Irvington High School
Mr. Markic
AP Chemistry
Chapter 5 - Gases
All gases have the following physical characteristics
 Gases assume the volume and shape of their containers
 Gases are the most compressible of the states of matter
 Gases will mix evenly and completely when confined to the same container
 Gases have much lower densities than liquids and solids
Pressure of a Gas
Gasses exert a pressure on any surface in
which they come in contact
Gas molecules are constantly in motion
Pressure =
Force
Area
(force = mass x acceleration)
Units of Pressure
Units are derived from
velocity and acceleration
1 pascal (Pa) = 1 N/m2
1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
Atmospheric Pressure
Is the pressure exerted by Earth’s atmosphere
Density of air decreases very rapidly with increasing distance from Earth
Denser the air is, the greater the pressure it exerts
The force experienced by any area exposed to Earth’s atmosphere is equal
to the weight of the column of air above it
Standard Atmospheric Pressure
 1 atm
 760 mm Hg


760 torr
101.325 kPa
Sample Exercise
The pressure outside a jet plane flying at high altitude falls considerably below standard atmospheric
pressure. Therefore, the air inside the cabin must be pressurized to protect the passengers. What is
the pressure in atmospheres in the cabin if the barometer reading is 688 mmHg?
Convert 749 mmHg to atmospheres
Page 1 of 14
Irvington High School
Mr. Markic
AP Chemistry
The atmospheric pressure in San Francisco on a certain day was 732 mmHg. What was the
pressure in kPa?
Convert 295 mmHg to kilopascals
Review of Concepts
Rank the following pressures from lowest to highest:
(a) 736 mmHg
(c) 728 torr
(d) 1.12 x 105 Pa
(b) 0.928 atm
Manometers Used to Measure Gas Pressures
closed-tube
open-tube
Review of Concepts
Would it be easier to drink water with a straw on top or at the foot of Mt. Everest?
Apparatus for Studying the Relationship Between Pressure and Volume of a Gas
As P (h) increases
V decreases
Page 2 of 14
Irvington High School
Mr. Markic
AP Chemistry
Boyle’s Law
• Pressure – volume relationship
• The volume of a fixed quantity of a gas maintained at constant temperature is inversely
proportional to the pressure
• Volume decreases, pressure increases (inverse relationship)
• PV = constant (hyperbola)
• V = constant x 1/P (linear)
Graphs based on Boyle’s Law
(a) Volume versus pressure
(b) Volume versus 1/P
Charles’s Law
• Temperature relationship
• The volume of a fixed quantity of gas at constant pressure increases linearly with temperature
• 0K or -273C is called absolute zero
• V/T = constant or V = constant x T
V1 𝑉2
• 𝑇1 = 𝑇2
• Temperature must be in Kelvin
• T (K) = t (0C) + 273.15
Avogadro’s Law
V  number of moles (n)
V = constant x n
𝑉1
𝑉2
= 𝑛2
𝑛1
Constant temperature
Constant pressure
Summary of Gas Laws
Boyle’s Law
Page 3 of 14
Irvington High School
Mr. Markic
AP Chemistry
Charles’s Law
Review of Concepts
Compare the changes in volume when the temperature of a gas is doubled at constant pressure from
(a) 200 K to 400 K
(b) 200C to 400 C
Avogadro’s Law
Ideal Gas Equation
1
Boyle’s law: P ∝ 𝑉
(at constant n and T)
Charles’s law: V ∝ T (at constant n and P)
Avogadro’s law: V ∝ n (at constant P and T)
V∝
𝑛𝑇
𝑃
V = constant x
𝑛𝑇
𝑃
𝑛𝑇
=R𝑃
R is the gas constant
PV = nRT
The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.
PV = nRT
R=
PV
nT
=
(1 atm)(22.414 L)
(1 mol)(273.15 K)
= 0.082057 L • atm / (mol • K)
Sample Exercise
Sulfur Hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the
pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at
69.5 C°.
Page 4 of 14
Irvington High School
Mr. Markic
AP Chemistry
Calculate the volume (in liters) occupied by 2.12 moles of nitric oxide (NO) at 6.54 atm and 76 °C.
Calculate the volume (in liters) occupied by 7.40 g of NH3 at STP.
What is the volume (in liters) occupied by 49.8 g of HCl at STP?
Review of Concepts
Assuming ideal behavior, which of the following gases will have the greatest volume at STP? Which
gas will have the greatest density?
(a) 0.82 mole of He.
(b) 24 g of N2.
(c) 5.0 x 1023 molecules
of Cl2.
