[MUSIC]
Lighthouse Scientific
Education presents a lecture
in the Gas series
The topic; Gas:
Advanced Concepts.
Much of this material is at
best briefly covered in an
average chemistry course.
Some courses, however do
venture deeper into these
topics and it is for those
students that this
lecture is intended.
Know what material
is expected of you.
Material in this lecture
relies on an understanding
of the previous lectures;
The Basics of Gas
Fundamentals of Gas Law and
Gas Law: 1 Condition
This lecture begins with
brief review of gas basics
and a re-examination of
the Kinetic Molecular
Theory (KMT).
That requires a review of
KMT as covered in the
'Basics of Gas' lecture
and an expansion of the model.
This leads to a discussion
on random motion of particles
which is used to describe
diffusion and effusion.
Graham's Law is introduced
as a way to quantify rates of
diffusion and effusion.
As a note, one advanced
concept involving gas that
is not covered in this
lecture is stoichiometry.
It is however covered in the
lecture 'Stoichiometry:
Advanced Concepts'
which is found
in the Stoichiometry
Series of lectures.
Any discussion involving
gases starts with a review
of the four basic
properties of gases.
They are amount in moles,
temperature in Kelvin,
volume and pressure.
These properties can be
viewed from the perspective
of energy which focuses on
temperature and pressure.
Energy is the central theme of
this lecture and a brief
review of it and its effects on
pressure is warranted.
Motion is a form of energy.
Motion energy is heat.
While heat is a form of energy,
temperature is a measurement
of the amount of
that heat energy.
Higher temperatures
reflect greater amounts
of heat, which means more
motion and generally
faster gas particles.
And like any moving object,
the faster a gas particle
moves the harder it
strikes or collides.
Fast moving and harder
colliding gas particles
create higher pressure.
Pressure is the lens in which
gas behavior can be most
readily rationalized.
Pressure is defined as a force
exerted over some set area.
For a gas, the force is gas
particles colliding with the
side of the container or
any object for that matter.
Bottom line, more collisions
or harder collision means
more force which
means more pressure.
This is the connection
between energy
and pressure.
In the 'Basics of Gas'
lecture we looked at the
Kinetic Molecular Theory
(KMT) as a way of
understand behavior of gases.
In this lecture we will expand
upon that understanding after
providing a review of what
has already been covered.
KMT treats gases like
they are ideal gases.
There are 3 basic
assumptions that make
a gas ideal.
The opening assumption
is that a gas is
composed of particles.
Very tiny ones.
For the most part they
are compounds or atoms.
The particles are modeled
as small hard spheres.
They are said to have
no volume and do not
experience intermolecular
interactions.
Real gases do have volumes
and do experience
intermolecular interactions.
When dealing with gases
the term volume refers to the
space available for the gas
particles to roam and not
the volume of the particles.
The KMT argues that for dilute
gases the gas particles are
separated by such large
distances that the volume that
the gas occupies is
mostly empty space.
Gas particles make up such
a tiny part of the available
volume that the gas can be
treated as if it essentially
take up none of the
available volume.
The volume of the
particle is neglected.
As for intermolecular
interactions, a useful real
world model is billiard balls.
They are relatively small
(compared to the table) and
do not stick to, or repel,
each other.
In the previous lecture
'Gas Law: 1 Condition'
deviations to the concept
of an ideal gas is covered
in Van Deer Waals modification
to the Ideal Gas law.
The second assumption is
that the particles in the gas
move rapidly and are in
constant random motion.
More specifically the motion
of the particles are in
straight lines and only change
direction upon colliding
with another particle
or some surface.
As mentioned earlier
particles speed up
when heated.
An increase of heat leads
to an increase of collisions
and promotes random motion.
The third assumption is
that the collisions are
perfectly elastic.
In other words, the energy
of motion is
transferred without loss.
In the billiard ball
analogy, on a break of a
rack of balls, the total
energy of the cue ball is
transferred into the other
billiard balls. No energy is
lost due to bending
or cracking of a ball.
For the most part, these
assumptions provide a
satisfactory understanding
of the model.
However, digging a bit
deeper we will find a broader
understanding of gases
and their properties with
this model.
As mentioned earlier,
energy is a useful viewpoint
of the study of gas.
The energy of a gas can be
viewed from 2 perspectives.
They give insight to different
aspect of gas behavior
but can be united into one
picture. The first perspective
is using
kinetic energy
or average
kinetic energy (AKE).
