Transcript Chemistry You Need to Know

Kinetic Molecular Theory and
Gas Behavior
Definition
Theory – An attempt to explain
scientific behavior and properties.
Kinetic Molecular Theory (KMT) – An
attempt to explain gas behavior based
upon the motion of molecules
Assumptions of the KMT
1
All gases are made of atoms or molecules
2 Gas particles are in constant, rapid, random motion
3
The temperature of a gas is proportional to the average
kinetic energy of the particles
4
Gas particles are not attracted nor repelled from one
another
5
All gas particle collisions are perfectly elastic (no kinetic
energy is lost to other forms)
6
The volume of gas particles is so small compared to the
space between the particles, that the volume of the
particle itself is insignificant
What is a “real gas”?
Ideal Gas – a gas that is a gas under any conditions of
temperature and pressure. There is no such thing as a
real gas! Only Real gases that behave ideally!
Real Gas – 2 of the assumptions of the Kinetic Molecular
Theory are not valid
Gas particles are not attracted nor repelled from one
another
Gas particles do have attractions and repulsions towards one
another
The volume of gas particles is so small compared to
the space between the particles, that the volume of
the particle itself is insignificant
Gas particles do take up space—thereby reducing the space
available for other particles to be
What are the measurable quantities
of a gas:
1.The Amount of the gas in Moles (n)
2.The Pressure of the gas (P)
3.The Temperature of the gas (T)
4.The Volume of the gas (V)
Pressure
Gas Pressure – Caused by the
collisions of billions of gas
particles against a surface
Watch the Can!
Pressure Units
Several units are used when describing pressure
Unit
Symbol
atmospheres
atm
Pascals, kiloPascals
Pa, kPa
millimeters of mercury
mm Hg
pounds per square inch
psi
1 atm = 101300 Pa = 101.3 kPa = 760 mm Hg = 14.7 psi
What is Atmospheric Pressure?
Atmospheric Pressure – Pressure due
to the layers of air in the atmosphere.
Climb in altitude
Less layers of air
Lower
atmospheric
pressure
As altitude increases, atmospheric pressure decreases.
Pressure In Versus Out
A container will expand or contract until the
pressure inside = atmospheric pressure outside
Example: A bag of chips is bagged at sea level. What happens if the
bag is then brought up to the top of a mountain.
The internal pressure is from low
altitude (high presser)
Lower
pressure
Lower
Higher
pressure
The external pressure is high
altitude (low pressure).
The internal pressure is higher than the external pressure.
The bag will expand in order to reduce the internal pressure.
When Expansion Isn’t Possible
Rigid containers cannot expand
Example: An aerosol can is left in a car trunk in the summer. What
happens?
The temperature inside the can
begins to rise.
Lower
pressure
Higher
Can
Explodes!
pressure
As temperature increases, pressure
increases.
The internal pressure is higher than the external pressure.
The can is rigid—it cannot expand, it explodes!
Soft containers or “movable pistons” can expand and contract.
Rigid containers cannot.
Pressure and Volume
As volume increases,
pressure decreases
because the molecules
have to travel farther
before colliding with the
container!
Boyles’ Law – Mathematical Relationship
Boyles’ Law relates pressure and volume
Where temperature and # of molecules are
held constant
P1V1  P2V2
P = pressure
V = volume
The two pressure units must match and
the two volume units must match!
Example:
A gas sample is 1.05 atm in a 2.5 L container. What
pressure is it if the volume is changed to 2.7 L?
Boyles’ Law
Boyles’ Law relates pressure and volume
Where temperature and # of molecules are
held constant
P1V1  P2V2
P = pressure
V = volume
The two pressure units must match and
the two volume units must match!
Example:
P1 = 1.05 atm
V1 = 2.5 L
P2 = ? atm
V2 = 2.7 L
A gas sample is 1.05 atm in a 2.5 L container. What
pressure is it if the volume is changed to 2.7 L?
1.05atm 2.5L  2.7 L  P2
1.05atm  2.5L
 P2
2.7 L
P2 = 0.98 atm
What is “Temperature”?
Temperature – proportional to the
average kinetic energy of the molecules
Energy due to motion
(Related to how fast the
molecules are moving)
As temperature
increases
Molecular
motion increases
Temperature Units
Kelvin (K)– temperature scale with an
absolute zero
Temperatures cannot fall below an absolute zero
A temperature scale with absolute zero is needed in Gas Law
calculations because you can’t have negative pressures or
volumes

C  273 K
STP
Standard Temperature and Pressure
(STP) – 1 atm (or the equivalent in
another unit) and 0°C (273 K)
Problems often use “STP” to indicate quantities…don’t forget
this “hidden” information when making your list!
Pressure and Temperature
As temperature increases, pressure
increases because the particles are
moving faster and can collide with
the wall at a faster pace.
Gay Lussac’s Law – A mathematical
relationship
Gay Lussac’s Law relates pressure to temperature
P1 P2

T1 T2
Example:
Where Volume and # of molecules are held constant
P = Pressure
T = Temperature in Kelvins
A gas at a pressure of 2.0 atm and 273K is heated to 285K.
What is the new pressure of the gas?
Gay Lussac’s Law
Gay Lussac’s Law relates pressure to temperature
P1 P2

