Introduction to Gases
& The Kinetic Molecular
Theory (KMT)
Note: The content in this presentation is not
required in the IB course syllabus for topic 1
but will help you to deepen your understanding
of the gas laws and help you later in Kinetics.
Learning Objective from
Chapter 6 (Kinetics)

6.2.1 - Describe the kinetic theory in
terms of the movement of particles
whose average energy is proportional to
temperature in kelvins.
The Kinetic Molecular Theory of
Gases
This theory tries to model gas particles
themselves at a microscopic level and
consists of 5 main postulates.
1. Gases are composed of very small
particles, either molecules or individual
atoms.
2. The gas particles are tiny compared to
the distances between them, so we
assume that the volume of the gas
particles themselves is negligible.

3.
These gas particles are in constant
motion, moving in straight lines in a
random fashion and colliding with each
other and the inside walls of the
container. The collisions with the
inside container walls are what
comprise the pressure of the gas.
Q - What would increasing the
number of gas particles do to the
number of collisions (pressure)?
Check it!
Q - What would increasing the size of
the box do to the number of
collisions (pressure)?
Check it!
Q - What would increasing the
temperature of the gas particles do
to the number of collisions
(pressure)? Why?
Check it!
Balloons and Tires and Sodas
1. What happens when you add additional air to a
balloon? When you add additional air to your bicycle
tire?
2. What happens to a balloon when you squeeze it?
3. What happens to a helium balloon when you place it
in your car on a cold winter day? on a hot summer
day?
4. What happens to your tire pressure on a cold winter
morning? on a hot summer day?
5. What happens to soda when you shake it up before
opening it? What happens after you open the soda?
Factors influencing gases:
P, V, T, n
Learning Objective from
Chapter 6 (Kinetics)

6.2.5 - Sketch and explain qualitatively
the Maxwell–Boltzmann energy
distribution curve for a fixed amount of
gas at different temperatures and its
consequences for changes in reaction
rate.
The Maxwell–Boltzmann distribution
Go back to
describes particle speeds in gases, where the simulation
particles do not constantly interact with each
other but move freely between short collisions.
The speed probability density functions of the speeds of a few noble gases at a temperature of 298.15 K (25 °C).
The y-axis is in s/m so that the area under any section of the curve (which represents the probability of the speed
being in that range) is dimensionless.
…now back to the kinetic molecular theory…
4.
The gas particles are assumed to
neither attract nor repel each other.
They may collide with each other, but if
they do the collisions are assumed to
be elastic. No kinetic energy (KE) is
lost, only transferred from one gas
molecule to another.
KE per molecule = 1/2 mv2
(m=mass of the individual
molecule)
The average kinetic energy of the gas is
proportional to the Kelvin temperature.
5.
•
•
KE per mol = 3/2 RT
KE = 3/2 RTn
or…
A gas that obeys these five postulates
is called an ideal gas.
•
•
•
Q - Do we live in the ideal world?
A - No, because the universe hates you…
but real gases, which we will discuss later
do behave much like the ideal ones.
Pressure
Q - According to the KMT, what is
pressure?
 A - P is the force exerted by gas
molecules colliding with the walls of their
container.
 Q - How do we measure pressure?

 Atmospheric Pressure - Barometer
 Container Pressure - Manometer
Barometers
Manometers
Units of Pressure
Be careful to note the units given in a
problem!
 Most gas law formulas can use any
pressure unit as long as you use the same
one on both sides (ex. PV=PV)
 kPa must be used for the ideal gas law
(PV=nRT) if 8.314 is used for R


1 atm = 760 mm Hg = 760 torr = 101.3kPa =
14.5psi
Gases

Keywords & Equations
 urms=root mean square speed=(3kT/m)1/2=(3RT/M)1/2 *
 r=rate of effusion
 STP=0oC & 1 atm
 PV=nRT
 PV/T=PV/T (Combined Gas Law)
 PA=Ptotal x XA, where XA=moles A/ total moles *
 Ptotal= PA + PB + PC + … (Dalton’s Law of Partial Pressures) *
 KE per molecule = 1/2 mv2 *
 KE per mol = 3/2 RTn
 r1/r2=(M1/M2)1/2 (Graham’s Law) *
 1 atm = 760 mm Hg = 760 torr = 101.1 kPa
* = probably not on IB test but still something you would get in
any college chemistry class
Root Mean Square Speed

The third postulate can be quantified by
calculating the average velocity of the gas
particles. This quantity is written as urms

It is the speed of a gas particle having the average
kinetic energy of the all the gas particles in the
container.
 Q - How do we measure this KE?
 A - A thermometer!

urms=(3RT/M)1/2




R=8.3145 J/K x mol (The “Universal” gas constant)
T= Temperature in K
M=the molar mass of the gas
For Hydrogen at room temp, urms= 2000m/s!
Root Mean Square Speed
urms=(3RT/M)1/2

Calculate the urms for the following gases at
20oC.
 Argon
 Carbon dioxide
 Oxygen
Q - Which is the highest? Lowest? Why?
 Q - Would that change if you increased the
temperature?

Root Mean Square Speed
urms=(3RT/M)1/2
Q - Remember that urms is an “average”
speed. What does that mean?
 A – Some particles in the sample are going
faster than urms and some are going slower.