It is the average energy
of motion all particles.
The term kinetic means motion.
The other perspective
is with thermal energy
(heat energy).
It is concerned with
total energy of all of the
particles that make up the
gas and is helpful
in viewing the role of
mass in motion.
We will look at these
perspective's one at a
time starting the average
kinetic energy.
Here we focus on the
energy of motion.
Broadly speaking, we
know that fast moving
objects have more energy than
slower moving objects.
Who wants to be hit by
the faster moving baseball?
Also, for two objects
moving at the same speed,
the heavier one
has more energy.
Who wants to be hit
by a bowling ball?
This intuitive understanding
has a mathematical
definition:
kinetic energy (KE)
It is equal to one half the
mass (m) of an object times
the square of its
velocity (v).
Speed can be used for
velocity in most cases.
That definition tells us that
the more mass an object has
the more energy it will have.
Also the faster an object
goes (larger velocity) the more
energy it will have.
This is consistent with our
understanding of
heat as energy.
Particles speed
up when heated.
And since temperature
is a measurement of heat;
the average kinetic energy
is proportional to the
measured temperature.
We will limit that
statement to within
any one specific gas.
Temperature is a reflection
of heat which relates to speed
or velocity which
relates to kinetic energy.
Now to the term average
in average kinetic.
When dealing with the AKE,
the kinetic energy of all
the particles have to
be known considered.
Importantly, in a gas, the
particles do not all have
the same velocity.
Individual particles will not
all have the same kinetic energy.
Returning to the
billiard ball analogy.
Not all of the balls
have the same speed coming
out of a break.
Additionally, when the balls
begin to collided with
each other some balls gain
speed while others loss speed.
Colliding gas particles will
do the same thing. KMT says
that the total energy of the
collision is conserved but it
allows for the energy of
motion of one particle to be
transferred to that
another particle.
That is where average comes.
For example, here is a graph
of the distribution of
the speeds of gas particles
in a sample of the
noble gas xenon.
The velocity or
speed (x-axis) of
the individual gas particles
are plotted against the
population (y-axis) of
particles in the gas with
such speed.
Another way to say that is
what fraction of the
gas has what speed.
This is a bell shaped curve.
There is a distribution
of velocities or speeds.
Not all the particles are
going the same speed.
There are fewer
particles (low population,
small fraction) with really
slow or really fast velocities.
The majority of the
particles are centered around
an average velocity which
is the peak of the curve.
In fact the velocity at the
peak is representative of the
average velocity
of the particles.
This velocity can be used,
along with mass, to calculated
average kinetic energy
It makes sense to use
the peak as an average
since about half the particles
are moving slower than
the average speed and
half are moving faster.
We can use this curve to
ask what happens when heat is
added to the sample of gas.
Adding heat is adding
kinetic energy.
Having a higher
kinetic energy means
overall faster particles.
That comes right from the
definition of kinetic energy.
If the energy goes up and,
the mass of the particles stays
the same, then the only
way to keep the sides of the
equation equal is for the
velocity to go up.
What should we expect
to happen to the peak of
the curve if heat was
added to the sample of xenon
displayed in the graph?
The peak should shift to
a high velocity.
And that is what we see.
A new distribution of
speeds with a new peak (T2).
Overall the particles
are going faster.
With these two curves we can
make a couple observations.
The first one is a recognition
that heat was added to
the sample of gas to get it
to the higher temperature T2.
So the average kinetic
energy (AKE) of the gas at T1
is less than the average
kinetic energy of the
gas at T2.
That can be seen
with a shift in the
peak of the curve.
As the temperature is raised
particles move faster and T2
reflects a higher average
speed then T1 does.
Putting the respective
velocities in the average
kinetic energy equations
would indeed show that
the AKE attached to
T2 was larger than the
AKE attached to T1.
The second observation
is that the spread of
the curve is increased.
The T2 curve is
shorter and fatter.
With higher velocities comes
more collisions and that
leads to a broader
distribution of speeds.
Looking at gas from the
perspective of kinetic energy
is about the speed of
the particles. The other
energy perspective
is thermal energy.
It is concerned with
the total energy of
the particles.
The total energy
of the sample of gas, at
a particular temperature,
is proportional to the
area under the curve.
The thermal energy under the
first condition (T1) is
proportional to the area
under this bell shaped
curve and the thermal energy
under the second condition
(T2) is proportional to the
area under this
bell shaped curve.
