1 P2V2
• V2 P1V1 (99 kPa)(300 mL)
• P2 188 kPa
• 158 mL

17
Practice Problems
18
Practice 1

• The pressure of a sample of helium in a 1.00-L
  container is 0.988 atm. What is the new pressure
  if the sample is placed in a 2.00-L container?
• 0.494 atm

19
Practice 2

• Air trapped in a cylinder fitted with a piston
  occupies 145.7 mL at 1.08 atm pressure. What is
  the new volume of air when the pressure is
  increased to 1.43 atm by applying force to the
  piston?
• 110mL or 0.110 L

20
Homework

• Daltons Law of Partial Pressures and Boyles Law
  Handout

21
Review Questions
22
Problem 10

• An ion with 8 protons, 8 neutrons, and 10
  electrons is represented by
• Ne
• O2
• O-2
• O

23
Problem 11

• What is the mass number of an atom which contains
  28 protons, 28 electrons, and 34 neutrons?
• 28
• 56
• 62
• 90

24
Problem 12

• The chart shows isotopes of some common elements.
  In what two properties do the isotopes of carbon
  differ?
• Atomic number and number of neutrons
• Atomic mass and number of neutrons
• Atomic mass and number of protons
• Number of protons and number of neutrons

25
Day 2
26
Charless Law
27
Jacques Charles

• French physicist that studied the relationship
  between volume and temperature
• Observed that volume rose as temperature did when
  the pressure was held constant

28
Charless Law and KMT

• As stated in the KMT, at higher temperatures, gas
  particles move faster, striking each other and
  the walls of their container more frequently and
  with greater force
• If pressure is constant, volume must increase so
  the particles have farther to travel before
  striking the walls, which decrease the frequency
  at which the particles strike the walls of the
  container

29
Charless Law

• States that the volume of a given mass of gas is
  directly proportional to its Kelvin temperature
  at constant pressure
• V1 V2
• T1 T2
• V1 and T1 represent initial conditions and V2 and
  T2 represent the final conditions of the gas
• TEMPERATURE MUST BE IN KELVINS IN ORDER TO USE
  CHARLESS LAW
• TK 273 TC
• TK is the temperature in Kelvin and TC is the
  Celsius temperature

30
Isolating a Variable

• Charless Law
• V1 V2
• T1 T2
• Cross Multiply
• V1T2 V2T1
• Isolate the variable by dividing on both sides
• V1T2 V2T1
• T2 T2
• V1 V2T1
• T2

31
Example

• A gas at 89C occupies a volume of 0.67L. At what
  Celsius temperature will the volume increase to
  1.12L?
• TK 273 89 362K
• V1 V2
• T1 T2
• T2 T1V2
• V1
• T2 (362 )(1.12) 605 K
• .67
• TC 605 273 332 C

32
Practice Problems
33
Practice 1

• The Celsius temperature of a 3.00-L sample of gas
  is lowered from 80C to 30C. What will be the
  resulting volume of this gas?
• 2.58L

34
Practice 2

• What is the volume of the air in a balloon that
  occupies 0.620L at 25C if the temperature is
  lowered to 0C?
• 0.56L

35
Gay Lussacs Law
36
Joseph Gay-Lussac

• Studied the relationship between temperature and
  pressure of a contained gas at a fixed volume
• Discovered that temperature in Kelvin and
  pressure are directly proportional

37
Gay-Lussacs Law

• States that the pressure of a given gas varies
  directly with the Kelvin temperature when the
  volume remains constant
• P1 P2
• T1 T2
• P1 and T1 are the initial conditions and P2 and
  T2 are the final conditions of the gas

38
Example

• A gas in a sealed container has a pressure of
  125kPa at a temperature of 30C. If the pressure
  in the container is increased to 201 kPa, what is
  the new temperature?
• TK 273 30 303K
• P1 P2
• T1 T2
• T2 T1P2
• P1
• T2 (303)(201) 487K
• 125
• T2 487-273 214C

39
Practice Problems
40
Practice 1

• The pressure in an automobile tire is 1.88atm at
  25C. What will be the pressure if the
  temperature warms up to 37C?
• 1.96atm

41
Practice 2

• If a gas sample has a pressure of 30.7 kPa at
  0C, what would the temperature have to be to
  lower the pressure to 28.4 kPa?
• -21C

