Title: Aim:%20Students%20will%20be%20able%20to%20understand%20why%20gases%20behave%20the%20way%20they%20do%20by%20examining%20the%20Kinetic%20Molecular%20Theory
1Aim Students will be able to understand why
gases behave the way they do by examining the
Kinetic Molecular Theory
- Do Now What is the total number of joules
absorbed by 65.0 g of water when the temperature
of the water is raised from 25.0C to 40.0C?
2Do Now
- q mC?T
- q (65.0g)(4.18 J/gC)(15.0C)
- q 4076 J
3Gases
- Have you ever seen
- a hot air balloon?
- Have you ever opened a
- shaken bottle of soda?
- Why do they work the way they do?
4In order to explain WHY gases work the way they
do
- Scientists have come up with the.
5KINETIC MOLECULAR THEORY
6The Kinetic Molecular Theory describes the
behavior of gases
- The KMT (kinetic molecular theory) describes the
relationships among pressure, volume,
temperature, velocity, frequency, and force of
collisions.
7Kinetic Molecular Theory
- Particles in an ideal gas
- have no volume.
- have elastic collisions (there is no loss of KE)
- are in constant, random, straight-line motion.
- dont attract or repel each other.
- have an avg. KE directly related to Kelvin
temperature
8Now that you know the laws that make up the
Kinetic Molecular Theory
- You are ready to understand the relationships
that make up the KMT. - Relationship between pressure and of particles
- Relationship of pressure and volume of gas
- Relationship of temperature and pressure of gas
- Relationship of temperature and volume of gas
- Relationship of temperature and velocity
9Pressure
10Pressure
- Pressure is defined as the force the gas exerts
on a given area of the container in which it is
contained. The SI unit for pressure is the
Pascal, Pa. - Pressure Force
- Area
- Units of pressure atmospheres (atm), torr,
millimeters of Mercury (mmHg), and kilopascals
(kPa) - Normal atmospheric pressure is 760 torr, 760
mmHg, 1 atm, and 101.3 kPa
11Pressure vs. Number of gas particles
- What happens when you shake a full bottle of
soda? What happens when you open it after shaking
it?
12Pressure vs. of gas particles
- The pressure in the soda bottle builds up and if
opened, the contents in the bottle rush out.
13Pressure vs. of gas particles
- Think about it!
- Would a partially filled bottle of soda create a
greater amount of pressure when shaken compared
to a full bottle of soda?
14Pressure vs. of gas particles
- A filled bottle of soda would create more
pressure when shaken due to the number of gas
particles present inside and the increased number
of collisions between those particles. - Gas particles not only collide with each other,
but also with the walls of their container. - As the number of gas particles increases, the
pressure increases.
15Pressure vs. of gas particles
- Basically, a container with more gas particles
would have a greater pressure than a container
with very few gas particles. -
- LESS Particles MORE Particles
- LESS PRESSURE MORE PRESSURE
16Boyles Law
- States that there is an inverse relationship
between the volume and pressure of a gas.
17Relationship of pressure and volume of a gas
Boyles Law
- Volume refers to the amount of space an object
takes up. - For example, think about this classroom. Its
volume is comfortable for us. Now, what would
happen to us (the particles) if the walls began
to close in? - Answer this question in terms of pressure!
18Pressure vs. Volume Boyles Law
- If the walls began to close in, particles would
collide more with each other, causing pressure to
increase. - So, as volume decreases, pressure increases.
- PV k (a constant) P1V1 P2V2
19Example of Boyles Law
- Suppose that you have 5.00 liters of a gas at
1.00 atm pressure, and then you decrease the
volume to 2.00 liters. What is the new pressure?