So, the total area under
these curves should
not be equal because
their thermal energies are
not equal.
Heat energy was added to
get the T2 curve.
The T2 curve is shorter
and fatter but will have a
greater total area.
If we were to print out
separate graphs of these two
distributions and then cut out
the bell shaped curves, the
one representing T2 would
weigh more than the
one representing T1.
T2 has more area.
Now let's return to one
temperature for xenon,
say T1, and reconsider the
distribution of particles
of a gas from the
perspective of mass in the
kinetic energy equation
since distribution is
dependent on size
as well as velocity.
Keeping to the one
temperature, same heat,
we can bring in another curve
of a different kind of gas
(helium) that has the same
number of particle and is in
the same size container.
Amount, temperature, and
volume are the same for these
two gases and yet they have
different distributions
of velocity.
How is that? Well, it's
not all about speed.
Because when they have the
same basic gas properties
they have the same
average kinetic energy.
The average kinetic energy of
the xenon particles is equal
to the average kinetic energy
of the helium particles.
One might expect the AKE for
the helium to be larger since
it has a larger average
velocity. It is not true
because there are additional
factors to consider.
Keep in mind the equation for
kinetic energy; 1 half mass
of the particle times
velocity squared.
Note that these two average
kinetic energies have
different size masses. Xenon
is much heavier than helium.
For these two energies to
remain equal to each other
with different masses the
velocity squared term in the
AKE of xenon has to be
smaller than the velocity
squared term in
the AKE of helium.
That is under the same
conditions, larger mass gases
have slower average speeds
and smaller mass gases have
larger or faster average speeds.
They have the same
average kinetic energy but
one does it by being heavier
(xenon) and the other
by being faster (helium).
Because they have
equivalent AKE's they exert
the same force on the
container and therefore
produce the same pressure.
That is kind of the take home
lesson here. At the same
temperature, with all things
being equal, all gasses
produce the same pressure.
Some produce the force by
moving faster and making
more collisions and some
by moving slower but hitting
harder due to being heavier.
We can take this new
understanding and
revisit collisions.
From the average kinetic
energy we know that
gas particles have
large velocities.
At room temperature, some
of xenon's particles have
velocities of over
500 meters per second.
At such speeds, however, it is
not long before a particle
will collide with another
particle or some other object.
Collisions between particles
creates, what appears to be,
random motion.
Another commonly used
term is that the
particles appear to be on
a random walk. To be sure
that we are on the same page
consider this carton that
follows just one of the
gas particles in container.
It appears to rapidly change
directions for no
observable reason.
But if we were able to track
that motion it would be a
series of straight lines
in which every change
of direction is the result
of a collision with another
particle or with the sides
of the container.
The path is called a random
walk because every particle
in the gas would have
its own unique set of
collisions and its
own unique path.
There is no knowing where
any 1 particle will
end up at any one time.
It is random. Some gas
behavior can be best
understood from an
understanding of the overall
pattern or distribution
of the gas particles
taking random walks.
There are factors which
influence the overall
distribution of gas particles
and they include time,
amount as in the numbers
of moles of gas and
the average kinetic energy
of the gas.
The kinetic energy can
be broken down into the
factor of speed (or velocity)
which is associated with
the temperature of the gas
and mass of the particle
which will be found with the
molar mass of
the gas particles.
Time, amount, speed and
mass effect the overall
distribution of a gas because
they affect the random walk of
the individual particles.
As an illustration consider
a small collection of
gas particles initially
located closely together.
An example would
be a small spray of a
room deodorant like Lysol.
Now being a gas these
particles instantly begin
moving and wandering
about the available space.
We fully expect the
collection of particles to
spread out from its
original position.
Looking at the
spread under different
conditions will
give us perspective on gas
behavior as reasoned
from random motion.
Condition 1 and we will
fill in what those conditions
are momentarily.
The particles begin
to randomly walk about
and will disperse over
a broad area.
This circle roughly gives an
area in which that the
particles could have
spread out into. If were to
re-run the distribution from
the initial closely packed
collection, under the
same condition 1, then a
different spread would have
been seen but most likely
it would have fallen within
that circle.
This circle represents
the boundary of the
spread at condition 1.
Now we change conditions,
condition 2, and will reset
the particles to their
original position.
Being only concerned with
the final position of the
particles after their
random walk we see
a new distribution,
or spread of particles.
