Tro Chapter 4 Burns 4/e Chapter 12

1
Chemistry A Molecular Approach, 1st Ed.Nivaldo
Tro

• Chapter 5
• Gases

• Atmospheric Pressure, Pressure Units
• Boyles Law Gas Pressure and Volume
• Charles Law Gas Volume and Temperature
• Avogadros Law Gas Volume and Moles
• Gay-Lussacs Law Gas Pressure and Temperature
• Standard Temperature and Pressure
• The Combined Gas Law
• The Ideal Gas Law
• Molar Volume and Gas Density at STP
• Daltons Law of Partial Pressures
• Gas Stoichiometry
• The Kinetic Molecular Theory
• Mean Free Path, Diffusion, and Effusion of Gasses
• Real Gasses The effects of size and
  intermolecular forces

2
Elements that exist as gases at 250C and 1
atmosphere
3
The Atmosphere

• The atmosphere is the thin layer of gases that
  surround the earth.
• Air is composed of a mixture of gases
• 78 Nitrogen, N2
• 21 Oxygen, O2
• 1 Argon, Ar
• 365 ppm carbon dioxide, CO2
• 0-4 water, H2O

4
Physical Properties of Gases

• No definite shape or volume
• expand to fill container, take shape of
  container.
• Compressible
• increase pressure, decrease volume.
• Low Density
• air at room temperature and pressure 0.00117
  g/cm3.
• Exert uniform pressure on walls of container.
• Mix spontaneously and completely.
• diffusion

5
Properties of Gases

• There are four basic properties that describe a
  gas.
• Volume (V) The space occupied by the gas.
• Pressure (P) The force that the gas exerts on
  the walls of the container.
• Temperature (T) A measure of the kinetic energy
  and rate of motion of a gas.
• Amount (n) The quantity of the present in the
  container (moles or grams).

6
Pressure

• Pressure is the force exerted per unit area
• Pressure Force/Area
• Atmospheric Pressure is the force per unit area
  exerted by the earths atmosphere.
• Atmospheric Pressure is measured with a
  barometer.
• Pressure can be measured by the height of a
  column of mercury that can be supported by a gas.

7
Barometer

• A barometer measures the pressure that is exerted
  by the atmosphere around us.
• The atmospheric pressure is measured as the
  height of a column of mercury, or sometimes as
  the height of a column of water.

8
Pressure Units

• mm of mercury (mm Hg)
• 1 mm Hg 1 torr
• 760 mm Hg 1 atm
• 1 atm is 1 atmosphere of pressure, sometimes
  called standard pressure.
• 1 Pascal, Pa, is the SI unit of pressure
• 1 Pa 1 N/m2 9.9 x 10-6 atm
• Inches of mercury, similar to mm of mercury, is
  the height of a column of mercury 29.92 in Hg

9
Common Units of Pressure
Unit Average Air Pressure at Sea Level
pascal (Pa), 101,325
kilopascal (kPa) 101.325
atmosphere (atm) 1 (exactly)
millimeters of mercury (mmHg) 760 (exactly)
inches of mercury (inHg) 29.92
torr (torr) 760 (exactly)
pounds per square inch (psi, lbs./in2) 14.7
10
Example 5.1 A high-performance bicycle tire has
a pressure of 132 psi. What is the pressure in
mmHg?
132 psi mmHg
Given Find
1 atm 14.7 psi, 1 atm 760 mmHg
Concept Plan Relationships
Solution
since mmHg are smaller than psi, the answer makes
sense
Check
11
Kinetic Theory of Gases

• 1. Gases move continuously, rapidly, randomly in
  straight lines and in all directions.
• 2. Gas particles are extremely tiny and
  distances between them are great.
• 3. Gravitational forces and forces between
  molecules are negligible.
• 4. Collisions between gas molecules are elastic
  (no loss of energy in collision).
• like billiard balls

12
Kinetic Energy

• 5. The average kinetic energy of the gas
  particles (molecules or atoms) is the same for
  all gases at the same temperature.
• Kinetic Energy, K. E., is proportional to the
  Kelvin temperature.
• K. E. ½mv2
• m mass of the gas particle
• v velocity of particle
• When temperature increases velocity of particles
  increases.
• At a fixed temperature, lighter particle move
  faster.