T1 T2
Example:
P1 = 2.0 atm
T1 = 273 K
T2 = 285 K
P2 = ? atm
Where Volume and # of molecules are held constant
P = Pressure
T = Temperature in Kelvins
Temperature must be in K and units must match!
A gas at a pressure of 2.0 atm and 273K is heated to 285K.
What is the new pressure of the gas?
2.0atm
P2

273 K
285 K
2.0atmx 285 K
 P2
273 K
P2 = 2.1 atm
Volume and Temperature
As the temperature of a gas increases the
volume of the gas increases because the
gas particles have more kinetic energy
and will spread farther away from each
other.
Charles’ Law
Charles’ Law relates temperature and volume
V1 V2

T1 T2
Example:
V1 = 10.5 L
T1 = 25C
Where pressure and # of molecules are held
constant
V = Volume
T = Temperature
The two volume units must match and
temperature must be in Kelvin!
What is the final volume if a 10.5 L sample of gas is changed
from 25C to 50C?
Temperature needs to be in Kelvin!
25C + 273 = 298 K
V2 = ? L
T2 = 50C
50C + 273 = 323 K
Charles’ Law
Charles’ Law relates temperature and pressure
Where pressure and # of molecules are held
constant
V1 V2

T1 T2
Example:
V = Volume
T = Temperature
The two volume units must match and
temperature must be in Kelvin!
What is the final volume if a 10.5 L sample of gas is changed
from 25C to 50C?
V1 = 10.5 L
T1 = 25C = 298 K
V2 = ? L
T2 = 50C = 323 K
10.5 L
V2

298 K 323 K
323 K 10.5L
 V2
298 K
V2 = 11.4 L
Moles
What is a mole?
A mole is a counting unit
Other counting units include
• Dozen = 12
• Gross = 144
• Baker’s Dozen = 13
• You can have half or part of a mole just like you can have
half or part of a dozen
Volume and Moles
The volume of a gas increases as the
moles of the gas increase because the
more gas particles you have the larger the
space they will take up.
Avogadro’s Law
Avogadro’s Law relates # of particles (counted in a unit
called moles) and volume.
Where Temperature and Pressure are held constant
V1 V2

n1 n2
Example:
V = Volume
n = # of moles of gas (A mole is a counting term like a dozen)
The two volume units must match!
A sample with 0.15 moles of gas has a volume of 2.5 L.
What is the volume if the sample is increased to 0.55 moles?
Avogadro’s Law
Avogadro’s Law relates # of particles (moles) and
volume.
Where Temperature and Pressure are held constant
V1 V2

n1 n2
Example:
V = Volume
n = # of moles of gas
The two volume units must match!
A sample with 0.15 moles of gas has a volume of 2.5 L.
What is the volume if the sample is increased to 0.55 moles?
n1 = 0.15 moles
V1 = 2.5 L
n2 = 0.55 moles
V2 = ? L
2.5L
V2

0.15mole 0.55mole
0.55mole  2.5 L
 V2
0.15mole
V2 = 9.2 L
Combined Gas Law
P1V1 P2V2

n1T1 n2T2
Example:
P = Pressure
V = Volume
n = # of moles
T = Temperature
Each “pair” of units must
match and
temperature must be in
Kelvin!
What is the final volume if a 0.125 mole sample of gas at 1.7
atm, 1.5 L and 298 K is changed to STP and particles are
added to 0.225 mole?
Combined Gas Law
P = Pressure
V = Volume
n = # of moles
T = Temperature
P1V1 P2V2

n1T1 n2T2
Example:
P1 = 1.7 atm
V1 = 1.5 L
What is the final volume if a 0.125 mole sample of gas at 1.7
atm, 1.5 L and 298 K is changed to STP and particles are
added to 0.225 mole?
n1 = 0.125 mole
T1 = 298 K
P2 = 1.0 atm
V2 = ? L
n2 = 0.225 mole
T2 = 273 K
Each “pair” of units must
match and
temperature must be in
Kelvin!
STP is standard temperature (273 K) and pressure (1 atm)
1.7atm 1.5L
1.0atm  V2

0.125 mole  298 K 0.225 mole  273 K
0.225 mole  273 K 1.7atm 1.5 L
 V2
1.0atm  0.125 mole  298 K
V2 = 4.2 L
Transforming the Combined Law
Watch as variables are held constant and the
combined gas law “becomes” the other 3 laws
Hold pressure and
temperature constant
P1V1 P2V2

n1T1 n2T2
Avogadro’s Law
Hold moles and
temperature constant
P1V1 P2V2

n1T1 n2T2
Boyles’ Law
Hold pressure and
moles constant
P1V1 P2V2

n1T1 n2T2
Charles’ Law
Can you show how to prove Gay Lussac’s Law? Which two variables are constant?
Effusion & Diffusion
Effusion
Effusion –gas escapes from a tiny hole
in the container
Effusion is why
balloons deflate
over time!
Diffusion
Diffusion –gas moves across a space
Diffusion is the reason we can smell perfume across the room
Effusion, Diffusion & Particle Mass
How are particle size (mass) and these concepts
related?
As mass of the particles
increases, rate of effusion
and diffusion is lowered
because heavier particles,
move slower.
Rate of Diffusion & Particle Mass
Watch as larger particles take longer to get to your nose