# Gases

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```					                                     Gases
In Unit 6 you learned some basic properties of gases. I have cut and pasted the
pertinent paragraphs below:
Gases have neither a fixed shape nor a fixed volume. Thus if somebody released a
liter of bad smelling gas into the room, the gas would fill the entire room (take the
shape and volume of the room). Let’s not try this one.

Gas particles don’t stick to each other, which means that the intermolecular
forces are small or the particles are moving too quickly to be captured by the
intermolecular forces. A schematic of a gas is shown in Figure 3:

Figure 3 It’s a
Gas

Cool Gas                    Warm Gas

So you see, gases are more elusive than solids or liquids. Because they don’t have
a fixed volume, we have to take other measures to quantify (measure) them.
Another important property needed to measure gases is pressure. Pressure is
defined as force per area. Look at Figure 3 again. In the two compartments are
equal number of particles, their volumes of confinement are identical (each box is
the same area). The only difference is that the particles of the cool gas are not
moving as quickly (have a lower average kinetic energy) than the warm gas
particles. Do you suppose that the pressures are equal in both boxes? Of course
not, silly! The warm gas will have a higher pressure because the warmer, faster
gas particles exert more force on any given area of the box than the cool gas
particles. Force per area is pressure, thus the warm gas particles are at a higher
pressure.

The Kinetic Molecular Theory, KMT, is a model that explains the behavior of
gases. Many aspects of it have already been covered in this paper. To
summarize, the parts of the KMT are:

1. The particles are so small compared with the distance between them that
the volume of the individuals particles can be assumed to be negligible
(zero). Note that Fig 3 is not shown to scale, if it were, the particles would
be few and far between.
2. The particles are in constant motion. The collisions of the particles with
the walls of the container are the cause of the pressure exerted by the gas.
3. The particles are assumed to exert no forces on each other; they are
assumed neither to attract nor to repel each other. (not true in reality)
4. The average kinetic energy of a collection of gas particles is related to the
temperature of the gas.

Temperature, Volume and Absolute Zero (Charles)

Let’s look at an experiment that could be done before all
mercury was removed from the classroom (Darn our luck!!!).
It involved using a length of a glass tube that was sealed at one
end and had a plug of mercury trapped in it.

This device would then be put into different temperature
water baths and the height of the trapped gas would be
measured. I will be doing a similar demonstration in class,
except in the demo we will be examining the affect of
temperature on Pressure of a gas, not volume.

When this information is graphed on a volume vs temperature scale it looks as
follows:
Volume-Temp C

12
y = 0.03x + 8.19
10

8
Height in cm

6

4

2

0
-300   -250   -200   -150       -100       -50        0   50   100
-2
Temp Celsius

Note that the temperature axis has been extended to the left by 300 degrees. The
data points form a straight line. When a trendline is added the equation V =
.03Tc + 8.19 is produced. If you solve this equation for Tc when V = 0, you will
get a temperature of –273°C. Or, just looking at the graph shows that the line
crosses the temperature axis at –273°C. Is this significant? You bet!!
The graph says that as you continue to cool the trapped volume of a gas, its
volume decreases in a linear manner. This must mean that the gas molecules are
moving slower and slower and are taking up less and less space, until you reach a
temperature at which they are taking up no space at all. For this to be true, the
molecules must not be moving at all. But since temperature is a measure of the
average kinetic energy of the gas particles, the average kinetic energy ( KE = 1/2
mv2)can get no smaller than zero if the particles aren’t moving. We have thus
determined the absolute lowest temperature possible, otherwise known as
absolute zero.
The absolute zero scale is also known as the Kelvin scale. A Kelvin degree is the
same size as a Celsius degree (that is, there are 100 of them between the freezing
and boiling temperatures of water), however they start at different points.
Whereas the Celsius scale has the freezing temperature of water as its zero,
Kelvin has absolute zero as its zero. To convert from Celsius to Kelvin, just add
273.
Lets now plot the above data of Volume vs Temperature using the Kelvin Scale
and see what we get:
Volume-Temp Kelvin