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Apparatus for Studying the Relationship between
Pressure and Volume of a Gas
As P (h) increases
V decreases
14
Boyles Law

• As the pressure of a gas is increased the volume
  decreases
• V ?1/P
• This is an inverse proportion
• V k/P
• PV k
• P1V1 k
• P2V2 k
• P1V1 P2V2
• V2 P1V1/P2, P2 P1V1/ V2

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Boyles Law Graph
Insert figure 12.9
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17
Relation of Volume and Pressure

• As the container volume decreases at constant
  temperature, the smaller volume has shorter
  distances between gas molecules and the walls, so
  collisions are more frequent. Hence, the pressure
  increases at lower volume.

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Example 5.2 A cylinder with a movable piston
has a volume of 7.25 L at 4.52 atm. What is the
volume at 1.21 atm?
V1 7.25 L, P1 4.52 atm, P2 1.21 atm V2, L
Given Find
P1 V1 P2 V2
Concept Plan Relationships
Solution
since P and V are inversely proportional, when
the pressure decreases 4x, the volume should
increase 4x, and it does
Check
19
A sample of chlorine gas occupies a volume of 946
mL at a pressure of 726 mmHg. What is the
pressure of the gas (in mmHg) if the volume is
reduced at constant temperature to 154 mL?
20
Practice A balloon is put in a bell jar and the
pressure is reduced from 782 torr to 0.500 atm.
If the volume of the balloon is now 2780 mL, what
was it originally?

21
CHARLESS LAW

• In a closed system at constant pressure, if you
  change the temperature, what will happen to the
  volume?

• V ? T
• Volume is directly proportional to Kelvin
  Temperature.
• V kT
• V/T k

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CHARLESS LAW (CONT.)
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Charless Law Graph
Insert figure 12.11
Temperature must be in Kelvin T (K) t (0C)
273.15
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Relation of Volume and Temperature

• As the temperature increases, the most probable
  molecular speed and average kinetic energy
  increase. Thus the molecules hit the walls more
  frequently and more energetically. If the
  pressure is to remain constant, the volume of the
  container must increase.

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Example 5.3 A gas has a volume of 2.57 L at
0.00C. What was the temperature at 2.80 L?
V1 2.57 L, V2 2.80 L, t2 0.00C t1, K and C
Given Find
Concept Plan Relationships
Solution
since T and V are directly proportional, when the
volume decreases, the temperature should
decrease, and it does
Check
26
Practice The temperature inside a balloon is
raised from 25.0C to 250.0C. If the volume of
cold air was 10.0 L, what is the volume of hot
air?

27
A sample of carbon monoxide gas occupies 3.20 L
at 125 0C. At what temperature will the gas
occupy a volume of 1.54 L if the pressure remains
constant?
28
Gay-Lussacs Law

• At constant volume, the pressure exerted by a gas
  is directly proportional to the Kelvin
  temperature
• P ? T
• P kT
• k P/T
• P1/T1 P2/T2
• P2 P1T2/T1
• T2 T1P2/P1

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Relation of Pressure and Temperature

• As the temperature increases, the most probable
  molecular speed and average kinetic energy
  increase. Thus the molecules hit the walls more
  frequently and more energetically. A higher
  frequency of collisions causes higher internal
  pressure.

