Chapter 7 Gas Laws
Consider the Kinetic Molecular Theory
We have learned in previous courses (Science 10 for example) that
according to the Kinetic Molecular Theory (KMT) when you add
energy to atoms or molecules in solid state, you actually increase
their kinetic energy (energy of motion) in other words, they vibrate
faster and to a greater degree. Increasing the energy will cause
them to break free and move around each other. At this point the
solid has become a liquid. Continuing to add energy will cause the
particles to break free and move at extremely high speeds (~1600
kph). If you remember correctly, we have now entered the gas phase.
When speaking about gases we run into the concept of ideal gases.
Although they do not actually exist in nature, gases for the most part
do approximate the behaviours described by the gas laws.
For the purpose of this course we will assume that all gases are ideal
gases.
When speaking about gases, it is advantageous to come to an
understanding of how they behave so far as the KMT is concerned.
For that reason, behold:
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The Kinetic Molecular Theory
of Ideal Gases
These statements are made only for what is called an ideal gas. They cannot all be
rigorously applied (i.e. mathematically) to real gases, but can be used to explain their
observed behavior qualitatively.
1. All matter is composed of tiny, discrete particles (molecules or atoms).
2. Ideal gases consist of small particles (molecules or atoms) that are far apart in
comparison to their own size. The molecules of a gas are very small compared to the
distances between them.
3. These particles are considered to be dimensionless points which occupy zero volume.
The volume of real gas molecules is assumed to be negligible for most purposes.
This above statement is NOT TRUE. Real gas molecules do occupy volume and it does
have an impact on the behavior of the gas. This impact WILL BE IGNORED when
discussing ideal gases.
4. These particles are in rapid, random, constant straight line motion. This motion
can be described by well-defined and established laws of motion.
5. There are no attractive forces between gas molecules or between molecules and the
sides of the container with which they collide.
In a real gas, there actually is attraction between the molecules of a gas. Once again, this
attraction WILL BE IGNORED when discussing ideal gases.
6. Molecules collide with one another and the sides of the container.
7. Energy can be transferred in collisions among molecules.
8. Energy is conserved in these collisions, although one molecule may gain energy at
the expense of the other.
9. Energy is distributed among the molecules in a particular fashion known as the
Maxwell-Boltzmann Distribution.
10. At any paticular instant, the molecules in a given sample of gas do not all possess
the same amount of energy. The average kinetic energy of all the molecules is
proportional to the absolute temperature.
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Pressure
pressure - a force per unit area.
In the Metric system, on Earth, acceleration due to gravity is 9.8
meters/sec2. So (Mass)*(Acceleration due to gravity) has the units
Kilograms*meters/sec2. These units of force are known as
Newtons. Thus, an object with a mass of 2 Kilograms has a weight
of:
Mass *Acceleration due to gravity =(2 Kg)*(9.8 meters/sec2)
= 19.6 Kg*m/sec2
= 19.6 Newtons.
Consider the following brick. A common brick weighs about 22
Newtons (a little over 2 kg). Observe what happens to the pressure
[force (N)/ area (cm2)] as you decrease the area.
22 N / 180 cm2
= 0.12 N/cm2
22N / 120 cm2
=0.18 N/cm2
22 N / 54 cm2
= 0.41 N/cm2
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Yep, it increases. What does this tell you? That pressure depends on
area over which the force is exerted. Ever been stepped on by a
woman wearing high heeled shoes? Now you’ve got the picture!
Pressure of a Gas
So what has this to do with gases? Well, in the case of gases,
pressure is a measure of collisions of gas molecules with the sides of
the container; the more collisions per second, the higher the
pressure.
We measure pressure in units called pascals (Pa) where
1 Pa = ___1 N___
m2
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We can use a number of different tools to measure pressure, but they
all have one thing in common, they have a method of pushing back.
Consider the following:
fig 1.
fig 2.
fig 3.
What are these and how do they work? What is pushing back?
Figure 1 is called a mercury barometer and is used to measure air
pressure.
standard pressure - air pressure at sea level.
101,325 Pa (101.325 kPa) =1 atmosphere of pressure = 1 atm and
standard temperature – freezing point of water.
0oC or 273oK
STP – when standard temperature and pressure prevail.
Consider the manometer.
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Given the hint that the device is used to measure gas pressure, how
would you propose it works?
Daltons Law Of Partial Pressures (Heath p184)
Often more than one gas occupies the same container. Consider the
evolution of hydrogen gas by the reaction of an acid with zinc.