20- Suppose that you have 5.00 liters of a gas at
1.00 atm pressure, and then you decrease the
volume to 2.00 liters. What is the new pressure? - P1V1 P2V2
- (1.00 atm)(5.00 liters) P2 (2.00 liters)
- Divide both sides by 2.00 liters to find P2
- 5.00 atmliters P2 (2.00 liters)
- 2.00 liters 2.00 liters
21- Suppose that you have 5.00 liters of a gas at
1.00 atm pressure, and then you decrease the
volume to 2.00 liters. What is the new pressure? - 5.00 atmliters P2 (2.00 liters)
- 2.00 liters 2.00 liters
- 2.50 atm P2
22Relationship of Temperature and Pressure of a
Gas Gay-Lussacs Law
- Recall the temperature of a substance is the
measure of the average kinetic energy of its
particles. - As temperature rises, what happens to the kinetic
energy??
23Relationship of Temperature and Pressure of a Gas
Gay-Lussacs Law
- Yes, as temperature rises, the kinetic energy of
particles increases. - As kinetic energy increases, the particles hit
the walls of the container more frequently and
with greater force. - So, as temperature increases, pressure increases.
24Relationship of Temperature and Pressure of a
Gas Gay-Lussacs Law
- Pressure is directly proportional to temperature.
- P kT or P/T k
- P1 P2
- T1 T2
25Example of Gay-Lussacs Law
- As you have a tank of gas at 800 torr pressure
and a temperature of 250 Kelvin, and its heated
to 400 Kelvin, what is the new temperature? - P1 P2
- T1 T2
26- As you have a tank of gas at 800 torr pressure
and a temperature of 250 Kelvin, and its heated
to 400 Kelvin, what is the new temperature? - P1 P2
- T1 T2
- (800 torr) P2
- 250 K 400K
- (800 torr)(400 K) P2 1280 torr
- 250 K
27Relationship between temperature and volume of a
gas Charless Law
- At constant pressure (meaning, pressure does not
change), as temperature increases, the molecules
push harder against the walls of a container
causing volume to increase. - As temperature increases, volume increases.
- V/T b (where b is a constant)
- V1/T1 b
28Example of Charless Law
- Suppose you live in Alaska and are outside in the
middle of winter where the temperature is -23C.
You blow up a balloon so that it has a volume of
1.00 liter. You then take it inside your home
where the temperature is a toasty 27C. What is
the new volume of the balloon? - Charless Law V1/T1 V2/T2
29- Suppose you live in Alaska and are outside in the
middle of winter where the temperature is -23C.
You blow up a balloon so that it has a volume of
1.00 liter. You then take it inside your home
where the temperature is a toasty 27C. What is
the new volume of the balloon? - V1/T1 V2/T2 (temp must be expressed in K)
- -23C 273 250 K
- (1.00 liter) V2 27C 273 300 K
- (250 K) (300 K)
30- V1/T1 V2/T2
- (1.00 liter) V2
- (250 K) (300 K)
- (1.00 liter)(300 K) V2 1.20 liters
- 250 K
31Relationship of Temperature and Velocity
- As temperature increases, the kinetic energy
increases. - Velocity refers to the speed of the particles
- The higher the temperature, the greater the
average velocity of the particles
32Gas variables
- VOLUME (V)
- UNITS OF VOLUME (L)
- AMOUNT (n)
- UNITS OF AMOUNT (MOLES)
- TEMPERATURE (T)
- UNITS OF TEMPERATURE (K)
- PRESSURE (P)
- UNITS OF PRESSURE (mmHg)
- UNITS OF PRESSURE (kPa)
- UNITS OF PRESSURE (atm)
- UNITS OF PRESSURE (torr)
33A little review
- BOYLES LAW
- PRESSURE VOLUME
- AS P? THEN V?
- AT CONSTANT T, n
P1V1 P2V2
34A Little review
- GAY-LUSSACS LAW
- TEMPERATURE PRESSURE
- AS P? THEN T?
- AT CONSTANT V, n
35A Little review
- CHARLES LAW
- TEMPERATURE VOLUME
- AS T? THEN V?