This circle represents
the boundary of the spread
at condition 2.
Removing the particles and
only focusing on the
spread we have the spread
at condition 2 and the
spread at condition 1.
With these two spreads we
can ask how the factors of
time, speed and mass
affect distribution.
Starting with time.
Say that condition 1
was the distribution
over a set time; T sub 1.
And condition 2 only varied
in its set time T sub 2.
Comparing the 2 circles
as spreads or distributions
brings up the conclusion
that T1 is less than T2.
The longer the particles
have to randomly walk
about the broader the
distribution of particles
will be. Given more
time, the probability
that any given particles
is further from its initial
position is greater.
Now say that the
two conditions are over
the same period of time but
differ in the
amount of particles.
We will use the variable n
for moles to represent amount
and the subscripts 1 and
2 to denote condition.
Condition 1 has less
particles then condition 2.
Condition 2 will have
a broader distribution.
With more particles there
are more collisions and it is
more likely that there are
particles that randomly walk
much further away than
the average particle does.
That is just statistics.
An analogy is that
25 first graders are bound
to spread out further on
a playground than 5
first graders. First graders
are prime examples
of random motion.
What should we excepted
if time and amount are held
constant in the two
conditions but that the
temperatures are different?
Remember, the average
speed or velocity of the
particles is proportional
to temperature.
Hotter particles move faster.
The average velocity of
particles in condition 1 are
different than the average
velocity of the particles
in condition 2.
This distribution
pattern occurs when the
temperature (and therefore
velocity) in condition 1
is less than the temperature
in condition 2.
Faster moving particles
can move further from their
initial position in
the same time period.
Their distribution
is therefore broader.
Finally, consider these
patterns of distribution in
which the only variable that
changes in condition 1 and
2 is the mass
of the particles.
Condition 1 has mass 1
and condition 2 has mass 2.
These circles represent the
distributions that occurs
when mass 1 is
larger than mass 2.
This is really an extension
of the argument made with
different velocities. In the
previous section we saw that
for identical conditions
a smaller mass gas, helium
in this example,
generally has faster moving
particles. Faster moving
particles travel further.
The broader distribution
of gas in condition 2 is due
to the smaller gas
particles having larger
average velocities. In
summation of the 4 variables
in the 2 conditions, the
spread is larger given
more time, more particles,
higher temperature
and a smaller particle.
This series of comparisons
takes us to our final
two topics. The first
is diffusion which is the
expansion of a gas to
occupy all available volume.
Diffusion is also used to
explain the mixing of gases.
And then there is effusion.
It is the escape of a gas
through a tiny hole
in its container.
Both of these properties
can be explained by the
random walk of gas particles.
Starting with diffusion as
a form of random motion.
It is defined as the
movement of particles
from and area of high
concentration to an area
of low concentration.
Diffusion is not
limited to gases.
We saw diffusion with osmosis.
There it is diffusion of
water across a semi-permeable
membrane. Still, it is
movement from an area
of high concentration to an
area of low concentration.
In practice, for gases, it
is the expansion of the gas to
fill a container or
any available volume.
In this carton there are
two spherical volumes that
are separated by a barrier.
Often such a barrier is a stop
cock which can be opened
with the twisting of a knob.
There are gas particles
random bouncing around
in the left volume.
The gas fully occupies
that volume.
The right volume is empty.
The concentration of
gas on the left is high.
The concentration of
gas on the right is low.
Diffusion is the movement
from an area of high
concentration to an area
of low concentration.
If the barrier were
removed the particles would
randomly walk about and
after a period of time
they would
fill the two volumes.
Random walking evens
out the concentration.
There are factors that
affect the rate of diffusion.
That is how long it takes
for the concentration
to even out.
Since random
walking is at the heart
of diffusion, factors
or conditions that affect
random walking will affect the
rate diffusion
in the same way.
Such as the role
of temperature.
At a higher temperature
(T2 in this case) a gas
will have a larger
average velocity.
It will have particles
that on the average move
faster than they did when
at temperature T1.
Faster moving particles
will diffuse faster.
That is, the concentration
will even out sooner.
And then there is
the role of mass.
All other condition being
equal lighter particles
(m2 in this case) will
move faster than particles
of a heavy gas.
We saw this explanation
in the section covering
the thermal energy of a gas.
The smaller mass gas helium,
on average, has faster
particles than the
larger mass gas xenon.