Because the hydrogen bubbles through the water/acid solution, water
molecules dissolved in the gas. So our gas sample was only partly
hydrogen, it was also partially water vapour.
Dalton’s law states that the total pressure of the gas was equal to the
sum of the pressure exerted by hydrogen and the pressure exerted
by the water.
Or
Ptotal = P1 + P2 + P3…
Work through Example 7-1 and Review and Practice (Heath p186)
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Charles Law (Heath p187)
Basically, Charles Law states that if you increase the temperature
on a gas in a closed container that is allowed to maintain
constant pressure (it is allowed to expand and contract) then the
volume will increase accordingly.
P = 1 atm
V = 100 cm3
T = 273oK
P = 1 atm
V = 200 cm3
T = 546oK
If you double the temperature, you double the volume. But notice
something else; if you divide volume by temperature, you get the
same number. As a matter of fact if this were a real system we would
find that no matter how we changed the temperature, the new volume
would be such that you would ALWAYS get the same number. This
same number is called a constant (duh!) and is commonly designated
“k”. (In this case it is 0.366 but this is just pretend numbers so don’t get too attached to it…you
will probably never see this number again)
You can state Charles Law is by
___V___ = k
T
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Or
___V1___ = ___V2___
T1
T2
Work through Examples 7-3, 7-4 in Heath
Before we go on it is important to review Kelvin temperature. Kelvin
temperature was discovered as a spin-off of some very interesting
experimental data of a gas sample at constant pressure. It was
shown that if you extrapolated the data backward, there would be
zero volume at -273oC and that for every degree you raised thte
temperature, the volume would increase by 1/273.
SO
ToK = ToC + 273
k again
Just so we understand each other…the value changes when you
change a system, but it remains constant within the system. Got it?
Boyle’s Law
Boyles law relates pressure to volume. It states that the pressure of a
sample of gas, if kept at constant temperature, will change inversely
to it’s volume
Huh?
Basically if you squish a volume of gas, then the pressure goes up.
The more you squish (decrease volume) the greater the pressure
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P = 1 atm
V = 1000 cm3
P = 2 atm
V = 500 cm3
If you multiply the pressure times the volume you will notice that you
get the same answer. (In this case it is 1000 cm3 – atm but this is just pretend numbers
so don’t get too attached to it…you will probably never see this number again)
This should seem obvious to you. You can express this relationship
by:
PV = k (another constant)
Or
P1V1 = P2V2
Okay, now for the magic…
The Combined Gas Law
Charles law and Boyles law can be combined into a simple
expression that will allow you to calculate any change in system
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provided you do not increase the amount of gas (a.k.a. “change the
number of moles”) in the system.
Yahoo! Do you Yahoo? Well, you can Yahoo now!
___P1V1___ = ___P2V2___
T1
T2
Example 7-8 and Review and Practice Heath p200
And now for La Piece de Resistance:
The Ideal Gas Law
Up ‘til know we have only studied how changes in conditions affect a
closed system…a constant number of atoms or molecules without
talking about how many there actually are. The Ideal Gas Law Takes
care of that:
Simply stated
PV = nRT
Where:
P is expressed in kPa
V is expressed in litres
n is the number of moles
T is expressed in oK
R is the Ideal Gas Constant = 8.31 __L • kPa__
mol • oK
If you can rationalize your way through a problem you can also use
this equation instead of all previous equations…but it will probably
take you longer.
How is that possible?
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Well if PV does equal nRT, then PV/nRT = 1 (Don’t get it? Go back to
the beginning of the course!) If you label all initial conditions by “1”
and the final conditions “2”, then,
___P1V1___ = ___P2V2___
nRT1
nRT2
Okay, time for practice
Review and Practice p 208
…and finally
Graham’s Law of Diffusion
Given that each of these gases is at the same temperature and
therefore molecules of each have the same average kinetic energy,
which will diffuse first?
NO2 at 1 atm and 20oC
Cl2 at 1 atm and 20oC
If the kinetic energies of the gases are equal and the temperature is
the same then
_1_ mv2(NO3) = _1_ mv2(Cl2)
2
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we also know that the mass of Cl2 is 71.0 g/mol and the mass of NO3
is 46.0 g/mol.
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What does this imply?
that the velocity of NO3 molecules must be proportionately
greater than the molecules of Cl2 in order to balance out.
therefore, NO3 will diffuse quicker because the molecules are
travelling faster!
Physics 1, 2 Software demonstrations.
Mathematically,
Instant Practice; Heath p213 Example 7-13
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