An inflated balloon with a volume of 0.55 L at sea level (1.0 atm) is allowed to rise to a height of 6.5
km, where the pressure is about 0.40 atm. Assuming that the temperature remains constant, what is
the final volume of the balloon?
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?
Argon is an inert gas used in lightbulbs to retard the vaporization of the tungsten filament. A certain
lightbulb containing argon at 1.20 atm and 18°C is heated to 85°C at constant volume. Calculate its
final pressure (in atm).
Page 5 of 14
Irvington High School
Mr. Markic
AP Chemistry
A sample of oxygen gas initially at 0.97 atm is cooled from 21°C to -68°C at constant volume. What
is its final pressure (in atm)?
A small bubble rises from the bottom of a lake, where the temperature and pressure are 8°C and 6.4
atm, to the water’s surface, where the temperature is 25°C and the pressure is 1.0 atm. Calculate the
final volume (in mL) of the bubble if its initial volume was 2.1 mL.
A gas initially at 4.0 L, 1.2 atm, and 66°C undergoes a change so that its final volume and
temperature are 1.7 L and 42°C. What is its final pressure? Assume the number of moles remains
unchanged.
Density (d) Calculations
𝑚
𝑃𝑀
d = 𝑉 = 𝑅𝑇 m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
𝑑𝑅𝑇
M= 𝑃
d is the density of the gas in g/L
Sample Exercise
Calculate the density of carbon dioxide (CO2) in grams per liter (g/L) at 0.990 atm and 55°C.
What is the density (in g/L) of uranium hexafluoride (UF6) at 779 mmHg and 62°C?
A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds
that its density is 7.71 g/L at 36°C and 2.88 atm. Calculate the molar mass of the compound and
determine its molecular formula.
Page 6 of 14
Irvington High School
Mr. Markic
AP Chemistry
The density of a gaseous organic compound is 3.38 g/L at 40°C and 1.97 atm. What is its molar
mass?
Chemical analysis of a gaseous compound showed that it contained 33.0 percent silicon (Si) and 67.0
percent fluorine (F) by mass. At 35°C, 0.210 L of the compound exerted a pressure of 1.70 atm. If
the mass of 0.210 L of the compound was 2.38 g, calculate the molecular formula of the compound
A gaseous compound is 78.14 percent boron (B) and 21.86 percent hydrogen (H). At 27°C, 74.3 mL
of the gas exerted a pressure of 1.12 atm. If the mass of the gas was 0.0934 g, what is its molecular
formula?
Gas Stoichiometry
• We can also use the relationships between amounts (moles, n) and volume (V) to solve
problems when the reactants and/or products are gases
Sample Exercise
Calculate the volume of O2 (in liters) at STP required for the complete combustion of 7.64 L of
acetylene (C2H2) at STP:
2C2H2(g) + 5O2(g)  4CO2(g) + 2H2O(l)
Assuming no change in temperature and pressure, calculate the volume of O 2 (in liters) required for
the complete combustion of 14.9 L of butane (C4H10):
2C4H10(g) + 13O2(g)  8CO2(g) + 10H2O(l)
Page 7 of 14
Irvington High School
Mr. Markic
AP Chemistry
Sodium azide (NaN3) is used in automobile airbags. The impact of a collision triggers the
decomposition of NaN3 as follows:
2NaN3(s)  2Na(s) + 3N2(g)
The nitrogen gas produced quickly inflates the bag between the driver and the windshield and
dashboard. Calculate the volume of N2 generated at 80°C and 823 mmHg by the decomposition of
60.0 g of NaN3.
The equation for the metabolic breakdown of glucose (C6H12O6) is the same as the equation for the
combustion of glucose in air:
C6H12O6(s) + 6O2(g)  6CO2(g) + 6H2O(l)
Calculate the volume of CO2 produced at 37°C and 1.00 atm when 5.60 g of glucose is used up in the
reaction.
Aqueous lithium hydroxide solution is used to purify air in spacecrafts and submarines because it
absorbs carbon dioxide, which is an end product of metabolism, according to the equation
2LiOH(aq) + CO2(g)  Li2CO3(aq) + H2O(l)
The pressure of carbon dioxide inside the cabin of a submarine having a volume of 2.4 x 10 5 L is 7.9
x 10-3 atm at 312K. A solution of lithium hydroxide (LiOH) of negligible volume is introduced into the
cabin. Eventually the pressure of CO2 falls to 1.2 x 10-4 atm. How many grams of lithium carbonate
are formed by this process?
A 2.14 L sample of hydrogen chloride (HCl) gas at 2.61 atm and 28°C is completely dissolved in 668
mL of water to form hydrochloric acid solution. Calculate the molarity of the acid solution. Assume
no change in volume.