30
A gas has a pressure of 2 atm at 18 oC. What is
the new pressure when the temperature is 62 oC
(volume and amount constant)?
31
Combined Gas Equation
Charles law V a T (at constant n and P)
Gay-Lussacs Law P a T (at constant n and V)
32
A sample of Helium gas has a volume of 0.180 L, a
pressure of 0.800atm and a temperature of 29 oC.
At what temperature will the sample have a volume
of 90mL and a pressure of 3.20 atm (n constant)?
33
Avogadros Law

• The volume of a gas at constant temperature and
  pressure is proportional to the number of moles
  of gas
• V ? n
• V kn
• V1/n1 V2/n2
• V2 V1n2/n1

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Avogadros Law

• volume directly proportional to the number of gas
  molecules
• V constant x n
• constant P and T
• more gas molecules larger volume
• count number of gas molecules by moles
• equal volumes of gases contain equal numbers of
  molecules
• the gas doesnt matter

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Example 5.4 A 0.225 mol sample of He has a
volume of 4.65 L. How many moles must be added
to give 6.48 L?
V1 4.65 L, V2 6.48 L, n1 0.225 mol n2, and
added moles
Given Find
Concept Plan Relationships
Solution
since n and V are directly proportional, when the
volume increases, the moles should increase, and
it does
Check
36
If 0.75 moles of Helium gas occupies a volume of
1.5 L, what volume will 1.2 moles of Helium
occupy at the same temperature and pressure?
37
Standard Temperature and Pressure

• Reference conditions for gases are called
  standard conditions.
• Standard Temperature is 273 K or 0oC.
• Standard Pressure is 1 atm or 760 torr.
• Together 273 K and 1 atm is called
• Standard Temperature and Pressure
• or STP.

38
Standard Molar Volume

• Experiments show that at STP, 1 mole of an ideal
  gas occupies 22.414 L.
• This is called the standard molar volume.
• The volume of any gas at STP can be calculated if
  the number of moles is known
• V (moles) x 22.4

39
Molar Volume
40
What is the volume at STP of 4.00 grams of CH4?
41
Density at Standard Conditions

• density is the ratio of mass-to-volume
• density of a gas is generally given in g/L
• the mass of 1 mole molar mass
• the volume of 1 mole at STP 22.4 L

42
DENSITY PROBLEM

• Calculate the density of CH4 at STP
• Assume 1 mole of CH4. The mass of one mol is the
  molar mass C H4 12 4x1 16 g/mol.
• V 22.4 L (the molar volume at STP)
• density mass/volume 16/22.4
• 0.714 g/L

43
Ideal Gas Equation
Charles law V a T (at constant n and P)
Avogadros law V a n (at constant P and T)
R is the gas constant
PV nRT
R 0.082057 L atm / (mol K)
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IDEAL GAS LAWPV nRT

• R GAS CONSTANT, 0.0821 L Atm/mol K
• P PRESSURE (in atm)
• V VOLUME (in L)
• n MOLES OF GAS
• T TEMPERATURE (in K)
• Be consistent with units!

45
Deriving a Gas Constant
PV nRT
At STP, P 1 atm n 1mol V 22.4 L T 0 oC
273 K
R 0.082057 L atm / (mol K)
46
Example 5.6 How many moles of gas are in a
basketball with total pressure 24.3 psi, volume
of 3.24 L at 25C?
V 3.24 L, P 24.3 psi, t 25 C, n, mol
Given Find
Concept Plan Relationships
Solution
1 mole at STP occupies 22.4 L, since there is a
much smaller volume than 22.4 L, we expect less
than 1 mole of gas
Check
47
What is the volume (in liters) occupied by 49.8 g
of HCl at STP?
48
Dinitrogen oxide (N2O), laughing gas, is used by
dentists as an anesthetic. If a 20 L tank of
laughing gas contains 2.8 moles of N2O at 23oC,
what is the pressure (in mmHg) of the gas?
49
Argon is an inert gas used in lightbulbs to
retard the vaporization of the filament. A
certain lightbulb containing argon at 1.20 atm
and 18 0C is heated to 85 0C at constant volume.
What is the final pressure of argon in the
lightbulb (in atm)?
50
Daltons Law of Partial Pressure

• Daltons Law of Partial Pressure states that the
  total pressure of a mixture of gases is equal to
  the sum of the partial pressures of the gases
• PT P1 P2 P3
• Partial pressure is the pressure the gas would
  exert in the same volume in the absence of other
  gases.

51
Daltons Law of Partial Pressures
V and T are constant
P1
P2
Ptotal P1 P2
52
The partial pressure of each gas in a mixture can
be calculated using the ideal gas law
53
Practice Find the partial pressure of neon in a
mixture with total pressure 3.9 atm, volume 8.7
L, temperature 598 K, and 0.17 moles Xe.