Lighter particles are faster
particles and they will
diffuse faster.
The other topic with diffusion
is that when different gases
mix they mix completely.
Gases are
homogenous solutions.
In this cartoon two gases are
separated into equal volume
vessels with a physical
barrier between them.
We will say that these
two gases do not interact
and do not participate
in a chemical reaction.
The container on the left has
a high concentration
of red sphere gas particles.
The container on the right
has no red sphere particles
so its concentration
is low or actually zero.
Conversely, the container on
the left has no green sphere
particles so it has a low
or zero concentration of the
green sphere gas. But the
container on the right has
a high concentration of
the green sphere particles.
If the barrier between the
vessels were removed the
gases would mix and the
concentrations would change.
For the most part, the
diffusion of one gas
occurs independently of
the other type of gas.
In this example, mixing is
really 2 diffusion events
happening at the same time.
When the barrier is finally
removed each type of gas,
through random walking,
diffusions from an area
of high concentration
(of its particle type) to
an area of low concentration
(of its particle type).
When the diffusion is
complete both containers will
have the same concentration
of red gas particles and
the same concentration
of green sphere particles.
The gases mix completely.
The mix is a
homogenous solution.
Since mixing is a
combination of individual
diffusion processes it is
independent of the type of
gases being mixed.
They will both diffuse
completely regardless of the
mass of their gas particles.
Weight can only influence
how long the process
of mixing takes. The initial
concentration of gases
also doesn't matter.
One of the gases
can be at a much higher
concentration than the other.
Still both gases will explore
all available space and
evenly distribute
throughout that space.
Same with temperature.
Higher temperatures will
speed up the particles
and that will speed up the
process of diffusion but
not change the final outcome.
A companion property
to diffusion; effusion
Effusion is the escape of
a gas through a tiny hole in
its container.
In most ways it is really
just the diffusion
through the tiny hole.
To reiterate, what drives
diffusion and effusion
is the movement of gas
particles from an area of
high concentration to an
area of low concentration and
that will happen through the
random motion of particles.
A demonstration of the
process of effusion has
two enclosed chambers
next to each other.
We will say that they are
both completely sealed even
though we can see inside.
The volume on the left has
a vacuum. There are no gas
particles in that
chamber so the pressure
is zero. The volume on the
right has mix of gas
particles zipping around
on random walks.
If a pin prick, or small
hole, was made between
the chambers and the
particles continued
their random walk
and random collisions
we would expect some of the
gas particles to find their
way through the hole.
Without a hole the particles
would have simply bounced of
that part of the wall but with
a hole there they
sail straight through.
We would also expect
to hear that pssss sound
of a small leak.
Effusion is influenced by
the same set of
factors as diffusion.
That can be viewed through
the kinetic energy of the gas.
Effusion is influenced
by the mass and velocity
of the gas particles.
Adding heat to a sample
of gas increases
its kinetic energy.
Since the mass of the
particles don't change with
heating the larger
kinetic energy means a
larger velocity
or faster particles.
Faster velocities affect
faster diffusion and
faster diffusion
creates faster effusion.
In this context faster
effusion refers to the time
it takes for the
pressure of the gas on the
two sides of the tiny
hole to become equal.
That is, enough
gas from the area of
high concentration has
moved into the area of low
concentration so that both
sides of the tiny hole have
the same concentration.
From a sound perspective it
would be where that pssss
sound of escaping gas
comes to an end.
Higher temperatures drive
higher effusion.
The other component in
the kinetic energy
equation is mass.
For that we return to
the distribution of speeds
for two gases at
the same temperature.
The atomic mass of xenon is
greater than that for helium.
Because they are at the same
temperature the smaller gas
has a higher average velocity
and a faster diffusion.
Faster diffusion
creates faster effusion.
Take home point: smaller
particles effuse faster.
But how much faster?
That understanding comes
right out of the kinetic
energy equation and
is summed up in what
is called Graham's law.
It states that the rate of
diffusion and effusion is
inversely proportional to the
square root of the molar mass
of the gas. Rate in
this context can be
thought of as how long it
takes the process of moving
from an area of high
concentration to an area of
low concentration.
Inversely proportional
means that the molar
mass quantity is in the
denominator.
The law doesn't look like
it comes straight out the
kinetic energy equation.
But if we make the argument
that diffusion and effusion
are proportional to the
velocity of the particles
then solving the kinetic
energy equation for velocity
is an indicator of rate.