12

10
y = 0.03x

8
Height in cm

6

4

2

0
0   100               200               300                400
Kelvin

The equation for this line is now V = 0.03Tk. The y intercept is now zero. Now,
instead of just a linear relationship between Volume of a gas and Temperature in
Celsius, we have a direct variation between the Volume of a gas and
Temperature in Kelvin. This means that if the temperature in Kelvin of a volume
of gas is doubled, its volume will also double. Piece of cake!!!
There is just one “fly in the ointment”, that is; do you really think that if you cool
down a volume of gas cold enough it will just disappear? Well, no it won’t, as a
matter of fact, it will liquefy before it gets anywhere near absolute zero (Helium
does liquefy at 4K). Thus real gases liquefy, however Ideal gases don’t liquefy.
Ideal gases don’t really exist in nature, only in the minds of chemists across the
world. An ideal gas molecule has mass, but no volume, thus you can compress
them to a volume of zero. They also don’t attract each other, thus they will never
liquefy. They also obey the ideal gas law equation exactly. The Ideal gas law
equation is PV=nRT where P is pressure, V is volume, n is the number of moles
of gas molecules, R is a constant, and T is temperature in Kelvin. In this section
you examined the effect of Temperature on Volume of a gas (we held pressure
and the number of moles of gas constant) and determined that V=kT.
But if ideal gases don’t exist, why even consider them? Well its because at
moderate temperatures (like room temp) and moderate pressures (like 1 atm
pressures, real gases behave rather ideally. Thus, you can approximate the
behavior of real gases by assuming ideal behavior under all conditions except
very low temperature and very high pressure. Cool!
Temperature and Pressure (Guy-Lussac)
and awed faces when you observe this class demo! 

Pressure and Volume
Think of a bicycle pump with its end stoppered up. You have a trapped quantity
of gas inside (the moles of gas are constant) and we will assume that you will keep
its temperature constant. As you apply pressure to the pump handle, the plunger
goes down and compresses the gas, thus you have a smaller volume. This
relationship, as pressure increases the volume decreases, is called Boyle’s law
because a guy named Robert Boyle discovered it.
A more controlled experiment might look as follows:

If measurements were carefully obtained and graphed, the graph would look as
follows:
Boyle's Law

25

y = 500x -1
20
2
R =1
Volume in mL

15

10

5

0
0     50          100     150    200        250
Pressure in kPa

The best fit for this relationship is a Power Trendline with the equation being
V=k/P or PV = k. SO, if the pressure doubles, the volume is halved.
A scuba diver must be carefully aware of Boyle’s law or he could blow a lung. A
scuba tank releases air at ambient pressure. (Ambient pressure means
“surrounding”) Thus if the diver is down 10 meters, the total pressure on him is 1
atm from the water and 1 atm from the air above the water. If he inhales deeply
from this depth, his lungs will fill with air at 2 atm pressure. If the diver made
the mistake of trying to hold his breath as he surfaced instead of normally
breathing, then as he ascends the pressure on his body would decrease, meaning
that the volume of air in his lungs would increase. Yikes! Dead diver.
Dalton’s Law of Partial Pressures
Mr. Dalton discovered a remarkably simple relationship of gases: The sum of all
the partial pressures of gas in a container will add up to the total pressure. It is
just that easy!!!
Here is an example: Consider the container pictured below that has 0.5 atm
pressure Argon, 1.0 atm pressure Helium and 0.25 atm pressure Oxygen. What
do you suppose the Total pressure would be? Try 0.5 + 1.0 + 0.25 = 1.75 atm
Regardless of how easy partial pressures are, here is a problem that tends to
confuse even the best of students.

PNe = 200 kPa                 PAr = 100 kPa

Valve

In the situation above you have Neon gas in the vessel on the left and Argon gas
in the vessel on the right at the pressures indicated. Both vessels are of the same
size.

After the valve is opened, what is
a. the partial pressure of Neon found in the vessel on the left?
b. The partial pressure of Argon in the vessel on the left?
c. The total pressure of the system?

Think you have it? Here are the answers:
a. 100 kPa, the gas now takes up twice the volume, thus its pressure is half
(Boyle’s Law)
b. 50 kPa for the same reason as in a
c. 150 kPa because the partial pressures add.

THERE, NOW YOU ARE A GAS EXPERT!!

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 views: 8 posted: 12/13/2011 language: pages: 7