54
Mole Fraction
the fraction of the total pressure that a single
gas contributes is equal to the fraction of the
total number of moles that a single gas
contributes
the ratio of the moles of a single component to
the total number of moles in the mixture is
called the mole fraction, c for gases, volume
/ 100
the partial pressure of a gas is equal to the
mole fraction of that gas times the total pressure
55
Consider a case in which two gases, A and B, are
in a container of volume V.
nA is the number of moles of A
nB is the number of moles of B
PT PA PB
PA XA PT
PB XB PT
Pi Xi PT
mole fraction, c
56
A sample of natural gas contains 8.24 moles of
CH4, 0.421 moles of C2H6, and 0.116 moles of
C3H8. If the total pressure of the gases is 1.37
atm, what is the partial pressure of propane
(C3H8)?
57
Gases are often collected over water

• Daltons Law of Partial Pressure is often used to
  correct for the vapor pressure of water, which is
  a function of temperature but not volume or
  amount. The vapor pressure of water can be
  looked up in standard reference books such as the
  Handbook of Chemistry and Physics.

58
Bottle full of oxygen gas and water vapor
59
Vapor Pressure Problem
A gas is collected over water at 300K (27 oC), at
1.00 atm(760 Torr). Calculate the pressure of the
dry gas.

• PT Pgas Pwater
• Pgas PT - Pwater
• At 27oC, the vapor pressure of water is 26.74 mm
  Hg
• The pressure of dry gas is Pgas760-26.74733 mm
  Hg

60
Practice 0.12 moles of H2 is collected over
water in a 10.0 L container at 323 K. Find the
total pressure.

61
Gas Volume Stoichiometry

• Do stoichiometry problems using gas laws.
• Law of Combining Volumes In chemical reactions,
  volumes of gases combine in small whole number
  ratios.
• The ratio of combination of volumes follow the
  moles This puts this unit together with the
  stoichiometry unit.

62
Reactions Involving Gases

• the principles of reaction stoichiometry from
  Chapter 4 can be combined with the gas laws for
  reactions involving gases
• in reactions of gases, the amount of a gas is
  often given as a volume
• instead of moles
• as weve seen, must state pressure and
  temperature
• the ideal gas law allows us to convert from the
  volume of the gas to moles then we can use the
  coefficients in the equation as a mole ratio
• when gases are at STP, use 1 mol 22.4 L

P, V, T of Gas A
mole A
mole B
P, V, T of Gas B
63
Gas Stoichiometry
5.60 g C6H12O6
0.187 mol CO2
V
4.76 L
64
Practice What volume of O2 at 0.750 atm and 313
K is generated by the thermolysis of 10.0 g of
HgO?

2 HgO(s) ? 2 Hg(l) O2(g)(MW HgO 216.59 g/mol)
65
Grahams Law Diffusion and Effusion of Gases

• Diffusion the process whereby a gas spreads out
  through another gas to occupy the space with
  uniform partial pressure.
• Effusion the process in which a gas flows through
  a small hole in a container.
• Grahams law of Effusion the rate of effusion of
  gas molecules through a hole is inversely
  proportional to the square root of the molecular
  mass of the gas at constant temperature and
  pressure.

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Effusion
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Grahams Law Diffusion and Effusion of Gases

• When comparing the effusion (or diffusion) rates
  for two different gases

68
Grahams Law Diffusion and Effusion of Gases

• E.g. determine the molecular mass of an unknown
  compound if it effused through a small orifice if
  it effused 3.55 times slower than CH4.