Page 8 of 14
Irvington High School
Mr. Markic
AP Chemistry
Dalton’s Law of Partial Pressures
V and T are constant
•
The total pressure of a mixture of gases
equals the sum of the pressures that
each would exert if it were present
alone
•
Partial pressure – pressure exerted by
a particular component of a mixture of
gas
Consider a case in which two gases, A and B, are in a container of volume V.
PA =
PB =
𝑛𝐴 𝑅𝑇
𝑉
𝑛𝐵 𝑅𝑇
𝑉
nA is the number of moles of A
nB is the number of moles of B
𝑛𝐴
PT = P A + PB
XA = 𝑛
PA = XA PT
PB = XB PT
Pi = Xi PT
𝐴 + 𝑛𝐵
XB = 𝑛
𝑛𝐵
𝐴 + 𝑛𝐵
𝒏
mole fraction (Xi ) = 𝒏 𝒊
𝑻
Sample Exercise
A mixture of gases contains 4.46 moles of neon (Ne), 0.74 mole of Argon (Ar), and 2.15 moles of
Xenon (Xe). Calculate the partial pressures of the gases if the total pressure is 2.00 atm at a certain
temperature.
A sample of natural gas contains 8.24 moles of methane (CH4), 0.421 mole of ethane (C2H6), and
0.116 mole of propane (C3H8). If the total pressure of the gases is 1.37 atm, what are the partial
pressures of the gases?
Page 9 of 14
Irvington High School
Mr. Markic
AP Chemistry
Collecting Gases Over Water
• The volume of gas collected is measured by raising or lowering the bottle as necessary until the
water levels inside and outside the bottle are the same
• When this condition is met, the pressure inside the bottle is equal to the atmospheric pressure
outside
• Ptotal = Pgas + PH2O
• This method of collecting gas is based on the assumptions that the gas does
not react with water and that is not appreciable soluble in it.
• These assumptions are valid for oxygen gas, but not for gases such as NH 3,
which dissolves readily in water.
• The oxygen gas collected in this way is not pure, because water vapor is also
present in the bottle.
• The total gas pressure is equal to the sum of the pressures exerted by the
oxygen gas and the water vapor
2KClO3 (s)  2KCl (s) + 3O2 (g)
Sample Exercise
Oxygen gas is generated by the decomposition of potassium chlorate is collected as shown in figure
5.15. The volume of oxygen collected at 24°C and atmospheric pressure of 762 mmHg is 128 mL.
Calculate the mass (in grams) of oxygen gas obtained. The pressure of water vapor at 24°C is 22.4
mmHg.
Hydrogen gas generated when calcium metal react with water is collected as shown in figure 5.15.
The volume of gas collected at 30°C and pressure of 988 mmHg is 641 mL. What is the mass (in
grams) of the hydrogen gas obtained? The pressure of water vapor at 30°C is 31.82 mmHg.
Review of Concepts
Each of the color spheres represents a different gas molecule. Calculate the partial pressure of the
gases if the total pressure is 2.6 atm.
Page 10 of 14
Irvington High School
Mr. Markic
AP Chemistry
Kinetic Molecular Theory of Gases
1. A gas is composed of molecules that are separated from each other by distances far greater than
their own dimensions. The molecules can be considered to be points; that is, they possess mass
but have negligible volume.
2. Gas molecules are in constant motion in random directions. Collisions among molecules are
perfectly elastic.
3. Gas molecules exert neither attractive nor repulsive forces on one another.
4. The average kinetic energy of the molecules is proportional to the temperature of the
gas in kelvins. Any two gases at the same temperature will have the same average
kinetic energy
KE = ½ mu2
Compressibility of Gases
• Boyle’s Law
P  collision rate with wall
Collision rate a number density
Number density a 1/V
P  1/V
• Charles’ Law
P a collision rate with wall
Collision rate  average kinetic energy of
gas molecules
Average kinetic energy  T
PT
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
• Avogadro’s Law
P a collision rate with wall
Collision rate a number density
Number density  n
Pn
• Dalton’s Law of Partial Pressures
Molecules do not attract or repel one
another
P exerted by one type of molecule is
unaffected by the presence of another gas
Ptotal = ΣPi
The distribution of speeds of three different
gases at the same temperature
𝟑𝑹𝑻
urms = √
•
•
•
•
𝑴
This equation shows that the root-mean-square speed of a gas increases with the square root of
its temperature (in kelvins)
Because M appears in the denominator, it follows that the heavier gas, the more slowly its
molecules move.
R = 8.314 J/K •mol
Convert molar mass into kg/mol
Page 11 of 14
Irvington High School
Mr. Markic
AP Chemistry
Practice Exercise
Calculate the root-mean-square speeds of helium atoms and nitrogen molecules in m/s at 25°C.