42
Homework

• Charless Law
• Gay-Lussacs Law

43
Review Questions
44
Problem 13

• What is the chemical formula for a compound
  formed from calcium ions (Ca2) and chloride ions
  (Cl1)?
• a. CaCl
• b. Ca2Cl
• c. CaCl2
• d. Ca2Cl2

45
Problem 14

• What is the correct formula for aluminum oxide?
• A AlO
• B Al3O2
• C AlO2
• D Al2O3

46
Day 3
47
Combined Gas Law
48
Combined Gas Law

• Combination of Boyles, Charless, Gay-Lussacs
  Laws
• States the relationship among pressure, volume
  and temperature of a fixed amount of gas
• Pressure is inversely proportional to volume
• Pressure is directly proportional to temperature
  and temperature is directly proportional to volume

49
Combined Gas Law

• P1V1 P2V2
• T1 T2

50
PTV NOT MTV
51
Isolating a Variable

• COMBINED GAS LAW
• P1V1 P2V2
• T1 T2
• Cross Multiply
• P1V1T2 P2V2T1
• Isolate the variable by dividing on both sides
• P1V1T2 P2V2T1
• V1T2 V1T2
• P1 P2V2T1
• V1T2

52
Example

• A helium-filled balloon at sea level has a volume
  of 2.1L at 0.998 atm and 36C. If it is released
  and rises to an elevation at which the pressure
  is 0.900 atm and the temperature is 28C, what
  will be the new volume of the balloon?
• 2.27L

53
Practice Problems
54
Practice Problem 1

• At 0C and 1 atm pressure, a sample of gas
  occupies 30mL. If the temperature is increased
  to 30C and the entire gas sample is transferred
  to a 20mL container, what will be the gas
  pressure inside the container?
• 1.66atm

55
Practice Problem 2

• A sample of gas of unknown pressure occupies
  0.766L at a temperature of 298K. The same sample
  of gas is then tested under known conditions and
  has a pressure of 32.6 kPa and occupies 0.644L at
  303K. What was the original pressure of the gas?
  
• 26.96 kPa

56
Ideal Gas Law
57
Ideal Gas Law

• Describes the physical behavior of an ideal gas
  in terms of the pressure, volume, temperature and
  number of moles of gas present
• PV nRT
• -where n is the number of moles of gas and R is
  the ideal gas constant

58
Ideal Gas Constant

• Pg. 435 Table 14-1

59
Example

• If the pressure exerted by a gas at 25C in a
  volume of 0.044L is 3.81 atm, how many moles of
  gas are present?
• PV nRT
• n PV
• RT
• n (3.81atm)(0.044L)
• (.0821)(298K)
• n .0069 or 6.9 x 10-3 mol

60
Practice Problems
61
Practice Problem 1

• Determine the Celsius temperature of 2.49 moles
  of gas contained in a 1.00L vessel at a pressure
  of 143 kPa.
• -266C

62
Practice Problem 2

• Calculate the volume that a 0.323 mol sample of a
  gas will occupy at 265K and a pressure of 0.900
  atm.
• 7.81L

63
Homework

• Gas Laws Handout

64
Review Questions
65
Problem 15

• What is the Stock system name for FeO?
• A Iron oxide
• B Iron (II) oxide
• C Iron (III) oxide
• D Iron oxygen

66
Problem 16

• What is the correct name for the compound NH4Cl?
• A nitrogen chloride
• B nitrogen chlorate
• C ammonium chloride
• D ammonium chlorate

67
Problem 17

• What is the formula for nitrogen trifluoride?
• A NiF3
• B NF3
• C N3F
• D Ni3F

68
Day 4
69
Test Content

• Kinetic Molecular Theory (KMT)
• 5 postulates
• Gas Laws
• Boyles, Daltons, Charless, Gay-Lussacs,
  Combined, Ideal
• Molar Volume
• Volume Stoichiometry
• Liters ? Liters
• Grams ? Liters

70
Molar Volume
71
Avogadros Principle

• States equal volumes of gases at the same
  temperature and pressure contain equal numbers of
  particles

72
Molar Volume

• Volume that one mole of gas occupies at STP
• Represented by the constant 22.414 L/mol
• the volume of one mole of gas at STP.
• Standard Temperature and Pressure (STP)
• atmospheric pressure of 1 and 0C or 273K