69
Ex 5.15 Calculate the molar mass of a gas that
effuses at a rate 0.462 times N2
Given Find
MM, g/mol
Concept Plan Relationships
Solution
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Ideal vs. Non-Ideal Gases

• Kinetic Theory Assumptions
• Point Mass
• No Forces Between Molecules
• Molecules Exert Pressure Via Elastic Collisions
  With Walls

(courtesy F. Remer)
71
Ideal vs. Real Gases

• Real gases often do not behave like ideal gases
  at high pressure or low temperature
• at low temperatures and high pressures these
  assumptions are not valid

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Ideal vs. Non-Ideal Gases

• Non-Ideal Gas
• Violates Assumptions
• Volume of molecules
• Attractive forces of molecules

(courtesy F. Remer)
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Real Gas Behavior

• because real molecules take up space, the molar
  volume of a real gas is larger than predicted by
  the ideal gas law at high pressures

74
The Effect of Molecular Volume

• at high pressure, the amount of space occupied by
  the molecules is a significant amount of the
  total volume
• the molecular volume makes the real volume larger
  than the ideal gas law would predict
• van der Waals modified the ideal gas equation to
  account for the molecular volume
• b is called a van der Waals constant and is
  different for every gas because their molecules
  are different sizes

75
Real Gas Behavior

• because real molecules attract each other, the
  molar volume of a real gas is smaller than
  predicted by the ideal gas law at low temperatures

76
The Effect of Intermolecular Attractions

• at low temperature, the attractions between the
  molecules is significant
• the intermolecular attractions makes the real
  pressure less than the ideal gas law would
  predict
• van der Waals modified the ideal gas equation to
  account for the intermolecular attractions
• a is called a van der Waals constant and is
  different for every gas because their molecules
  are different sizes

77
Ideal vs. Non-Ideal Gases
combining the equations to account for molecular
volume and intermolecular attractions we get the
following equation
a constant b constant

• Van der Waals Equation Accounts for
• Volume of molecules
• Attractive forces between molecules

(courtesy F. Remer)
78
Van der Waals Equation

• used for real gases
• a and b are called van der Waal constants and are
  different for each gas

79
Air Pollution

• air pollution is materials added to the
  atmosphere that would not be present in the air
  without, or are increased by, mans activities
• though many of the pollutant gases have natural
  sources as well
• pollution added to the troposphere has a direct
  effect on human health and the materials we use
  because we come in contact with it
• and the air mixing in the troposphere means that
  we all get a smell of it!
• pollution added to the stratosphere may have
  indirect effects on human health caused by
  depletion of ozone
• and the lack of mixing and weather in the
  stratosphere means that pollutants last longer
  before washing out

80
Pollutant Gases, SOx

• SO2 and SO3, oxides of sulfur, come from coal
  combustion in power plants and metal refining
• as well as volcanoes
• lung and eye irritants
• major contributor to acid rain
• 2 SO2 O2 2 H2O ? 2 H2SO4
• SO3 H2O ? H2SO4

81
Pollutant Gases, NOx

• NO and NO2, oxides of nitrogen, come from burning
  of fossil fuels in cars, trucks, and power plants
• as well as lightning storms
• NO2 causes the brown haze seen in some cities
• lung and eye irritants
• strong oxidizers
• major contributor to acid rain
• 4 NO 3 O2 2 H2O ? 4 HNO3
• 4 NO2 O2 2 H2O ? 4 HNO3

82
Pollutant Gases, CO

• CO comes from incomplete burning of fossil fuels
  in cars, trucks, and power plants
• adheres to hemoglobin in your red blood cells,
  depleting your ability to acquire O2
• at high levels can cause sensory impairment,
  stupor, unconsciousness, or death

83
Pollutant Gases, O3

• ozone pollution comes from other pollutant gases
  reacting in the presence of sunlight
• as well as lightning storms
• known as photochemical smog and ground-level
  ozone
• O3 is present in the brown haze seen in some
  cities
• lung and eye irritants
• strong oxidizer

84
Ozone Holes

• satellite data over the past 3 decades reveals a
  marked drop in ozone concentration over certain
  regions

85
Homework

• You should examine and be able to answer all of
  the Problemssome of them (or similar) may be
  on the test
• To be handed in for grading 5.30, 5.36, 3.39,
  5.46, 5.52, 5.58, 5.62, 5.67, 5.74, 5.77, 5.80,
  5.96, 5.100
• Bonus 5.100