Calculate the root-mean-square speed of molecular chlorine in m/s at 20°C.
Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of
their kinetic properties.
𝑟1
𝑟2
𝑀
= √𝑀2
1
Gas effusion is the process by which gas under pressure escapes from one
compartment of a container to another by passing through a small opening.
𝑟1
𝑟2
=
𝑡2
𝑡1
𝑀
= √𝑀2
1
A flammable gas made up only of carbon and hydrogen is found to effuse through a porous barrier in
1.50 minutes. Under the same conditions of temperature and pressure, it takes and equal volume of
bromine vapor 4.73 minutes to effuse through the same barrier. Calculate the molar mass of the
unknown gas, and suggest what this gas might be.
It takes 192 s for an unknown gas to effuse through a porous wall and 84 s for the same volume of N 2
gas to effuse at the same temperature and pressure. What is the molar mass of the unknown gas?
Review of Concepts
If one mole each of He and Cl2 gases are compared at STP, which of the following quantities will be
equal to each other?
(a) Root-mean-square speed
(c) Average kinetic energy
(b) Effusion rate
(d) Volume
Page 12 of 14
Irvington High School
Mr. Markic
AP Chemistry
Real Gases: Deviations from Ideal Behavior
• The ideal-gas equation is a very useful description of gases, all real gases fail to obey the
relationship to some degree
• Molecules of an ideal gas are assumed to occupy no space and have no attractions for one
another
• Real molecules do have finite volumes, and they do attract one another
• Because of these attractive forces, the impact with the wall of the container is lessened
• Temperature determines how effective forces between gas molecules are
• As the gas is cooled, the average kinetic energy decreases, whereas
intermolecular attractions remain constant
• The data for CO2 pertain to a temperature of 313K because CO2
liquefies under high pressure at 300K
•
•
PV/RT versus pressure for 1 mol of nitrogen gas at three different
temperatures
As temperature increases, the gas more closely approaches ideal
behavior
Effect of attractive intermolecular forces on the pressure exerted by a gas on its container
walls
• The molecule that is about to strike the wall experiences attractive forces from nearby molecules,
and its impact on the wall is thereby lessened
• The attractive force become significant only under high-pressure conditions, when the average
distance between molecules is small
The van der Waals Equation (nonideal equation)
(P +
𝑎𝑛2
Corrected
pressure
•
•
•
•
𝑉2
)(V- nb) = nRT
Corrected
volume
The volumes of both a and b generally increase with an increase in mass of the molecule and with
an increase in the complexity of its structure
Larger, more massive molecules not only have larger volumes, they also
tend to have greater intermolecular attractive forces
The value of a indicates how strongly molecules of a given type of gas
attract one another (i.e. Helium has weak attraction)
There is also a rough correlation between molecular size and b. Generally
the larger the molecule (or atom), the greater b is
Sample Exercise
Given that 3.50 moles of NH3 occupy 5.20 L at 47°C, calculate the pressure of
the gas (in atm) using:
(a) The ideal gas equation
(b) The van der Waals equation
Page 13 of 14
Irvington High School
Mr. Markic
AP Chemistry
Using the data shown in Table 5.4, calculate the pressure exerted by 4.37 moles of molecular
chlorine confined in a volume of 2.45 L at 38°C. Compare the pressure with that calculated using the
ideal gas equation.
Big Idea 2: Chemical and Physical Properties of materials can be explained by the structure and the
arrangement of atoms, ions, or molecules and the forces between them.
Duration: Middle October
Textbook Chapter: 5
Enduring Understanding
Essential Questions
2.A: Matter can be described by its physical
2.A.2: The gaseous state can be effectively modeled
properties. The physical properties of a
with a mathematical equation relating various
substance generally depend on the spacing
macroscopic properties. A gas has neither a definite
between the particles (atoms, molecules, ions)
volume nor a definite shape; because the effects of
that make up the substance and the forces of
attractive forces are minimal, we usually assume that
attraction among them.
the particles move independently.
Learning Objectives
2.4 The student is able to use KMT and concepts of intermolecular forces to make predictions about the
macroscopic properties of gases, including both ideal and nonideal behaviors.
2.5 The student is able to refine multiple representations of a sample of matter in the gas phase to
accurately represent the effect of changes in macroscopic properties on the sample.
2.6 The student can apply mathematical relationships or estimation to determine macroscopic variables
for ideal gases.
2.12 The student can qualitatively analyze data regarding real gases to identify deviations from ideal
behavior and relate these to molecular interactions.
Page 14 of 14