Going from v squared to
v is going to take a square
root. The student can either
do that algebra themselves
of just take it on faith.
Graham's law is
useful in comparing the
rates of two gases. The
comparison is done in a ratio.
The rate of diffusion
or effusion of gas 1
The rate of diffusion
or effusion of gas 1
over the rate of diffusion
or effusion for gas 2.
It is not a particular pretty
equation but some fraction
algebra solves it
to a more manageable
ratio of square roots
of the molar masses.
And another algebra step
puts both molar masses
under the same
square root sign and
we have a functional
form of Graham's law.
This form of Graham's law is
often provided to the student
so none of that more complex
algebra is really required.
The thing to note about
this equation is that on the
rate side, information
is gas 1 over gas 2
but on the molar mass side
it is gas 2 over gas 1.
An example of its utility
can help add perspective.
Say we are given a problem
that starts by noting that
hydrogen gas is lighter
than molecular oxygen gas
and should effuse faster.
But then specifically asked
what is the ratio of the rates
of effusion of these gases?
It assumes that the properties
of temperature, pressure
and amount are constant.
All it's looking for is a
comparison of how
long it takes the gases
to completely effuse
under identical conditions.
How does the rate
of effusion for H2
compare with the rate
of effusion for O2?
According to Graham's law
it is the square root of
the molar mass of O2
over the molar mass of H2.
That is the square root of 32
g per mole (molar mass
of O2) over 2.0 g per
mole (molar mass of H2).
Units cancel and 32
divided by 2 is 16.
The square root of 16 is 4.
The rate of effusion
for H2 is 4 times faster
than that of O2.
The ratio of masses
is 16 but the ratio
of effusion is only 4.
And that ends of the
material of the lecture.
Recapping the lecture;
We took a deeper look at
the Kinetic Molecular Theory
of gases and introduced the
term Average
Kinetic Energy (AKE).
It is the average energy
of motion for all particles
and allows energy to be
discussed in terms of motion.
AKE is proportional
to temperature since
temperature is a measure
of heat or motion energy.
Kinetic energy is defined
as one half mass times
velocity squared.
The average KE can
be estimated by using an
average for the velocity
of the particle and it
is an average because for
any gas the particles have
a distribution of speeds.
This makes sense because
the particles are constantly
colliding and changing speed.
Faster particles have
higher kinetic energy.
The speed at the peak is
representative of the
average speed of all particles.
If the temperature is
increased then there will be
a shift in the overall
distribution of velocities
and that includes a
shift in the peak.
A higher temperature
means a faster
average velocity and a
broader spread of speeds.
The energy of a gas can
also be looked at from a
thermal perspective. That is
looking at all of the energy
from all of the particles.
It also uses the features
of the kinetic energy
equation and includes the role
of mass as well as velocity
in comparing behavior
of gases.
In particular we looked at
the distribution of velocities
for gases of different masses
at the same temperature.
That means the two gases
have the same average
kinetic energy.
As such, the gas with the
larger mass will have a
smaller average velocity
while a gas of a smaller mass
will have a larger
average velocity.
From an understanding
of KMT collisions
between particles
creates a motion for
the particles that appear
to be a random walk.
This leads to a random
distribution of particles.
Factors that influence
the distribution include
how long the particles
have to walk, their average
velocity and their mass.
With and understanding
of random motion we looked
at two additional properties.
The first was diffusion.
It is the movement of particles
from and area of high
concentration to an
area of low concentration.
Factors that affect
the distribution of particles
on a random walk
will affect diffusion.
Adding heat produces a
larger average kinetic energy
with larger
average velocities.
That promotes
faster diffusion.
For a given kinetic
energy (a set temperature),
smaller particles
have larger velocities.
Smaller particles will
therefore diffuse faster
than larger ones.
The other property
was effusion.
It is the escape of a
gas through a tiny hole in
its container.
Essentially effusion is
diffusion through a small hole
therefore the same factors
that influence diffusion
will influence effusion
and will affect it
in the same manner.
Graham's Law is a way to
compare the rates of diffusion
or effusion of gases.
For any one gas the rate is
inversely proportional
the square root of the
molar mass of the gas.
For two gases the rates
of diffusion or effusion
can be compared by the ratio
of the individual rates which
is found with a comparison of
molar mass and some math.
And that completes our lecture
It is the mass and
velocity of gas particles
that dictate behavior.
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