- AT CONSTANT P, n
36Another step up
- If we combine all of the relationships from the 3
laws covered thus far (Boyles, Charless, and
Gay-Lussacs) we can develop a mathematical
equation that can solve for a situation where 3
variables change
PVk1
V/Tk2
P/Tk3
37Combined gas law
- AMOUNT IS HELD CONSTANT
- IS USED WHEN YOU HAVE A CHANGE IN VOLUME,
PRESSURE, OR TEMPERATURE
38Combined gas law
- AMOUNT IS HELD CONSTANT
- IS USED WHEN YOU HAVE A CHANGE IN VOLUME,
PRESSURE, OR TEMPERATURE
39Example problem
A GAS WITH A VOLUME OF 4.0L AT STP. WHAT IS ITS
VOLUME AT 2.0ATM AND AT 30C?
1atm
2.0 atm
4.0 L
?
273K
30C 273
303K
40PLUG CHUG
(1 atm)
(4.0L)
(2 atm)
( V )
2
(273K)
(303K)
2.22L V2
41Gas laws deal with one other variable. We have
discussed Pressure Temperature Volume What
else do you think would effect HOW a gas behaves?
42THE AMOUNT OF PARTICLES OF GAS This leads us to
AVOGADROS LAW (sounds kind of like avocado)
43- So far, weve compared all the variables except
the amount of a gas (n). - There is a lesser known law called avogadros law
which relates v n. - It turns out that they are directly related to
each other. - As of moles increases then v increases.
V1 V2 n1 n2
V/n k
44This leads us to the
45The Ideal Gas Law
- So far we have always held at least one of the
variables constant. - Now, we can set up a much more powerful equation
which can be derived by combining the proportions
provided by the other laws weve studied
recently.
46The Ideal Gas Law Equation
- PV nRT
- where R is the universal gas constant.
47The Ideal Gas Law
- R is a constant that connects all four variables.
- R is dependent on the UNITS of the variables for
P, V, and T. - Temp is always in Kelvin
- Volume is always in Liters
- Pressure is either in atm, mmHg, kPa
48- BECAUSE OF THE DIFFERENT PRESSURE UNITS THERE ARE
3 POSSIBILITIES FOR OUR R
- IF PRESSURE IS GIVEN IN atm
- IF PRESSURE IS GIVEN IN mmHg
- IF PRESSURE IS GIVEN IN kPa
49Using Ideal gas law
EG 1 WHAT VOL DOES 9.45g OF C2H2 OCCUPY AT
STP?
50Using Ideal gas law
EG 1 WHAT VOL DOES 9.45g OF C2H2 OCCUPY AT
STP?
P ?
R ?
1atm
V ?
T ?
?
273K
n ?
.3635 mol
51(1.0atm)
(V)
(.3635mol)
(273K)
V 8.15L
52Using Ideal gas law
EG 2 A CAMPING STOVE PROPANE TANK HOLDS 3000g
OF C3H8. HOW LARGE A CONTAINER WOULD BE NEEDED
TO HOLD THE SAME AMOUNT OF PROPANE AS A GAS AT
25C AND A PRESSURE OF 303kPa?
53Using Ideal gas law
P ?
R ?
303kPa
V ?
T ?
?
298K
n ?
68.2 mol
54(303kPa)
(V)
(68.2mol)
(298K)
V 557.7L
55Ideal versus Real Gases
56What does the term ideal mean?
57The ideal meal
58The ideal weather
59The ideal place to be instead of work/school
60When something is ideal
- It is the best, perfect option or idea for a
particular situation.
61Ideal versus Real Gases
- The Kinetic Molecular Theory explains the
behavior of gases using a model gas called an
ideal gas. - When the gas laws are used to solve real problems
using real gases, the results do not always
match the results obtained in the lab. - This is because ideal gas model does not match
the behavior of real gases.
62Ideal vs. Real
63When ideal gases do not match the behavior of
real gases
- It is due to the fact that two of the assumptions
made by the KMT are not exactly correct - - gas particles do not attract one another. (in
extreme conditions, particles do attract each
other) - - gas particles do not occupy volume. (while
they typically occupy little to no volume, under
high pressures, increased concentration of
particles means far greater chances of combining)
64What makes a gas truly ideal?
- When it behaves exactly as predicted.
- Gases vary from ideal behavior because of 2
factors (increasing mass increasing polarity) - Gases are most ideal at low pressures and high
temperatures.