73
The Molar Volume Conversion Factor

• Molar Volume Conversion Factor
• 22.414L/mol
• Can be used to calculate the volume that a gas
  occupies at STP conditions given any of the
  following
• moles of a sample of gas
• grams of a sample of gas
• atoms, molecules, or particles of a sample of gas

74
Calculations
75

• Once you have the number of MOLES of a sample of
  gas, you can use the formula below to calculate
  the molar volume of a gas at STP
• Molar volume (V) number of moles of gas x
  22.414L
• 1 mol

76
Example- Given Moles

• 0.250 mole of HCl gas will occupy how many liters
  at STP?
• 0.250 moles 22.414L
• 1 mol
• 5.604 liters of HCl

77
Given Mass

• Example What volume is occupied by 100 grams of
  chlorine gas (Cl2) at STP?
• 100 g 1 mol Cl2 22.414L
  70.906 g 1 mol
• 31.611 liters Cl2

78
Given Volume

• If given the volume of a gas at STP, you can
  calculate the moles of gas by dividing the molar
  volume by 22.414L/mol.
• Example How many moles are equivalent to 2L of
  dry H2 at STP?
• 2 L H2 1 mol H2
• 22.414L
• .089 moles of H2

79
Practice
80

• What volume is occupied by 8 moles of any gas at
  STP?
• 8 moles 22.414L
• 1 mol
• 179.312 liters

81

• What volume is occupied by 3.49 moles of gas at
  STP?
• 3.49 moles 22.414L
• 1 mol
• 78.224 liters

82

• What volume is occupied by 27.48 moles of
  nitrogen gas at STP?
• 27.48 moles 22.414L
• 1 mol
• 615. 937 liters nitrogen gas

83

• How many liters will 94.5 grams of O2 occupy at
  STP?
• 94.5 grams O2 1 mol 22.414L
• 32 g 1 mol
• 66.12 liters O2

84

• How many liters will 38.57 grams of CO2 occupy at
  STP?
• 38.57 grams CO2 1 mole 22.414L
• 44 g 1 mol
• 19. 657 liters CO2

85
BONUS

• What is the mass of 5 liters of O2 gas?
• 5 liters of O2 1 mol 32 grams
• 22.414 L 1 mol
• 7.136 grams O2

86
Volume Stoichiometry
87
Volume Stoichiometry

• Liters ? Grams
• Given 1 mol molar molar mass
• 22.414L ratio 1 mol
• Grams ? Liters
• Given 1 mol molar 22.414L
• molar mass ratio
  1 mol
• Liters ? Liters
• Given 1 mole molar 22.414L
• 22.414L ratio 1 mol

88
12 CO2 (g) 11 H2O (l) ?C12H22O11 (s) 12 O2
(g)

• a.) How many liters of sucrose (C12H22O11) are
  produced from 25.0 grams of carbon dioxide (CO2)
  at STP?
• b.) How many liters of carbon dioxide (CO2) are
  necessary to produce 2.0L of oxygen (O2)? (4 pts)

89
Consider the following equation P4 (s) 5O2 (g)
---gt P4O10 (g)

• a.) If 3.54 liters of phosphorus (P4 ) is ignited
  in a flask containing oxygen (O2) at STP, how
  many grams of O2 are needed?
• b.) How many liters of tetraphosphorus decaoxide
  (P4O10) are produced from 3.0 L of oxygen (O2)?

90
Test Cheat Sheet

• You are allowed to fill 1 3x5 index card front
  and back with as much as you can to use on the
  test tomorrow
• Suggestions
• Volume stoichiometry problems in notes
• Example of each gas law
• PTV

91
Review Questions
92
Problem 18

• A physical change occurs when
• A a peach spoils
• B a bracelet turns your wrist green
• C a copper bowl tarnishes
• D a glue gun melts a glue stick

93
Problem 19

• What substance has a melting point of -94C and a
  boiling point of 65C?
• a. Ethanol
• b. Chlorine
• c. Hexane
• d. Methanol

94
Problem 20

• 22.4 liters of a gas has a mass of 36.5 grams.
  What is the identity of the gas?
• a. Chlorine
• b. Hydrogen chloride
• c. Nitrogen
• d. Hydrogen