Chapter 10
Physical Characteristics of Gases
Section 10 – 1
THE KINETIC-MOLECULAR THEORY OF
MATTER
Kinetic-Molecular Theory of
Matter
• Kinetic Molecular Theory—based on the idea that
particles of matter are always in motion
• Can be used to describe the behavior of solids,
liquids, and gases
• Describes the energy and forces that act between
particles
The Kinetic-Molecular Theory
of Gases
• The theory provides a model of an ideal gas
• Ideal Gas—an imaginary gas that perfectly fits all the
assumptions of the kinetic-molecular theory
• Based on the following 5 assumptions:
1. Gases consist of large numbers of tiny particles that
are far apart relative to their size
• Gases occupy a space about 1000 times larger than a
liquid or solid
• Take up a lot of empty space
• Are easily compressed
2. Collisions between gas particles and between
particles and container walls are elastic collisions.
• Elastic Collision—one in which there is no net loss of
kinetic energy
• Kinetic energy is transferred between two particles,
but the total energy between the two remains the
same as long as temperature remains constant.
3. Gas particles are in continuous, rapid, random
motion. They, therefore possess kinetic energy,
which is energy of motion.
• Gas particles move in all directions
• Overcome attractive forces
4. There are no forces of attraction or repulsion between
gas particles.
• Think of ideal gas particles as behaving like billiard balls—
when they collide they do not stick together, but
immediately bounce apart
5. The average kinetic energy of gas particles depends on
the temperature of the gas.
• Use the following equation:
KE = ½ mv2
• m = mass
• v = speed
• As temperature increases, speed increases
The Kinetic-Molecular Theory
and the Nature of Gases
• Applies only to ideal gases
• Ideal gases do not exist, but certain gases do behave
ideally if:
• Pressure is not very high
• Temperature is not very low
Expansion
• Gases do not have definite shape or volume—
completely fill any container they are placed in
• Gas particles move rapidly in all directions without
significant attraction or repulsion
Fluidity
• Gas particles glide easily past one another, causing
gases to flow similarly to liquids
• Fluids—have the ability to flow
Low Density
• Density in gaseous state is about 1/1000 the density of
the liquid or solid state
Compressibility
• Gas particles are pushed close together
• Volume can be greatly decreased
• Ex: Steel cylinders may contain 100 times as many
particles of gas as would be contained without
pressurizing it
Diffusion and Effusion
• Gases spread out and mix with one another, even
without being stirred
• Diffusion—the spontaneous mixing of the particles of
two substances caused by their random motion
• The rate of diffusion of one gas through another
depends on three properties:
• Speed
• Diameters
• Attractive forces
• Hydrogen gas diffuses rapidly into other gases at the
same temperature because its molecules are lighter
and move faster
• Effusion—a process by which gas particles pass
through a tiny opening
• Directly proportional to the velocities
Deviations of Real Gases from
Ideal Behavior
• All real gases deviate by some means from the ideal
gas behaviors
• Real Gas—a gas that does not behave completely
according to the assumptions of the kineticmolecular theory
• Johannes van der Waals—accounted for the
deviations by pointing out that particles occupy
space and exert attractive forces on each other
• Very high pressures and low forces
• Noble gases are likely to exhibit ideal gas laws
• Diatomic molecules are nonpolar and exhibit ideal
gas laws
• The more polar a gas is, the more likely they will
deviate from the ideal gas laws.
Section 10 – 2
PRESSURE
To describe a gas:
1)
2)
3)
4)
Volume
Temperature
Number of molecules
Pressure
Pressure and Force
• Pressure—(P) is defined as the force per unit area on a surface
Pressure = force
area
• Measured in Newtons (N)
• Pressure is the force that will increase the speed of a one
kilogram mass by one meter per second each second it is
applied.
• On Earth each kilogram of mass exerts 9.8 N of force (due to
gravity)
• Calculate the pressure of the following:
A dancer covers an area of about 325 cm2 and has a mass of 51
kg. What is the pressure applied, or exerted?
• Gas molecules exert pressure on any surface they come into
contact with.
• For every force applied to a gas, the gas will apply an outward
force back.
Measuring Pressure
• Barometer—a device used to measure atmospheric
pressure
• First barometer was introduced by Evangelista
Torricelli in the early 1600s
• Learned that at sea level at 0 degrees Celsius, the
average pressure of the atmosphere can support a
760 mm column of mercury
• Changes depending on elevation and weather
conditions
• All gases exert pressure
• Manometer—can be used to measure the pressure
of an enclosed gas sample
Units of Pressure
• A barometer measures pressure in heights of a
mercury column.
