AP Chemistry
“The Behavior of Gases”
Effusion and Diffusion
 Root Mean Speed
Average Kinetic Energy

Diffusion is:
u
Molecules moving from areas of high
concentration to low concentration.
uExample:
perfume molecules spreading
across the room.

Effusion: Gas escaping through a tiny
hole in a container.
 Both
of these depend on the molar
mass of the particle, which
determines the speed.
•Diffusion:
describes the mixing
of gases. The rate of
diffusion is the rate
of gas mixing.
•Molecules move
from areas of high
concentration to low
concentration.
Effusion: a gas escapes through a tiny
hole in its container
-Think of a nail in your car tire…
Diffusion
and effusion
are
explained
by the next
gas law:
Graham’s
Graham’s Law
RateA
RateB
=
 MassB
 MassA
The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules.
 Derived from: Kinetic energy = 1/2 mv2
 m = the molar mass, and v = the
velocity.

Comparing distance traveled
You can compare the distanced traveled by 2
gases in the same amount of time using this
equation also.
Distance traveled by A =  MassB
Distance traveled by B
 MassA
Graham’s Law
Sample: compare rates of effusion of
Helium with Nitrogen –
 With effusion and diffusion, the type of
particle is important:



Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass.
Helium effuses and diffuses faster than
nitrogen – thus, helium escapes from a
balloon quicker than many other gases!
How much faster does methane (CH4) effuse
than propane (C3H8)?
Determine molar masses of each gas
CH4 = 16.04 g/mol
C3H8 = 44.09 g/mol






Plug into formula
Rate CH4
 M C3H8
Rate C3H8
 MCH4
=  44.09 = 1.65
 16.04
This means that methane diffuses 1.65 times
faster than propane gas
Graham’s Law of Effusion Examples
1) A compound effuses through a porous
cylinder 1.41 times faster than helium. What
is it’s molar mass?
Rate Gas x
Rate He
1.41 = √4
√x
= √He
√X
1.41 (√x ) = 2
√x = 2/1.41
X = (1.41)2 = 2.01 g/mole =
Hydrogen (H2)
If
0.00251
mol
of
NH
effuse
through
a
hole
3
Assuming the time is the same, we can use the
in 2.47relationship
min, how
following
withmuch
Graham’sHCl
Law would effuse in
the same time?

Moles NH3
=
Moles HCL
√MHCl
√MNH3
0.00251
Moles HCl
=
√36.45
√17
0.00251
Moles HCl
= 1.46428
Moles HCl =
0.0017 Moles

A sample of N2 effuses through a hole in 38
seconds. what must be the molecular weight
of gas that effuses in 55 seconds under
identical conditions?
Moles / 55sec
= √ MN2
Moles / 38sec
√Mgas
38
55
=
√28
√Mgas
Mgas = 58.5 g/mol
Molecular Speeds and
Average Kinetic Energy
The Kelvin temperature scale is a measurement
of the average kinetic energy of gas particles.
 KE = ½ mv2
 As kinetic energy increases, then the
temperature increases, and molecules move
faster.
 KEavg = 3 RT
2
Where = 8.3145 J/Kelvin Mole
 This formula represents the average energy of
the particles at a given temperature.

Maxwell Speed Distribution Curve
•Peaks represent the
average speeds
•Remember, some are
moving faster and some
slower at the same
temperature!
•Peak moves to greater
speed with higher temps.
•Curve flattens due to
more molecules moving
at greater speeds.
Root Mean Square Speed (or Velocity)
 rms or μrms (Units are meters/sec)

Estimates the average molecular speed based on
molecular mass and temperature.
 Μrms =




√3RT
√M
M = Molar Mass in kg/mole
R = 8.3145 J/K Mol
T = Temperature in Kelvin


This Formula relates the difference in speed (not
kinetic energy!) to the molar mass of the gas.
Maxwell Speed Distribution Curve
•These are speed
distribution curves for 3
different gases a the same
temperature
Oxygen
(O2)
Helium
Hydrogen (H2)
•Shows that lighter
molecules (like
hydrogen) move faster
on average than
heavier ones (like
oxygen)
Big Points to Remember:





All gases at the same temperature have the same
average kinetic energy.
But, they do not have the same average velocity
(or speed!)
Speed depends on Molar Mass (root mean
square speed!)
The heavier the gas, the slower it moves!
The lighter the gas, the faster it moves!