• Units Millimeters of mercury (mm Hg)
• 1 mm Hg is now called a torr
• Often measured in units of atmospheres
• 1 atmosphere of pressure (atm) is defined as being
exactly equivalent to 760 mm Hg
• In SI, pressure is expressed in derived units
• Pascals (Pa)—is defined as the pressure exerted by a
force of one newton (1N) acting on an area of one
square meter
• May be expressed a kPa (kilopascals)
• In order to compare volumes of gas, scientists have
agreed on the standard conditions:
1 atm = 0 degrees Celsius
• Called standard temperature and pressure (STP)
Solve the following:
The average atmospheric pressure in Denver, Colorado, is 0.830
atm. Express this pressure (a) in mm Hg and (b) in kPa.
Convert a pressure of 1.75 atm to kPa and to mm Hg.
Section 10 – 3
THE GAS LAWS
The Gas Laws
• Gas Laws—simple mathematical relationships
between the volume, temperature, pressure, and
amount of gas
Boyle’s Law: Pressure - Volume
• As pressure increases, volume decreases
• Pressure is caused by moving molecules hitting the
container walls
• Boyle’s Law—the volume of a fixed mass of gas
varies inversely with the pressure at constant
temperature
V = k 1/P or PV = k
• k is constant for a given sample of gas and depends
on the mass and the temperature
• Boyle’s law can be used to compare changing
conditions for a gas:
P1V1 = k (initial)
P2V2 = k (new)
The two quantities, equal to the same thing, are equal
to each other
P1V1 = P2V2
A sample of oxygen gas has a volume of 150 mL when
its pressure is 0.947 atm. What will the volume of the
gas be at a pressure of 0.987 atm if the temperature
remains constant?
A balloon filled with helium gas has a volume of 500
mL at a pressure of 1 atm. The balloon is released and
reaches an altitude of 6.5 km, where the pressure is
0.5 atm. Assuming that the temperature has remained
the same, what volume does the gas occupy at this
height?
Charles’s Law: VolumeTemperature
• Absolute zero-- -273 degrees K = value of zero
K = 273 + °C
Charles’s Law
• As temperature (in Kelvin) increases, so does the
volume
V = kT
or
V/T = k
• Can also be written as:
V1/T1 = V2/T2
Example:
A sample of neon gas occupies a volume of 752 mL at 25
degrees Celsius. What volume will the gas occupy at 50 degrees
Celsius if the pressure remains constant?
A helium-filled balloon has a volume of 2.75 L at 20
degrees Celsius. The volume of the balloon decreases
to 2.46 L after it is placed outside on a cold day. What
is the outside temperature in K? In degrees Celsius?.
Gay-Lussac’s Law: PressureTemperature
• States that the pressure of a fixed mass of gas at
constant volume varies directly with the Kelvin
temperature
P = kT
or
P/T = k
Can also be found using the following:
P1/T1 = P2/T2
The gas in an aerosol can is at a pressure of 3.00 atm
at 25 degrees Celsius. Directions on the can warn the
user not keep the can in a place where the
temperature exceeds 52 degrees Celsius. What would
the gas pressure in the can be at 52 degrees Celsius?
A 120 degrees Celsius, the pressure of a sample of
nitrogen is 1.07 atm. What will the pressure be at 205
degrees Celsius, assuming constant volume?
The Combined Gas Law
• Combines Charles’s Law, Boyle’s Law, and GayLussac’s Law
• Combined Gas Laws—expresses the relationship
between pressure, volume, and temperature of a
fixed amount of gas.
PV/T = l
• Can also be expressed as:
P1V1/T1 = P2V2/T2
• If temperature, pressure, or volume are held
constant they can be cancelled out on both sides.
Example: A helium-filled balloon has a volume of 50.0
L at 25 degrees Celsius and 1.08 atm. What volume
will it have at 0.855 atm and 10 degrees Celsius?
Dalton’s Law of Partial
Pressure
• In the absence of a chemical reaction, the pressure of a
gas mixture is the sum of the individual pressures
• Partial Pressure—the pressure of each gas in a mixture
• Dalton’s Law of Partial Pressure—the total pressure of a
mixture of gases is equal to the sum of the partial
pressures of the component gases.
• PT = P1 + P2 + P3….